(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 10.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 294382, 6543] NotebookOptionsPosition[ 279953, 6323] NotebookOutlinePosition[ 280468, 6343] CellTagsIndexPosition[ 280425, 6340] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ RowBox[{ RowBox[{"Quit", "[", "]"}], ";"}]], "Input", CellChangeTimes->{{3.7311072152584*^9, 3.7311072163036003`*^9}},ExpressionUUID->"ad8591ff-5b42-4c26-962c-\ 848863189d68"], Cell["Mec\[AAcute]nica Cl\[AAcute]sica 2019 2c", "Chapter", CellChangeTimes->{{3.7311487609214*^9, 3.7311487993634*^9}, { 3.7311557874128*^9, 3.7311557877404003`*^9}, {3.775569085033969*^9, 3.7755690931223297`*^9}},ExpressionUUID->"9c4e5505-f8f1-481d-984d-\ 2299da6278e6"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Algunos sistemas de la Gu\[IAcute]a 2 resueltos \ num\[EAcute]ricamente.", FontSize->36], " ", StyleBox["(Versi\[OAcute]n h\[IAcute]per-comentada).", FontSize->24], "\n", StyleBox["\nSi ya usaron el ", FontSize->24], StyleBox["Mathematica", FontSize->24, FontSlant->"Italic"], StyleBox[", si son buenos entendedores o gente de poca paciencia", FontSize->24], StyleBox[",", FontSize->24, FontSlant->"Italic"], StyleBox[" la explicaci\[OAcute]n detallada que se da en este notebook les \ va a resultar cansadora: vean los notebooks ", FontSize->24], StyleBox["m\[IAcute]nimos", FontSize->24, FontWeight->"Bold"], StyleBox[" subidos aparte para cada problema.", FontSize->24] }], "Title", CellFrame->{{0, 0}, {0, 3}}, CellChangeTimes->{{3.7310896361156*^9, 3.7310896501706*^9}, 3.7310995396004*^9, {3.7311557931303997`*^9, 3.7311558014768*^9}, { 3.7311831648501997`*^9, 3.7311833420741997`*^9}, {3.7311872335882*^9, 3.7311872905902*^9}, {3.7311922905912*^9, 3.7311923145752*^9}, { 3.7312323139576*^9, 3.7312323537472*^9}, 3.775569096061471*^9},ExpressionUUID->"8bdad1dd-09dc-4155-b357-\ b1d930cbc3f4"], Cell[TextData[{ StyleBox["\[FilledSquare] Recomendaci\[OAcute]n general: la ayuda de los \ comandos del ", FontSize->18], StyleBox["Mathematica", FontSize->18, FontSlant->"Italic"], StyleBox[" es complet\[IAcute]sima. Incluye muchos ejemplos, y siempre se \ descubre una manera m\[AAcute]s eficaz o prolija de hacer las cosas. Adem\ \[AAcute]s es navegable. Nunca saben d\[OAcute]nde van a terminar. Pueden \ apretar F1 para el men\[UAcute] principal de la ayuda o F1 luego de \ seleccionar una palabra o comando. Por ejemplo, ubiquen el cursor sobre la \ palabra NDSolve y tecleen F1.", FontSize->18], "\n", StyleBox["\n\[FilledSquare] Aquellos que no hayan usado nunca el ", FontSize->18], StyleBox["Mathematica", FontSize->18, FontSlant->"Italic"], StyleBox[" deben saber s\[OAcute]lo esto: para evaluar una celda se usa el \ Enter del teclado num\[EAcute]rico, o bien la combinaci\[OAcute]n de teclas \ Shift+Enter. Para que eso tenga efecto, el cursor tiene que estar dentro de \ la celda que quieren evaluar, o la celda tiene que estar seleccionada con el \ mouse usando las barritas que aparece en el extremo derecho de la pantalla. \ Pero no se apresuren a\[UAcute]n.\n\n\[FilledSquare] No todas las celdas \ pueden evaluarse. \[CapitalEAcute]sta, por ejemplo, es una celda de texto. \n\ \n\[FilledSquare] Cada celda est\[AAcute] abarcada por un corchete en el \ costado derecho de la pantalla. As\[IAcute] saben qu\[EAcute] l\[IAcute]neas \ incluye. Las celdas pueden agruparse jer\[AAcute]rquicamente.\n\n\ \[FilledSquare] Un \"punto y coma\" luego de una serie de comandos hace que \ el resultado no se muestre en pantalla. Eso es \[UAcute]til para pasos \ intermedios que no estamos interesados en ver, por ejemplo asignarle cierto \ valor a una variable. No es \[UAcute]til si se trata de mostrar en pantalla \ el gr\[AAcute]fico de una funci\[OAcute]n.\n\n\[FilledSquare] En una primera \ lectura, eval\[UAcute]en las celdas con los par\[AAcute]metros y condiciones \ iniciales tal como figuran. Est\[AAcute] chequeado que as\[IAcute] las \ soluciones num\[EAcute]ricas son bien comportadas y los resultados no \ producen mensajes de error. Luego experimenten.\n\n\[FilledSquare] Para los \ que no usaron antes el ", FontSize->18], StyleBox["Mathematica,", FontSize->18, FontSlant->"Italic"], StyleBox[" antes de pasar al par de problemas de la gu\[IAcute]a 1, abajo \ tienen un ejemplo de celdas evaluables con unos cuantos comandos \ t\[IAcute]picos. Prueben ejecutarlas una por una. F\[IAcute]jense en la \ figura d\[OAcute]nde tienen que hacer doble click para desplegar estas \ celdas.\n\nNoten el formato que se usa para incluir comentarios: (* blah \ blah blah *). Las celdas est\[AAcute]n agrupadas y ocultas, para no ocupar la \ pantalla.\n\n", FontSize->18], Cell[BoxData[ GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJztnQmcFOWd9xtRIxodjbmcBBMNcTFGcox5jStBsglCdIMs8QgS4saMrye6 AQxxI4IawFXCC0YjOCuaOEkQg6KueIFGEYEsIoiAHIo4IEcYcTiGY4D/+1R1 VU91d91d3VXd/f1+Pt9EZqbqOerpqvp1VT110uU39P+/h6RSqaFHqP/p/7Ph 3x0y5Gc3/ehY9Y+Lrh969ZXXX1H/g+uHXXHlFUO+fXlH9cMtyvnqPw5V/y8i iIiIiIiIiFWhQkvPw5V/Un4r7vogIiIiIiIillpFJ+UM7VKx4Ya464SIiIiI iIhYahV3WrKx5o6464SIiIiIiIhYShWfUe7LyccNcdcLERERERERsZQqrs/J xk3KY+KuFyIiIiIiImKpNJ47ficnH/8w7nohIiIiIiIillLFL3Ky8fy464SI iIiIiIhYarU8bMnGHyhPjLtOiIiIiIiIiKVU8WnlQUs+7hV3nRARERERERFL reIHlmz8x7jrg4iIiIiIiBiHlmePN2rXkuOuDyIiIiIiImIcKi5Rvqf8Ztx1 QURERERExPhVHKY8Rdlb2d3478PjrhciIiIiIiJWloqfG3Mjv6U8L+76GHX6 rPI65cvKtpx3HGm2KP+g/H6B5XxPOUJ5t/J25WDlBcrTlccqOyiPVH7Dx7qO Un5X+UvteWHl08p5yleVjynHKX+Us8yhyvuUM5QPKicZTlY+pJymfMl4B/Iu 5QrlYuXryr8p71V+Lu7thYiIiIiIWO4q+uTkTi2LdouxPp8zMt9em0zs5FPK k0KUlftuYTvbLPlcy7e3KNcqO+es63LlZp/1HWRZ7skA7XTyubjHESIiIiIi YrmreM0mb82KoR7addoblXtCZsTdyp8FLO/9AjLpD3LW948Ay46wLLcqgnw8 Pe5xhIiIiIiIWM4qznDJXGeUsB61ytkO9diRSt9n/C/KLyq/qbzD+Hnu32rv Cr7cZ5lnFphJu+as75cBlv25ZTmtXe+ErIPWXu0e8yPjHkuIiIiIiIjlrGK0 S/bSnpvtUII6dE05X8edqDzKYTktKz9vs4x2X/bXfJTbKZWeGzpIHl2aSt/7 fbXDOocZmdVu2QPKZ1PpZ4uPy1nuY0Ze/7+p9L3bfuryivLbcY8hRERERETE StDIe24Z7CdFLl+7Fmx3X7J2r/RPfa7jdzbLL1Me42PZw1Ppdyj9zUce/bXy EB/rvDBlP5/YKJ/t+YTyBY+6jPCzLkRERERERPRWu4bpcq3T9M0iln+ScovD 9d9zAqxHe/fTPJv1aNdqOwZYz59d+mFawLb92mYdpwdY/hyXurQqO8U9fhAR EREREStFxbk+rplq1hah7BrjGq9def8eYn2nOazrvgDrOMGlDy4JWB/tnU37 c9Zhe5+4w/Knu9TlxbjHDiIiIiIiYiWZ8j+f1DlFKPsvDmXdW8A6X3FY5zCf yx/l0ge9Q9TH+kx1c8BlP+dSlyfjHjuIiIiIiIiVpOIBn/l4UMTl/qtDOdq9 3l8qYL1XuKy3l4/lO6Sc7zcP3Aep7Hu+VwVc9giX7fF43GMHERERERGxUjSy 4Fs+8/F/RljuESnnuaoLum9Y8TWXNizwsfwxLssPDVGfWZbl3wqxfCvXjxER EREREYur4ic+s3FB9zzblHuVSzm/KHDd2jxde13W73oNWXGqy7J3hKjP05bl F4VYvsmhLrPjHj+IiIiIiIiVYCr93l9r9npVucYlG86MqNyOHuVcEEEZTplS 8yGPZb/vsuwfQ9RlumX5wPOAK5Y41MXzWjgiIiIiIiJ6q/gP63XNVPpea+1d T/Md8tj6iMr1mi+7WwRluN0z7nqPs+JSl2VfCVEX6/ui3gmx/IsOdSnaO7cQ ERERERGrRSMLr7Jkre9Zfvczl3z42QjKnuiRj4+JoAy79yCbau9bOsJl2atd ll0Xoi5/siy/McTyjznUZWXc4wgREREREbHczbmG+1bO77T3/x5wyGS/iqDs 1S75c19E7VvokcGPdVl2uEe2PjRgXaZalm8J0ZY/OtRlcdzjCBERERERsdxV PGHJWZNtfu/0DuG1ykMKKPcwj9waVT5+06Oco12WHeOx7KcC1uVRy7JtIdry e4d6zHBYZhQiIiIiIqKXr762Xtfv79ra2kY1NzeP2rBhw6gtW7aM+vDDD0dt 27bN1o8++ijLlpYW/e/Vcj0lAZnYVNE55/pw3jt9FeNc8uF5BZT9+RLlY7fn j9u0nO6y7O886hjoHvNU/v3RQa8/3+lQj4kOywAAAAAAAHgy97X1un5/t3// flEZV1Q+FpVz9f9WWTijysG2qmws27dv1/9ey9WSgFxsqvhPS8bS7hf+vM3f jHXJh07XLf2U7fZu4ijz8VKXMrzm57rPo46fC1iXJ3OWPzLg8rc41GOYwzIA AAAAAACekI/1vPW2JWO9avP7U5TbXPKh9m7hUHNoKb7okT33R9RGp3ciaTZ6 LHu/Rx1PCFiXZ3OWd3z22WH5YQ71+LHDMgAAAAAAAJ5Uez5WfDsnY7Uqf6k8 Q3ma8kblBx750C2beZV/pPKgx7qPj6Cdi13Wf7nHslM86hf0+eNXc5b/dMDl b3SoR3eHZQAAAAAAADwhH3veO+zXRwqog1t21Yzi/ceLHNbd5pW/FX/wqF/Q 679v5Cyfdz+7x/K/cqhHF4dlAAAAAAAAPKnmfKw4IuV+33QQW1Iuc1x51OMO j3X/IIK2Pu2w7md8LPuAR/0C3Vueyn7PtObJAZf/tUM9jnNYBgAAAAAAwJMq z8cDIsrGpt8PWY8vKPe5rLc+grZe7bDuc30s+1uPdgd9/nhDzvKfCbi83fxc 2rxqHRyWAQAAAAAA8KTK8/ELDjnrReN3TykvUH5P2U85IuU+D/TdBdSlwWW9 /y+CttrNk73I57JO80WbnhKwLrtzlj884PK32tThHy7LAAAAAAAAeFKt+di4 Zps7L5b2HLDrXFHaNUrlDIecuK6A+pyUSj8LbLfe+RG0t6fNei/2uewNHvn4 jAD1OD5n2W0h2jLJpg5bXZYBAAAAAADwpIrzce41yK3KE30ue3TK+X5o31nR Zr12uU9Te3/UEQW296qcda5RdvS57E898vGFAeqRex17Toi2zLSpwy6XZQAA AAAAADypxnys6KTckpOv7gm4jmUOWXFsAfU6Rvmew3p75Pzt51LpeaoeUy5M pZ/p1e4Lv035bZt1T85Z3xUB6nWmRz7+XYB1nV9Iv7v0/QGXZQAAAAAAADyp 0nx8rU2+6h1wHdMdsuK7ykMKqFsPLevZrPcvxu9rlU+m0s9Jaz94M5V+X/M1 yrWWv9fuAT/Wst5VOXX0Pdd2Kv2O5v02dTJ9M8C6/jNn2b4h+miHQz0+4bAM AAAAAACAJ9WWjxUdjXyYm62+F3A9T7jkxYsKrON/2V0fVZ6jfNv4t/as9A9y lvt8zjJNysuVg3J+fnmIOi13aa/2HPdJPtfzqmW5rUFyurH8F13q8W8OywEA AAAAAHhShfl4iEO2ujLgeha45LT/TTm/a8jPug9Ppe+ZtsvI2v8PTzlco05l X0O2c7Xy0BB1ethjvY96LK/Na3ZjKvva+PgQ9XB6T5XmvQ7LAQAAAAAAeFJN +TiVnsPZaY7oXcp+PtfzKeU2j7x4f4EZuYtyu816/6H8istyz3jUK/C1Y2O9 Z3msV/O3dtk7lZ6z+smcv9X67/iAdThMucKlfO16+VE2ywIAAAAAAHhSDfk4 lZ5f6o+p/Pfu2jlV+Zmc5bV3L/1Y+XPlSOUiH+vR3GFktvXG/2v3RGvP3/q6 p1hxqct6f+KwzP0u9WlOFTAPtuJ5H21ebfSRNue1dm/371L2zwv/R4Byz1De rpzvo/xpWkZWdrasAwAAAAAAwJNKzseKHyjn+MyyVrXnYi8y1qHdF2z3vHIh /nOANtznsp4/K4/L+fu7Xf7+TwX25+kp7/u3/ah9B+Hr2rriNyHWr30Pot0n 8H+EfAwAAAAAAD6pxHycSr8n6YUIctxNytMizsYtKZ/vWTbacqjyOZf1bUpZ 3j+smO3yt7dG0Lfau7EGK9eFbP/cVIBr2Cn7dx0H/R4CAAAAAADAkwrNx7cF yFCtqfS7g5con06l70++3ciA2juTvqd8JJW+p3qfsYz2/88qf6E8T3mF8s5U +l3ES411muvfqPzA+G/t3uN/CdGew4022T2PbPq6ssGjrRMj7GNtHvD+qfQ9 127vfrKqzfF1ZMByzjba9bKRybX3Vq9UjlBerLzDWO/jqfQ7rTS169MXWtYD AAAAAADgSYXm4yNS6Wd3tWd9RymvU16i/K6yWyr9jqBPpALO46w4zlje9fpn Kn1P9onKUy0/+3iqgPciS3smrVP+h/IuLe8a2VGb69pp3jGri4rU358xvkvQ vl/Qro/vTKWvE2tq76PS7k+/upjb3MNANK98SaZPbZSZi5qkNejCduuaPEom T39JVjZ7/rWsfGm6TB41Waa/tFI8/9yjzPGNM2VRU/gWUPdwZRZad09am2TR zEaZ6qttfommDyqHgP3RvFJemj5ZRk2eLi9Ft1EST2vTIpk5e5Z3m83+GTVe GmcukmJ+PCAgVTp2S4v9/sT35wcASk4l5uNqVLsua+Rlr4z8gxLUJfS83UXS P+pcYfrYq6T/ZUOkYW7h+Xj1U6NkYF1K6gaOkqdWe/61PDVqoNSl6mTgqKfE 8889yuzc53p5YH744y51D1dmoXX3ROXjuQ1D5LL+V8nY6VFl2Wj6oHII2B+r n5JRA+skVTdQRnkPuMpA7StnTrxKzrzkGo82t0rTrAlS371Warv1lRGN5ONE UY1jt+TY7E98f34AIA7Ix5WlYrxHPtau72rzSvuaQ7tC9EmzrJw+Vgb0vljq J8yK5ByunHMadQ9XZtHzsWgReZZMqL9Yeg8YK9MjufZAPs6GfOyJ3zY3L5bG m/tJXd2ZctXEmRHe8wCRUI1jt+TY7E/od4BEQz6uLBUn+HweeLPyUeUQbZm4 611kfZHOHOdLj343S+PiiK7KlXFOo+7hyixFPta+y1nceLP069FdBoydHkHm IB9nQz72xHc+Tt+/W/TnDiAc1Th2Sw75GKDcIB9XnoqXfM6XZbos7joXWR+Y eeP8yK4da2TltPnmM3ijdPPPF13OyY1nTscbyzqvIyenvbQke7nx/p+rpu7x 1N0vrauelNHq/Kpr93qZMKvQdReQjwP0URrzWbzsv/f3rLh32e7raZWmRTOl cby1bLtnjJ37Q39msHF8dnnzXc514+wf3+0NUraxzpsHSM9utZKq7SY9BwzO f341QLuz5gtYnf15DfXZCdzn7XWw9tF6Y1tnLWfN+0sWZ9VVq/+8ec7zEGTG jqWvstq+Prvert8phGhj0seuXf9krz7os9I2499rPPncp7jNN5HfDuv+ZJq8 FPHnx6hRhPsN+7YWdYx6fK5WNodYp5/2BNrfhBhPjiRlbCZs+yYI8nHlacxD FiQfvx53nYusJ+lrx92lrvdgmTwvug9qJqf1HiBDbxyaPh4a/V7T5UzpO6LR cky0PyfX910T6qXvmV2kJmfb5a/DktN69JNrhw2TQdblarrImYPukOk+9ufU PZ66+6Z1lTw5WtW7s6r36CdlVUErDpePg/ZR+ng6Ua7q2U1qc/6+tltP/Vq4 37lq9ON8w5C8srX1aPfx5h2f9bIbZEjfM6VLjbXsWunWc4CMzTpGO4+JxhF9 5cwuNVnlaWNsQO/8jBFn/wRrb5Cym2X+A9dLn845xxFL28N+drp27ytXXXNV 1udV/+z0HSGNPueNC9znxnnqxKt6Srdaax9dJbeMuFb69eicfU+Icd1P/5xf e430Neuq6tnv5kZ59CHn+0ia5z8g1/fpnNVXmX1V/3q59Y47svYb9vUN08by GLvmd341tb1l8OR5edu7ed5kGdy7Vmr9HKf18/EJUp87/vXxVC8TbM7Jg+xT 3O4Xyt/O1v3JH+ThiD8/ke43bCjJGPX4XGm39IUZ927tCbS/CTGeHEnU2EzO 9k0a5OPKVHGlcq+PbKy9q+q8uOtbZD1olVVPjlb7h67Se/BkiTAeZ/Y7tbXq mN61h77vG659Zza4/bvj9vtj7efwmD52gDpvq5EuZ/aV+uGW7+ky6+iedc3b LLNGldlZldnLLHO4sS/zuT+i7vHU3T/muO0sdQNHy5MFBeQQ+ThwH6kcMlfl tV5dpLN2/Kwf3v73Zh/l9Klz09NzlPVS5/o11nUZ5dZ06Sc3Ny62nN80y0rt /FEvw7heY5Q9vD6dGWq7DbDMd+Y2JoxzzsHp5QcP6Cm962r1sZaVMeLsn8Dt DVK2x/XjQj47NWp7du3eXl/z71Ve9bVvDlF2a9NcaRjSS52nWpcZLAN6dpe6 2s5qu9bY5uO8z7lx7efNkOemtV26SNe6Pu3rs91XhWtj2Yxd8zu/mq7Sf/hU WZL1t80yb/Jg6V3rYyxoebFxRPocPGf8a21O90POXHEB9ynh87HH9eNY9xv2 lGSMenyuWsOs06M9vvc3YcaTE4kbmwnZvh7dFgfk48pVcZbyfZdsrL2v+ctx 17MEupO5DtdD6sfPFvtPQzjM/U7e9UNz7krtPDVzf2z+Obn5fXlNl14ypGFu 9r7XmPdGO6/rUT9eZq/3KFPtY2dNqJfuav/btf9wmbrEfY9E3eOpexDM6y2d 1bFu9JOrCjjGBM/HwftovcweXy89amqle/0EmWVdIHOflr/3/7RfZ+qmf09t vfc1fdzOPr8x7w+p1c5HhjZkfa+tfS8//Y5Bakx0tdTLbUxkzzPVvFK79mhc B7BeA4qzfwK3N0TZDs9PFvzZuWqizGzv3Eyu8/PZCV62+R1TTc45qeX7hVTK Nh+nUurcsFf+ew7Cnpvq16y161au+6pw/Vs+Y9flO7/meTJ5cG81pu2vLWet xbJ/yB3/2nWvhqE90+f2lrlGgu5Twudj9+eP49xvOFGKMer1uQq1Tq/2+Nzf hBlPTiRvbCZj+yYR8nFlm0q/5/lB5ZPKRuVtyouUXeKuWwl1Z/1sGV/fQ2q6 9pfhU5c4f2aN5yeCPCuR+Z7SJr9kzmFrzFxuc07u8BxJ+ufDM/fnWOehyuzr bNqzfvZ4qe9RIzU96mW8x0GEusdTd0th3uOtdYlMHd5futYU+t1OiHwcuI/a z+O69RwqDaHfs2zJNDb3Wea/+7r9nNvp/CX/e4bc/jCvXdXYXKtvr0/ePZKx 9k+Q9oYo2+n8PsbPTuCyM9+N2tzbYfleyzYf19g/1xD23DT/nge7fVWY/i2n sev8nZ//e6vd9w/WdbWPt6D7lCLm4xj73onij1Hx/FyFWqdHe/ztb8KMJyeS ODaTsX2TCPkYq0BXWpdMleH9uzqcf6m9U6umGDn6X+Vfje/E0j/3dx3T/tqH eVwz7yVzyij5826Y9+GY9wLYnWvatcdu30jdk1T3oOMtty2u3eLWYyHn5wrS R5ZzceMZ2MGh5ucw2+zvWoFknpe1uRcs9z5Ex+9MzH/b97O5D8nfvnH0T5j2 hijbdf7deD73gcv2+G7UPFe2zced+8j1D8zPyyJhz0397avC9G85jV1xmFch wL3VfvYP5rXozPgPuk8pXj421hBP33u0tXhjVDw/V6HW6dEef/ubMOPJiSSO zSRt32RBPi5PFV9Tnhx3PcpEV2zPgUzUsXru9AYZPdw8p/yufLfXIBkyepQM Hz5aGqbPdb1nyf09Q+Z5bGfpc/0DMr/Z5hjqNO+G/txKveu1GL/7RuqeoLoH Hm/tWcjvsdOhx4Ln4xB9pM8xMjFnPpSU5ZlIX/PSup/v52Me3z3nYlDm5mHj 3+Z1eqf+sTvXja1/wrQ3RNlO5/cxfu4Dl+3xjh2zbNt87JCpQ8+N42tfFaKN ZTV29TXl32Md4N5qf/uHYN9/2a6hWPk41r53b2vRxqi1P5yuwYZZp0d7gm27 IOPJseQEjs2EbN8EQj4uPxU/VO5QrlAeG3d9ykBXXN9bazy/M7renPezRp/T oXOdNkfCaM9negrLae3zbuTOsZM+3q3OzCObvIxJ3UPVPfB4a7atS3CC5uNw fZSusuV9Gpn5UNqPr1nPV7nW1e/5gvn3LtdTM5rvPio0Hyehf4K0N0TZtuf3 cX7uQ5Ttcc7mmo8d6lPcc9MQbSyrsWtsyZx7rJuNa9y+5q1OZAbxm4/j73u3 thZtjDr2h0kB/eLSHvJxifZB6ULK7n3f5OPyUvEL5QFjv7dSeVLcdSoDXXG9 fmyQuQdbm++wxv98wa73reTN1Zm7X2y/r8b+OcL260TFzJjUvbR116voe7zF df04XB/lV7/9nM6cV9numXGnsv21Ofj9aUHPUfLvUS2n/glZtu35TpyfnRBl m/dXO9zz53p/dcT52N++Kkz/ltPYzWm3fo/1IzLzkSDvl0jiPax+83EC+t6l rcUbo079kbtMgf2S0x5/267K768uyfZNJuTj8lBxqHKS5d6ZF5XHxV2vMtEV c3/hOP+LdqxpGCo9u/eQXoOulqsHXSh9emlznXo/2+M6T1Teux6dzskt97Vk 1cvYj6ay92tRZ0zqXtq6BxtvcT1/HKKPMnOp5lyzNMhsF8/nk9znK9HvNWwc b7mn0PL3ljk4s+trnE9m3jVR6PxcCekfv+0NU7bt+U6cn50wfe4yP1dmmzvM z+VQH+f5xOznwgq3rwrSv+U0dnPr1Vnq+l0mV1zWT+q6+rm3OrtNUc2BlL9P Cbqd/ebjJPR9PsUfo079kalBuHV6tMff/ibZ83MVPjaTsH2TCfk4+Wr3UCtf sGTj/1YeFne9ykhXMp9/p32bnldGSP3QO6Rh7ipZNbdB7hhaLyMa/Odju/cI ZObNz+zz/F/HzH3eyLqfjzpjUvfS1j3QeItt/uoQfZT5HjrnHRLppdrv2fLx fJLj+y4s74m0nku0z8GZ8+4tDfP7CFVf13d+LW6Um/ul3zE66I7pmTLt35ET c/8EbW+Ysm3vTY7zsxOmbJf3O73UIEON5+uC5OPM9disd4Zq74yeLncMyn+X UrB9Vbj+Laexm1nKvMdae1+qsquve6uzl43kHTpO+5RA29klHxf6+SlC3+dS ijEa9vqx6zo92uN3f5PY9ztFMjaTsH2TCfk42WpzcBnPGYtxX/Uv465TGeqO n4zR3CRN65vS506txn/7OFRn3ruuju+1db3z30Oftf+yeQ521gSp757/Hnn9 nqm6Oumm2SX7e8KoMyZ1L23d0wv4HG9O8+8Gfu+l2QfZ85/amZ4TNUwfWc7V tONw33oZnlmv+U4IVf6AsTLd64sny3mB9k7XvvXDs+dlztq+eofKyuljZYC2 7XPL9jUmnMvU5uzsXVerj7WsZzjj7J/A7Q1Rtjn2zL/Xr0WvklWxfXbCfW5b m+ZKw5Be+vs625/XHiwDenaXutrOarsGu7+6/f2flvmR9D7sJX3qukqXLrW2 56ZO+6rsdxaHa2N5jV1zc5q5L/1eVn/3VpvLqv1f4wjp2y2/DeYcu9nfhzj3 keM+JdB2ttmfRPb5CdH3AY8PJRmjXs8fh1mnR3t872/CjCcnEjc2k7B9kwn5 OLkquiv/YWTjXcp+cdepTPUgyLsjgpGZ96D3ABl649CsOTP0/dZY67ySNsdQ 7VqPti/V9oG581Le3CjTHxong7XvCS35KPI5rqh7SeseBMd3gjbPlweu7yOd ne6Byu8xow+85zzOPFMUoo/S52XqXM6Y39K63vRxf4LtPYJ26N9Vq3MG2/Kz tq/ZJ9o9xRMyc2u2l23kogkeY0Lyvx83y9PG2IDeOcf+mPsnWHtDlG05Z9P/ zrx/M87PTpg+16+raNdRre8m0b4nukpuHDpI5ceA+Tj3Oo1lfRMn3ir1/ets z02d9lXaeWnWvEqh2lhmY9fox8y9oL7mrbYZC3bj38iQE2zefRRsnxJkO7t/ 31bo5ydw3wc8PpRkjHp+7xRu3Lu1J9D+JsR4ciRRYzMh2zeBkI+TqWKQco8x 7jYovxl3ncpYT8z7z4Lcw+VrvSst725fbZlf0vbdhOb75CbnnYemv+vNvYYn Ns9NtpeZ++729Kryn1Wh7smqu3+M73W62jw7Gfj6cf67DN2vH4frI2MhPY80 js9er12/eeJWvv0CNmXb9ZHDmBBLu6zlmWMsd/vG3T++2xuu7My41v7O2o44 Pzuh+ry9DtZ5vefbzVvT7LCtXfvRGEc2y2bNHTvfa19VWBvLa+y2ZxV/81bb YVMfu37JWiTIPsXvdrbfn0T1+XFsq1PfZ97Pc75cHiQfF3OM+vlchR33OYTf 34QYT44kZWwmaPsmDPJxslR0UN5u+f5vkfJzcderzPVGfdZnTaiX7nXdpX7C LB95AiBmjHkw6pzmYAIAd1znNmqf16qwueHdcX+3SjVjXj/2O281BCE9R0G9 XOtjXkfGaGXD9rWHfJwcFUcoH7Fk4xnKo+KuVwXoi/Q15Dr5rs93NwHEh/EM 0Pk9bObdBQBfZN4NnP9sbPPK6TJ2QDeprdHeMfSkFOuQwLmpA8YzlHV1/eTm xsWh5l0GJ7TvHu6RkVf/UibO9L7nnTFa2bB97SEfJ0PFZ5TzLdn4LuUhcder QvSH8TzQhX0u43gMyUY/d7xM+lw4RBrmcu0YIBzNsrjxZumnPQNqO1dOjXTp VdzPGOemViz3hOpzA9VJ9/oJMosbuiJG6+e5Mn+un2dvGKOVDtvXHvJx/CpO V64zcvE+ZX3cdaowfZOey/Qy6T8o9z0JAAnBmP9yUP/LZEjDXJ4FACgAp3lv 0nPlqGzs6/n98HBuaqVVlkwdLv27mvPIXeXr+iYUF8ZoZcP2tYd8HK+K85Tb jWPyh8p/ibtOFWgAjO+vHwg75wJAkTGemXwg5Jw3AJCDzVwz4efdCUbWXIIE Qcs8aX7nFoRiwxitbNi+9pCP41NxvXK/kY1XK/8p7jpVqAAAAAAAAJ6Qj0uv oqPyXsuzxi8rj4+7XhUsAAAAAACAJ+Tj0qo4RvmsJRs/pDw87npVuAAAAAAA AJ6Qj0un4ovKt4xcfFB5U9x1qhIBAAAAAAA8IR+XRsVZys1GNm5VXhh3napI AAAAAAAAT8jHxVcxQLnHyMYfKL8Vd52qTAAAAAAAAE/Ix8VVMdLyrPFiZee4 61SFAgAAAAAAeEI+Lo6Kjyn/bMnGTyk/Hne9qlQAAAAAAABPyMfRq/i08jVL Nh6vPCTuelWxAAAAAAAAnpCPo1VxmnKtkYvblFfGXScEAAAAAADwhnwcnYre yhYjG3+k7BV3nVAXAAAAAADAE/JxNCquUe43svE7ylPjrhNmBAAAAAAA8IR8 XJiKjsqJlmeNX1V+Mu56YZYAAAAAAACekI/Dqzha+bQlGz+szVsdd70wTwAA AAAAAE/Ix+FUnKh808jFB5Uj4q4TOgoAAAAAAOAJ+Ti4ijOVm4xsvFt5Sdx1 QlcBAAAAAAA8IR8HU3GxkYnFyMhnxl0n9BQAAAAAAMAT8rF/FTcb91Jr/1iq /ELcdUJfAgAAAAAAeEI+9lZxuPKPlnm4Zmpzc8VdL/QtAAAAAACAJ+Rjd7V3 NSnnWLLx3do7neKuFwYSAAAAAADAE/Kxs4quyneMXLxfeW3cdcJQAgAAAAAA eEI+tlfxfeU2Ixu3KPvEXScMLQAAAAAAgCfk43wVVyrbjGy8Vnla3HXCggQA AAAAAPCEfNyu4hDleMuzxq8pPx13vbBgAQAAAAAAPCEfp1V8XPmkJRv/WXlE 3PXCSAQAAAAAAPCEfKxn488rF1uycaLqhwULAAAAAACQjcqv8r//KzJ1qsi4 cSIPPyxvNjwpf5+5xPbPqyEfK85QfmDk4j3KS+OuE0YuAAAAAABUM/v2pXPw pSrufetbIp/4hJYGnT3mGJFvfEPkootEGhpEdu2q+Hys+JFyl5GNtyj/Oe46 YVEEAAAAAIBqROVWueUWkRNOENsc3KGDSG2tyJlnipx4osghh9j/3bHHyoYf XyGvPzIna/WVko8Vv1IeNLLxMuVJcdcJiyYAAAAAAFQTr7wicuGFIoceKpmM e/jhIj/+cfpe6hkzRJYu1a8LW5n38ruy6C9/E/mf/xGZOFHk8stFjj5asvJ0 794iTz2l/32552PF4coHLc8aP6esias+WBIBAAAAAKAa2LNH5LrrJOvab+fO IqNHi2zenPfnm7fskoWvb8rcO/3Ioyvktfkbsv9I5Vj5/e9l18n/lL3eiy6S /Vu3JjofKzq4/O4Tyr9ZsvHvlYcWqy6YGAEAAAAAoNJZvlykWzfJ5NeePUUe f1y7yOu4SG4+1rLx+vXbbf9W+/3S+6aLXHJJ+jqyVsYXviDbn302yfn4Coef n6JcbeTi/cobilUHTJwAAAAAAFDJ3H+/yJFHip5ZO3USmTw58iKy5ud6+mmR T34yXV7HjrL9l7+ULZs2JSofK05XLrH5+XeVHxrZeLvy/GKUj4kVAAAAAAAq EZUz9TmmzWvG2vXjZcuKUlTe/NXr18vBHj0yZe87+2z56O23E5GPtfuklcuV i3J+/nPlPiMbr1N2i7psTLwAAAAAAFBpaM8aa/dQm9l48OD0z4qE7fud9u6V 3cOHZ+a93v/Vr8pH69YlIR+PNDLwTOPfhyjvtDxrvED52ajLxbIQAAAAAAAq iYMHRS6+WMz7m2XatKIX6fb+462PPioHjzpKr09b9+6ybdOm2PKxdk3Yco34 fuVRysct2XiaslOUZWJZCQAAAAAAlcQNN0jmunFDQ0mKdMvH2vxcH2kZ/bDD 9Drt69dPtjU3lzwfW+6r1ubcalP+Vvm6JRv/xm1Oa6wKAQAAAACgUrjzTslk 49tvL1mxXvlYm79656RJmbmt91xxRRz5WLuvutXIwruV24z/3qscFFU5WNYC AAAAAEAl0NjY/m6la64padF+8rH236233SZmft99yy0ly8fGfdV7LdeKDxr/ 36K8StlFWRNFWVjWAgAAAABAufPOOyJHHCF69vzRj0QOHChp8X7zsfbc8R4t u2v1VFl+x3PPFT0fW+6rPmDJx2L8e5dhm/Ez7dnkJcoLude6KgUAAAAAgHLn vPNEz5ynnCKye3fJi3+/abuuFad8vE39f9vZZ+v13X/aafLR1q3FzsejLPdV 23nQuN/6feWVzM9Vvb733nuCiIiIiIjl6xbtuV7jnuVNjY2x18d0q8q9tvlY uX3Bgsx8XbtHjy5aPra5r9rqfuN6sTZHVz/tPU9x5zOM17g/M4iIiIiIGN51 y5dL2wkniJYzd/7wh7HV45U5b+paf+aWj/X7rIcM0eutvftp+4oVkedj477q NTa5eK+RjZ9SfjvuTIaJEgAAAAAAypVhw0S/dnzMMSIffBBbNYI8f2zasnGj HDjxRL3++y64oBj5eIplHi4zF2tOVn4p7HqxogUAAAAAgHJk6VKRQw8VPR/f fXesVQmTj7UsvGvqVDHvDd/5179Glo+N+6rN+bi0jLzDeL/T8WHWh1UjAAAA AACUI337ip4tv/lNLYzGWpWw+VhznzG3mD5XVwT52DJftfaPLcoblUcEXQ9W pQAAAAAAUG68/75Ix46i5+MXXoi7NgXl4x3z54t5DXmHaksE+XiE8lVlX97R hAEFAAAAAIBy45ZbRM+UXbqIHDwYd20KyseabWedpbdn78CBBeVjRUfl14Is g2gRAAAAAADKibY2kdpa0fPxnXfGXRudQvPxroYGvT0HO3WS7U1Nkb7/GDGA AAAAAABQTjz2mOjZ+PDDRQXIuGujU2g+/mjzZjl4/PF6u3bfdRf5GOMSAAAA AADKid69Rc/Hl1wSd00yFJyPlXsGD9bbdeC008jHGJcAAAAAAFAuvPOOSIcO oufjF1+MuzYZosjH2xctyrRt16xZ5GOMQwAAAAAAKBfGjBE9G3/5y4mYl8sk inysz9N1zjl6+/bV15OPMQ4BAAAAAKBcOP980fPxjTfGXZMsosrHu8eO1dt3 4CtfIR9jHAIAAAAAQDmgXS8+7jjR8/GMGXHXJouo8vEO7Z5xrX0dOsi2tWvJ x1hqAQAAAACgHHjrLdGzo2ZC5q02iSoff7R1qxw88ki9jTsefZR8jKUWAAAA AADKgUmTJPPscQnYuXOfbPhgh7zftF23af122b5jr+3fRpaPtWeQe/TQ27l7 2DDyMZZaAAAAAAAoB37yE9Hz8b//e2Sr3Lxllyx8fVMm3/594UbZuGmn/rt/ /KNVXn9jk7yqfq75zPPvyrLlW23XE2U+3jN8uN5OLSeTj7HEAgAAAABAOXDS SaLn44aGyFaZm4+nP75Sz8gara1telY2rx/PfPadvAxsEmU+3vX443o7tfus t2zYcKvEn5mwegQAAAAAgKSjMmbm2ePlyyNdtTUjT522IlAGdvtd2Hy8XWtr x456W1seeGCyxJ+ZsHoEAAAAAICk8/LLomfjTp0if+9x0vJxS0uLHDjlFL29 u6677nGJPzNh9QgAAAAAAEnnscdEz8cnnljUYoJmYLffFZKP9599tt7e3QMH PivxZyasHh3YJq2rnpNNM6fIlmVvyZ69Xj8PwY53peWNqdI0c6o0r3pX2gpY VfKIsJ/8snej7Fj2hGyYeY/qU80HVdmvyrZlJa5HLqG3s1cfbpO2HZqR1jYc mb4vRT/HMLbcKGnbY6Dc9lPVPBYTR5T7qBIckwEg+dx/v+j5+JvfLGoxScnH bX376u3dc955r0j8mQmrRwfWSvPMobLkuh6ybNoj0rLT6+ch2DRLmqb8m8y7 7t9k1cxZ0lrAqpJHhP3kB+0cfsEEWXHXubLgulNVn2r2kbdn3C3rZpSwHnaE 3s7Ofdi2cYE0z/mNNM15Tlo2FaHOQdm5SDZN+7ksLEk/l3hseVHStsdAue2n qnksJojo91ElOCYDQPIZO1b0fHzuuUUtJin5eN/Pfqa3d9/ZZy+U+DMTVo8O OB1zI/yuutzOOwNR2nOWtjVTZe3d31F9+R1ZMnGorNWvH2vXu2arbVWu+dj5 eknLnNtl2U2nypIp90gz+TheyMfJoprHYmIoxj6KfAwAimHDRM/Hl15a1GKS ko/3Gu1t69ZtmcSfmbB6dKAEx9xyO+8MRGnPWVoX3yOrxpwq8266XNbOed1y D2gCzp0i385mm8jHiTgfJh8ni2oei4mhGPso8jEASPqdx1o+vv76ohaTlHy8 x7hevv/kk9dK/JkJq0cHyMeFEVM+HjNMmhavja0etpCPIyYB29QK+ThZVPNY TAzkYwAoEj/8oej5+LbbilpMUvLxbuN56wOf+cxmiT8zYZXYNGeRbFu3UQ5I LuHvr04/d2XOEaWc9YR9Ga7nnWY594SaF+fAh2/JtgUPttdBuWHBK7Ljw935 f5w7/07m39Z5roLeS+51zrJb9qx7WbbMuierjkHLMvt67ZSfypKbtOvHfWXZ lN/o69r0xt+ldYf3uVOgvrIpO/B29t2/+WPNfKZv1cS+6vz/VFk4+jJZNe2e 9DN+G7dF3r/efWWs70PvTBK2n/MpzdiKr+3mdtc+j8tlZ05b0uM67LrbKf74 NSn37eFGCcdi3rxj1mOE3zYErE+IY0Px9lFh83Fxxh8AxMRZZ4mej++9t6jF JCUft/71r3p7D37849qRP/bchNXhvJt+LkvvmyBb8vJniGOxcf6yzsxq5jxR Q8+1L8MxH2vnPY/IWv38Qnuedqxs8p2P0+dMHzReLUtHntFeB+WCkZfIisaH 8rO2pR7LpoyRpmeGyLLR37Ese4YsuutqWbcg+7zcHed+Sp+b3idr7rtYFg09 NauOZllrZueeS9mTuW58Xb7p6xZu504h+kqjgO0crH/z6+7YXst18yj717uv 0ut795kJsmbSpQ6ZJGQ/O1KasRVf2832aePlFlnTaG3Ld1QZU6VlRwH9WrLx Wynbw40SjkXrdfEpd6i8OSmTQf20IVR9Qmz74u2jgh+TizP+ACBWTjtN9Hzc 2FjUYpKSj3c9/3y6vYcdtk8SkJuwOtTu/9Iz6JRJ0lzQsViddy37g6zR50+2 zhFlfo9uU4ZtPta+61bnrveFycbWZevSx/4Z5nfllnpo58DW60SZenxHFt70 HVk07mJ1jjUuZzntOsBQaXrDb10c+kmdm7fMGSPLRtYZ53LjLN/nt5c176YB 6rzlVc/v9sNfPw7ZVwVt53T/LhzTXses/h13s3ywzFpWft09r81E3L/5fWUp 07LORTel27Ygsn52ozRjK762m+3L/zyum/GQbFm2XH0Gy2D8Vsz2cKOEYzGT j1XdR/ZJa23DtKFGdrVpQ9j6hDg2FG8fFfCYXJTxBwCx88//LFV5/fjoo7dL AnITVofN6ti/SjunKPRYvON1de5yuU2mVeejb0yyLyMvH2vnb8+pn2nfdQfN xlodlsuWGdeoZbVzv2HqfCX3HZHGNemh58rbM56Qnea1nkw90vlyxRNPWO7R s9Rff1/SU7LT13mEfT8d0MvqJwtUHZY9qn6edS+g9dy9TpY2PijbPvTX9MDP H4ftq4K2s5HftXZn8odluaHGOPA9BvOf7StK/2b1Ve51Quu9Dto1mYj62ZUS jq1Y2t6+fXM/jwf27tYth/FbOdvDjRKOxUw+PtWYp3+EfGC9P9j6jrucNoSu T+hjQzH2UcGOycU61gBAzJjPH996a1GLSUo+3j15svD8MZbcTf9tnC8WdizO vF8ob/5ksZyTOp17aOeV/yPbCsnGWrZe9pCsGWeX9U22yc4F4+XtkXWy8O7f yKY123LqcYYsmjRetryfc6/Zh3NlQ+OlNtdj3HA4ZzGf+3N61nGvdg57rSwK OK9LsHwcvq8K285B+zdEPi5C/7a32buv5kXUz+6UbmzF0/b27btg3M2yYfnG nOXKY/xWzvZwo4T7OUs+XjDyWlm3YLntvfPbZv9alt50alYbQten4H1XlPuo gPm4SMcaAIgZc/7qwYOLWkxS8vGeMWOE+aux9K7NzHGSPe9NkGPxbnVeNU7e HuV0PrvNvozMuUcfWXrfjbJqSvoZKcdzH1fUedEsdV409FTXc7sD7z8l6yb1 kXmj0mUcyKmH7fXhzHlEkO/Zg84pavZR+31vxcvHYfuq8O0crH+D52Nnwvav V5uNvjKv1UTSz16UamzF1fb27bto0jiVSXLnWyqX8etEuW0PN0q4n7PcX714 yn2ydZP9PFx7lk+RNePqfLbBoz4F77ui3EdFNX91YccaAIgZ8/3HAwYUtZik 5OO9Q4cK7z/GGHQgyLG4/dzL/nzWAct38wuG1inNOVbC5OP285HsZ/JyNJ9R G3qprJk1V/Zk1cPp/S1hznXczlns5hO1PA+WNb+Wv9YHy8dh+6rQ7Ry0f8Pm 4yj7d5u0zPmNLLvJo82Z8+Qo+tmLUo2tuNrutX3LZfxqVML2cKOE+7lMPu7t +pxLJuPntSFEfQred0W5jwqTj6M/1gBAzBjvA5ZevYpaTFLy8T7jevm+s89e KPFnJqweHQhyLA75rkfrs13682SXyzKnOXI8sTyz6EvL+U4p87E+d+4j8m7e fKLGXKLTbk4/P1eifBysrwrdziXIx5H3b3smcf/7KPvZi1KNrbja7j8fJ3r8 Vsz2cKOE+7lMPvaom932ClufYuTj0H0TfH6uYhxrACBmGhpEz8ff+EZRi0lK Pm4znrfec/75r0j8mQmrRwdKef3YfN74dWnJzJHTV1Y981yI9yl5XB/JaHmn cgnzcdv7T8i6Sblz51reRflh+zN2sV8/zuur5F8/jr5/S3DNzm5MulKqsRVX 2yO6fhzz+K2c7eFGCfdzBVw/Dl2fIuTj8H0TcE6QIh1rACBmHntM9HzcuXNR i0lKPt5vzNe9e+DAZyX+zITVY+YdQZn3T+hE+fyxQxl25x6ZOVaDvk8p5Lmv Uz2yiCofa+e3t+vnt45ty8z3Uprnj4P1VYTbOYuo8nEx+tfSZq1v31hr/zyj 7Tw9BYxJV0o1tuJqu9fnrRzGbyVtDzdKuJ+zPH/s9px3/vPHBdQn8nxcSN8E OSYX71gDADHz8sui5+NOnUQOHixaMUnJxwe+/GW9vbsGD35M4s9MWDWuzRxH s88ZI5y/2nKszirD6f3Hqx+Rd+9Of++9tPEhdR7k51xut7S+8XuVEetcn1+2 ndOzZPnYxzNp5hyzRc3H4fsquu1s11eF5uPi9G/mOozje2+s642mn90p3diK p+3ebUn++K2k7eFGCfdzlvmr89+VbrDjXWl+ZogsuanOMt90AfWJPB8X0jdR PvMU/lgDADGzUR2btHysuXx50YpJQj7erv5eOnbU29ry4IOTJPbMhNViy5yh su6+9DO/2Vk04LNOmeu+ue9m0uYHecK+DKdzj70b1XnqGFk2UjuX+5m8O2eh zbtI8jnw4avyQeMA492mOe/GlPS1oS1PXC1LR56RfX5VsnxsmUM27zt9bU5R rZ/anxUrXj4uoK+i3M6e/eudj7OvhRWpf63vjBl9mcpVue+cta43on52pYRj K5a2e3/ekj9+K2l7uFHCsWh9//HQc2XpfRNki/UecO39x3PGpucXy3qHVQH1 iSAfR7ePCvfMU9THGgBIACefLHo+1p5FLhJJyMe7Hn9cb+fBo46SLRs2aC98 jj03YXWoP8tmewwNOldm9nXf9uedxska4zicV4bLuUf7uVydLLp7jGxa7edc TTvuPyJr9Tm+6tJzkMxof6Zu7ZSfyhLt2tDIS9S50ys2728pdj526qP2OUUX jewri8f01fsryH2QQfNx6L6KeDu7969T3dvP/bT6rWgcZ9wPu7Fo/du28WU1 Hs32WZ/fTK93ychz1brPtXkPath+dqO0Y6v0bffzeUv6+K2k7eFGCcei5f7q hTf1UPbJXndm7m2VnRv/INsyzwoVUJ/Q+65i7KOCPfMUvhzLnNe+7yMAgJLy 05+Kno+1uZ2LRBLy8Z7hw/V2tp1zjrbcKElAbsLqUDvua8fOpqx3H2uEeJeE Pl/mE7LOOM9qny/zO/ZluJ57qHM5c64udb6z7FFVlq/7rNPvdvygMX0dJHtO 1nQ91i14RXZY11Xy+av/IGty3q+Rvh5yszQteE42PXu79zOGOQTPxyH7KtOG qLazW/+6fBeTudZnlG0+a1ik/s2cM84Ykj4Hz5kLdt3syfLuFO3cPcJ+dqS0 Y6v0bff7eUv4+K2Y7eFGCcdiJh/3kKWTbpF1z4zJzL+cNS/zTJtMF7Y+ofdd xdhHhZm/Okw57fPAzbvp57J2zqKA71oEgKIzebLo+Vh7NrdIJCEft/Xoobdz 9403ko+xpDapY779PKXp86hNM6ek57rc6/XzdjJz3HjNhardD/fGVB+/v0c2 BDpnszxH52dOVq96ZNp8j2zK+x7BCbd+al9fpm7WZyTN/gvw3b39HGte9UgT qK/syixa/wbow6y+ir5/89uSMxfsznTm2lCEfs6ntGOr9G0P9nlL7vjN/l35 bg83SjgWLflYz4Efmu3Mab/jszgh6hPlti94HxXmmBymHK4fAySet96SzDPI Km8Wg9jz8datcvDII/U27vjrX8nHWGoBAACSTW4+3um9CABARaLNW33ccaLn 4xkzilJE3Pl4x4svptt3yCGy7b33yMdYagEAAJIN+RgAoJ3zzxc9P954Y1FW b+bcAwcOygcf7JC/L9yY+dlfpq0oej7ePXas3r4DX/mK/vfkYyyxAAAAyYZ8 DADQzpgxknkGuQjvQbbm4/UbdsgTT62WCb9bKHf+doFusfNxW8+eevv21deT jzEOAQAAkg35GACgnXfeEenQQfSMPHt25Ku35ly7jFzMfLz9jTcybds1axb5 GOMQAAAg2ez1nncMAKCq6N1b9Hx88cUFr2rzll2y8PVNmXz7yKMr5LX5GzK/ z83IxczHe264QW/XgdNOk+3bt5OPMQ4BAAAAAKCceOwx0fPxYYepgLu5oFXl 5mMtG69fvz3rb8yM/MLs92TZ8q226yk4H6vfH/zkJ/V27b7rLvIxxiUAAAAA AJQTbW0itbWiZ+Q77ihJkVpG/qhlj8qt9jfxFJqPd02ZorfnYKdOsr2piXyM cQkAAAAAAOXGLbeIno9PPrko83QFpdB83Na9u96evQMHSktLC/kY4xIAAAAA AMqN998X6dhR9Iz87LNx16agfLz9739Pt0O544UXyMcYpwAAAAAAUI5ccIHo ubJbNy2MxlqVQvLxvvPO09ux/6tf1f9NPsYYBQAAAACAcmT58vQcXVpGHj8+ 1qqEzce7pk4V89rxzieeIB9j3AIAAAAAQLnyq1+Jni+PPlpUEI2tGmHyccvG jXLgxBP1+u/70Y8y15PJxxijAAAAAABQruzaJWJkzCjehxyWMPl4z5Aher0P fvzj0vL22+RjTIIAAAAAAFDOPP64mPcoy/PPx1KFoPl4+4IFmXvDd48dmzWX NfkYYxQAAAAAAMqd888XPR+fcorI7t0lLz5QPlb/33b22ZKZk6u5mXyMSREA AAAAAMqdd98V6dRJ9Izcv7/IgQMlLT5IPt5z9dXpenboIDueey4rG5OPMWYB AAAAAKAS+NOf9MypZ88rryxp0a/N26BrxS4f7x45Usx7wbX/zs3G5GOMWQAA AAAAqBTGjZPMs8i33FKyYv3k452/+12mbntUfrfLxuRjjFkAAAAAAKgkjHmh de+9tyRFet1f/dHDD4t07KjXaW///vozyORjTJqjRo0SRERERESsIEeOlDdP P130dyd16CDPDhwob7zxhgSlbf8B2blzn8qre3S1/9Z+ZodbPt46daocPOII vT5tPXvKts2b9eeQyceYNGP/7CIiIiIiYuTeNmKEvPOlL4l5HXmrNmeX9q7k HDZv2SULX9+Uybd/X7hRNm7aafu7Oa82yXvrWvLWoWGbj/fskd3Dhokccohe h/1f/7p8tH595h1P5GNMoAAAAAAAUInsVDn3Jz+RzL3WXbuKLF6c9Se5GXj6 4yv1jKzR3LxbVrzdLG8t+4fuE0+tltfmb7ArKT8fr10rB7/97UzZe7XrxqtX Z7Ix+RgTKgAAAAAAVDIPPSRy1FGiZ9WPfUxk4sSsX1sz8tRpK/KuA5vYXSO2 /d3UqSI1NenyDj1UWn79a9myeXP7+4/Jx5hcAQAAAACg0nn7bZGvf10y15LP OiudY/ftiyYfz22S5b99WKRPn/YyTjpJtr/wQt77j8nHmGABAAAAAKAa2LNH ZPBgyeRXzRNOELn1VpGN6XuqfV8jNlE5V8aPl92f/2L2ei++WPY3N+e9/5h8 jAkXAAAAAACqiQUL0s8la/dam3n2sMNELrlE3r1hlKz4rykib74psmNH1mLz Xloji/78ksjTT4vcc4/I5Ze337etzZV9SEeRCy4Qef55/e9z339MPsYyEAAA AAAAqhGVWWXMGJETT5Ssa79WP/lJka99TeSznxXp0MH+bz71KWn66XWy8PEF WasnH2MZCgAAAAAA1YzKsTJjhsjAgbL9tG/IvmOPF8e8rHnccSJ1dSIXXSTy 8MP6fdtu7z8mH2MZCQAAAAAAoJPJuSqfypIlIo89JnL33SLTpsmSKTNlwXPL 3JezQD7GMhQAAAAAAEAn8PxcLr8jH2MZCgAAAAAAoEM+xioXAAAAAABAh3yM VS4AAAAAAIAO+RirXAAAAAAAAB3yMVa5AAAAAAAAOuRjrHIBAAAAAAB0yMdY 5QIAAAAAAOiQj7HKBQAAAAAA0CEfY5ULAAAAAACgQz7GKhcAAAAAAECHfIxV LgAAAAAAgA75GKtcAAAAAAAAHfIxVrkAAAAAAAA65GOscgEAAAAAAHTIx1jl AgAAAAAA6JCPscoFAAAAAADQIR9jlQsAAAAAAKBDPsYqFwAAAAAAQId8jFUu AAAAAACADvkYq1wAAAAAAAAd8jFWuQAAAAAAADrkY6xyAQAAAAAAdMjHWOUC AAAAAADokI+xygUAAAAAANAhH2OVCwAAAAAAoEM+xioXAAAAAABAh3yMVS4A AAAAAIAO+RirXAAAAAAAAB3yMVa5AAAAAAAAOuRjrHIBAAAAAAB0yMdY5QIA AAAAAOiQj7HKBQAAAAAA0CEfY5ULAAAAAACgQz7GKhcAAAAAAECHfIxVLgAA AAAAgA75GKtcAAAAAAAAHfIxVrkAAAAAAAA65GOscgEAAAAAAHTIx1jlAgAA AAAA6JCPscoFAAAAAADQIR9jlQsAAAAAAKBDPsYqFwAAAAAAQId8jFUuAAAA AACADvkYq1wAAAAAAAAd8jFWuQAAAAAAADrkY6xyAQAAAAAAdMjHWOUCAAAA AADokI+xygUAAAAAANAhH2OVCwAAAAAAoEM+xioXAAAAAABAh3yM1ez/BzGZ OqU= "], {{0, 234}, {968, 0}}, {0, 255}, ColorFunction->RGBColor], BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{968, 234}, PlotRange->{{0, 968}, {0, 234}}]],ExpressionUUID-> "ae7cd758-d671-4146-a2c1-e23e15216ea7"] }], "Text", CellChangeTimes->CompressedData[" 1:eJxTTMoPSmViYGCQAGIQvXIJ25fGM68dhZbOZG4C0gkhcoIgesWxciEQLfBy fjaIvjf5fTGIXv5iQf0cIH3MW7wJRJs09CssAtLty4VVQLRI4nFdEK18e6ch iN5+cQvDYiDd4FGuDqInnU7WBtEnNLt0QLTt7KkPVwHpC5tT34Ho6f93fALR 9scuiK8G0p2X5M6tAdLdf7deBNFNgVtvgOgyf7m7IFpIJP4FiFY79A5MZ/l+ z10LpE8ZSRSC6CWMOWtB9BVOgXUgmm+fwda1YPV520D0W96wXSD6x5OFYJpp T+IREN0fHHMcRH/bucp5PZBesNoxbD04PJhjQHRORVQKiH6j73z+EJC+49Z/ AUR7vfpxD0R/2nDiA4i+dvTmFxDN2fWZ4TCQZpgoxQqiZaJOCIFoAFoe4hU= "], FontSize->16,ExpressionUUID->"8c96ebac-ca89-443f-967a-3e9ca7f35cf2"], Cell[CellGroupData[{ Cell["\<\ Desplegar este grupo de celdas haciendo doble click en la flechita de la \ derecha de la pantalla.\ \>", "Subsection", CellChangeTimes->{{3.7311885233361998`*^9, 3.7311885725601997`*^9}, { 3.7311892079362*^9, 3.7311892268691998`*^9}, {3.7311892644542*^9, 3.7311892684502*^9}},ExpressionUUID->"546f0bb7-0235-4b53-b156-7f64a522c9de"], Cell[CellGroupData[{ Cell["\<\ Vayan par\[AAcute]ndose en cada celda y apretando el Enter del teclado num\ \[EAcute]rico o Shift + Enter. Tambi\[EAcute]n pueden seleccionar con el \ mouse el corchete que engloba a todo el grupo de celdas y ejecutarlas de una \ sola vez a todas.\ \>", "Subsubsection", CellChangeTimes->{{3.7312329321948*^9, 3.7312329877202*^9}},ExpressionUUID->"5ed0f335-5563-42a9-97c3-29ef72b4edd4"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Un", " ", "cl\[AAcute]sico", " ", "siempre", " ", "vigente"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"1", " ", "+", " ", "1", " "}]}]], "Input", CellChangeTimes->{{3.7311655838900003`*^9, 3.7311656809374*^9}, { 3.7311657121948*^9, 3.7311657264708*^9}, {3.7311675944846*^9, 3.7311676520116*^9}, {3.7311690340076*^9, 3.7311690469948*^9}, { 3.7311838145322*^9, 3.7311841299332*^9}, {3.7311874419172*^9, 3.7311875369112*^9}, {3.7311926541182003`*^9, 3.7311926572872*^9}, { 3.7312344653336*^9, 3.7312344668206*^9}},ExpressionUUID->"3fa9c547-8fea-451c-bd1b-1ae2cb3296a4"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{ "Esta", " ", "instrucci\[OAcute]n", " ", "va", " ", "a", " ", "asignarle", " ", "el", " ", "valor", " ", "1", " ", "a", " ", "la", " ", "variable", " ", "\"\\"", " ", "pero", " ", "no", " ", "va", " ", "generar", " ", "una", " ", "salida", " ", "en", " ", "pantalla"}], ",", " ", RowBox[{"debido", " ", "al", " ", "\"\<;\>\"", " ", "final"}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"numero", " ", "=", " ", "1"}], ";"}], " "}]], "Input", CellChangeTimes->{{3.7311655838900003`*^9, 3.7311656809374*^9}, { 3.7311657121948*^9, 3.7311657264708*^9}, {3.7311675944846*^9, 3.7311676520116*^9}, {3.7311690340076*^9, 3.7311690469948*^9}, { 3.7311838145322*^9, 3.7311841299332*^9}, {3.7311874419172*^9, 3.7311875595692*^9}, 3.731233383626*^9, {3.731234414584*^9, 3.7312344243796*^9}},ExpressionUUID->"4fb22377-08c2-4ae8-9697-\ 0e2f74f3468a"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Aqu\[IAcute]", " ", "s\[IAcute]", " ", "muestra", " ", "el", " ", RowBox[{"resultado", "."}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ SqrtBox["2"], "+", "numero", " "}]}]], "Input", CellChangeTimes->{{3.7311655838900003`*^9, 3.7311656809374*^9}, { 3.7311657121948*^9, 3.7311657264708*^9}, {3.7311675944846*^9, 3.7311676520116*^9}, {3.7311690340076*^9, 3.7311690469948*^9}, { 3.7311838145322*^9, 3.7311841299332*^9}, {3.7311874419172*^9, 3.7311875595692*^9}, {3.731233383626*^9, 3.7312333864908*^9}, { 3.7312344388318*^9, 3.7312344442332*^9}},ExpressionUUID->"cf52d435-9dd1-44b8-a540-9195521b0511"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{ "\[Pi]", " ", "entendido", " ", "como", " ", "n\[UAcute]mero", " ", "de", " ", "precisi\[OAcute]n", " ", RowBox[{"infinita", ".", " ", "Para"}], " ", "escribir", " ", "el", " ", "s\[IAcute]mbolo", " ", "\"\<\[Pi]\>\"", " ", RowBox[{"usen", " ", "[", RowBox[{"Tecla", " ", "Esc"}], "]"}], RowBox[{ RowBox[{"p", "[", RowBox[{"Tecla", " ", "Esc"}], "]"}], ".", " ", "\[CapitalIAcute]dem"}], " ", "para", " ", "\[Mu]"}], ",", " ", "\[Epsilon]", ",", " ", "\[Theta]", ",", " ", RowBox[{"y", " ", RowBox[{"as\[IAcute]", "."}]}]}], " ", "*)"}], "\[IndentingNewLine]", "\[Pi]", " "}]], "Input", CellChangeTimes->{{3.7311655838900003`*^9, 3.7311656809374*^9}, { 3.7311657121948*^9, 3.7311657264708*^9}, {3.7311675944846*^9, 3.7311676520116*^9}, {3.7311690340076*^9, 3.7311690469948*^9}, { 3.7311838145322*^9, 3.7311841299332*^9}, {3.7311874419172*^9, 3.7311875425872*^9}, {3.7311881386542*^9, 3.7311881499182*^9}, { 3.7312345155726*^9, 3.7312345169046*^9}, {3.7312345544514*^9, 3.7312345551387997`*^9}},ExpressionUUID->"0dc369fc-41d3-49d4-80f0-\ 49e55ae0af5e"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Las", " ", "primeras", " ", "50", " ", "cifras", " ", "de", " ", RowBox[{"\[Pi]", "."}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"N", "[", RowBox[{"\[Pi]", ",", " ", "50"}], "]"}], " "}]], "Input", CellChangeTimes->{{3.7311655838900003`*^9, 3.7311656809374*^9}, { 3.7311657121948*^9, 3.7311657264708*^9}, {3.7311675944846*^9, 3.7311676520116*^9}, {3.7311690340076*^9, 3.7311690469948*^9}, { 3.7311838145322*^9, 3.7311841299332*^9}, {3.7311874419172*^9, 3.7311875310382*^9}, 3.7311876287111998`*^9, {3.7311881572032003`*^9, 3.7311882079222*^9}, {3.7311926883852*^9, 3.7311926975282*^9}, { 3.7311927294231997`*^9, 3.7311927359052*^9}, 3.7312330700584*^9, 3.7312345514774*^9, {3.7314180891646*^9, 3.7314180914154*^9}},ExpressionUUID->"d150aeb9-db72-4bb9-8eb9-\ 81ebb5667dd6"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ "Tambi\[EAcute]n", " ", "pueden", " ", "escribir", " ", "la", " ", "palabra", " ", "Pi", " ", RowBox[{"directamente", "."}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"Pi", "\[IndentingNewLine]", RowBox[{"N", "[", RowBox[{"Pi", ",", " ", "50"}], "]"}], " "}]}]], "Input", CellChangeTimes->{{3.7311655838900003`*^9, 3.7311656809374*^9}, { 3.7311657121948*^9, 3.7311657264708*^9}, {3.7311675944846*^9, 3.7311676520116*^9}, {3.7311690340076*^9, 3.7311690469948*^9}, { 3.7311838145322*^9, 3.7311841299332*^9}, {3.7311874419172*^9, 3.7311875310382*^9}, 3.7311876287111998`*^9, {3.7311881572032003`*^9, 3.7311882079222*^9}, {3.7311926883852*^9, 3.7311926975282*^9}, { 3.7311927294231997`*^9, 3.7311927359052*^9}, {3.7312330700584*^9, 3.7312330720768003`*^9}, {3.7312345736452*^9, 3.731234602282*^9}},ExpressionUUID->"69053c99-1681-4d93-ab6c-a145e058cdd0"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{ "Al", " ", "multiplicar", " ", "\[Pi]", " ", "por", " ", "un", " ", "n\[UAcute]mero", " ", "real", " ", "de", " ", "precisi\[OAcute]n", " ", "finita"}], ",", " ", RowBox[{ "indicado", " ", "por", " ", "el", " ", "\"\<.\>\"", " ", "luego", " ", "del", " ", "\"\<1\>\""}], ",", " ", RowBox[{ "el", " ", "resultado", " ", "tambi\[EAcute]n", " ", "es", " ", "de", " ", "precisi\[OAcute]n", " ", "finita"}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"1", " ", "\[Pi]"}], "\[IndentingNewLine]", RowBox[{"1.", " ", "\[Pi]", " "}]}]}]], "Input", CellChangeTimes->{{3.7311655838900003`*^9, 3.7311656809374*^9}, { 3.7311657121948*^9, 3.7311657264708*^9}, {3.7311675944846*^9, 3.7311676520116*^9}, {3.7311690340076*^9, 3.7311690469948*^9}, { 3.7311838145322*^9, 3.7311841299332*^9}, {3.7311874419172*^9, 3.7311875310382*^9}, 3.7311876287111998`*^9, {3.7311881572032003`*^9, 3.7311882079222*^9}, {3.7311926883852*^9, 3.7311926975282*^9}, { 3.7311927294231997`*^9, 3.7311927359052*^9}, {3.7312330700584*^9, 3.7312330744574003`*^9}, {3.7312346088238*^9, 3.7312346392386*^9}},ExpressionUUID->"18c605f7-584b-4ae2-b261-\ 1d1c7a22fc8f"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Eso", " ", "es", " ", "v\[AAcute]lido", " ", "en", " ", RowBox[{"general", ".", " ", "Comparen", "."}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ FractionBox["100371", "1000"], "\[IndentingNewLine]", "\[IndentingNewLine]", FractionBox["100371.", "1000"]}]}]], "Input", CellChangeTimes->{{3.7312359161372004`*^9, 3.7312359959639997`*^9}},ExpressionUUID->"3a2c607a-bab2-420e-a3e8-\ 0095090e046e"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ "Esta", " ", "celda", " ", "contiene", " ", "varias", " ", "operaciones", " ", "y", " ", "muestra", " ", "un", " ", "resultado", " ", "tras", " ", "otro"}], " ", "*)"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"La", " ", "constante", " ", "de", " ", "Euler", " ", RowBox[{"es", " ", "[", "Esc", "]"}], RowBox[{"ee", "[", "Esc", "]"}], " ", "o", " ", "E", " ", RowBox[{"may\[UAcute]scula", "."}]}], " ", "*)"}], " ", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"La", " ", "unidad", " ", "imaginaria", " ", RowBox[{"es", " ", "[", "Esc", "]"}], RowBox[{"ii", "[", "Esc", "]"}], " ", "o", " ", "I", " ", RowBox[{"may\[UAcute]scula", "."}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"10", "!"}], "\[IndentingNewLine]", SuperscriptBox["2", SuperscriptBox["2", SuperscriptBox["2", "2"]]], "\[IndentingNewLine]", RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Pi]"}]], "+", "1"}], " ", "\[IndentingNewLine]", RowBox[{"Log", "[", "E", "]"}], "\[IndentingNewLine]", SuperscriptBox["I", "2"], "\[IndentingNewLine]", RowBox[{"ComplexExpand", "[", SqrtBox["\[ImaginaryI]"], "]"}]}]}]], "Input", CellChangeTimes->{{3.7311655838900003`*^9, 3.7311656809374*^9}, { 3.7311657121948*^9, 3.7311657264708*^9}, {3.7311675944846*^9, 3.7311676520116*^9}, {3.7311690340076*^9, 3.7311690469948*^9}, { 3.7311838145322*^9, 3.7311841299332*^9}, {3.7311874419172*^9, 3.7311875499132*^9}, {3.7311876351702003`*^9, 3.7311878630542*^9}, { 3.7311880129572*^9, 3.7311880133302*^9}, {3.7311927188512*^9, 3.7311927198831997`*^9}, {3.7311927639351997`*^9, 3.7311927693882*^9}, { 3.7312331170438004`*^9, 3.7312332185218*^9}, {3.7312339305294*^9, 3.7312340041482*^9}},ExpressionUUID->"8eb7aded-d7db-46e8-8922-f0bbc7fc4cdc"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Una", " ", "primitiva"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"Integrate", "[", RowBox[{ FractionBox["1", "u"], ",", " ", "u"}], "]"}], " "}]], "Input", CellChangeTimes->{{3.7311878727452*^9, 3.7311879515452003`*^9}, { 3.7311879817441998`*^9, 3.7311879974902*^9}, {3.7311882360302*^9, 3.7311882685692*^9}, {3.7311927872142*^9, 3.7311927900092*^9}, { 3.7312332523046*^9, 3.7312333374066*^9}, {3.7312340250638*^9, 3.7312340369063997`*^9}, {3.7312346788691998`*^9, 3.7312346847986*^9}},ExpressionUUID->"b6005fc9-420b-4a37-9f8b-4a9a1da773b0"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Una", " ", "integral", " ", RowBox[{"definida", ".", " ", "El"}], " ", "s\[IAcute]mbolo", " ", "\[Infinity]", " ", RowBox[{"es", " ", "[", "Esc", "]"}], RowBox[{"inf", "[", "Esc", "]"}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"Integrate", "[", RowBox[{ FractionBox[ RowBox[{"Sin", "[", "x", "]"}], "x"], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", RowBox[{"-", "Infinity"}], ",", " ", "Infinity"}], "}"}]}], "]"}], " "}]], "Input", CellChangeTimes->{{3.7311878727452*^9, 3.7311879515452003`*^9}, { 3.7311879817441998`*^9, 3.7311879974902*^9}, {3.7311882360302*^9, 3.7311882685692*^9}, {3.7311927872142*^9, 3.7311927900092*^9}, { 3.7312332523046*^9, 3.7312333429188004`*^9}, {3.731234044124*^9, 3.7312340548314*^9}},ExpressionUUID->"be1296cf-2dc0-41ba-ae18-326cf85b0000"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{ "Si", " ", "tienen", " ", "fijaci\[OAcute]n", " ", "con", " ", "los", " ", "s\[IAcute]mbolos"}], ",", " ", RowBox[{ "la", " ", "integral", " ", "definida", " ", "se", " ", "escribe", " ", RowBox[{"con", " ", "[", "Esc", "]"}], RowBox[{ RowBox[{"dintt", "[", "Esc", "]"}], ".", " ", "Raramente"}], " ", "se", " ", "usa", " ", RowBox[{"as\[IAcute]", ".", " ", "Es"}], " ", "m\[AAcute]s", " ", "pr\[AAcute]ctico", " ", "el", " ", "comando", " ", RowBox[{"Integrate", "."}]}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ SubsuperscriptBox["\[Integral]", "0", "y"], RowBox[{ RowBox[{"Exp", "[", RowBox[{"-", "x"}], "]"}], RowBox[{"\[DifferentialD]", "x"}]}]}], "\[IndentingNewLine]", RowBox[{"Integrate", "[", RowBox[{ RowBox[{"Exp", "[", RowBox[{"-", "x"}], "]"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", "0", ",", " ", "y"}], "}"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.7311878727452*^9, 3.7311879515452003`*^9}, { 3.7311879817441998`*^9, 3.7311879974902*^9}, {3.7311882360302*^9, 3.7311882685692*^9}, {3.7311927872142*^9, 3.7311927900092*^9}, { 3.7312332523046*^9, 3.7312333517592*^9}, {3.731234063462*^9, 3.7312342520022*^9}, {3.7312343149334*^9, 3.7312343159972*^9}},ExpressionUUID->"22d704fa-fcc6-44fe-850a-663a45401845"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{ "Los", " ", "c\[AAcute]lculos", " ", "se", " ", "simplifican", " ", "si", " ", "aclaran", " ", "las", " ", "cosas", " ", "que", " ", "el", " ", StyleBox["Mathematica", FontSlant->"Italic"], " ", "puede", " ", "asumir"}], ";", " ", RowBox[{"si", " ", "no"}]}], ",", " ", RowBox[{"procede", " ", "con", " ", "morosa", " ", RowBox[{"cautela", "."}]}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "Comparen", " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"Integrate", "[", RowBox[{ FractionBox[ RowBox[{"Exp", "[", RowBox[{"\[ImaginaryI]", " ", "x", " ", "\[Lambda]"}], "]"}], RowBox[{"1", " ", "+", " ", SuperscriptBox["x", "2"]}]], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", RowBox[{"-", "\[Infinity]"}], ",", " ", "\[Infinity]"}], "}"}]}], "]"}], "\[IndentingNewLine]", RowBox[{"Integrate", "[", RowBox[{ FractionBox[ RowBox[{"Exp", "[", RowBox[{"\[ImaginaryI]", " ", "x", " ", "\[Lambda]"}], "]"}], RowBox[{"1", " ", "+", " ", SuperscriptBox["x", "2"]}]], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", RowBox[{"-", "\[Infinity]"}], ",", " ", "\[Infinity]"}], "}"}], ",", " ", RowBox[{"Assumptions", " ", "\[Rule]", " ", RowBox[{"\[Lambda]", " ", ">", " ", "0"}]}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.7311878727452*^9, 3.7311879515452003`*^9}, { 3.7311879817441998`*^9, 3.7311879974902*^9}, {3.7311882360302*^9, 3.7311882685692*^9}, {3.7311927872142*^9, 3.7311927900092*^9}, { 3.7312332523046*^9, 3.7312333517592*^9}, {3.731234063462*^9, 3.7312343632328*^9}},ExpressionUUID->"fb1e753b-3815-4d78-9fbb-32b2d8689dec"], Cell["\<\ Siguen varios ejemplos de c\[OAcute]mo simplificar expresiones [\[EAcute]sta \ es una celda de texto].\ \>", "Text", CellChangeTimes->{{3.7311928491962*^9, 3.7311928579611998`*^9}, { 3.7311930025202*^9, 3.7311930030702*^9}, {3.731233424125*^9, 3.7312334871832*^9}, {3.7312347357304*^9, 3.731234811828*^9}, { 3.7312348791046*^9, 3.731234879402*^9}}, FontSize->18,ExpressionUUID->"b70631b8-0243-40f2-b06e-c1f2020787b3"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Una", " ", "expresi\[OAcute]n", " ", "en", " ", "bruto"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ SuperscriptBox[ RowBox[{"Cos", "[", "x", "]"}], "2"], "+", SuperscriptBox[ RowBox[{"Sin", "[", "x", "]"}], "2"], " "}]}]], "Input", CellChangeTimes->{{3.7311928491962*^9, 3.7311928579611998`*^9}, { 3.7311930025202*^9, 3.7311930030702*^9}, {3.731233424125*^9, 3.7312334871832*^9}, {3.7312347357304*^9, 3.7312347794035997`*^9}, { 3.7312348155684*^9, 3.731234822244*^9}},ExpressionUUID->"f143dfec-1e17-47c7-9de1-2a05cb68b02b"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ "La", " ", "misma", " ", "expresi\[OAcute]n", " ", "pero", " ", "aplicando", " ", RowBox[{"Simplify", ".", " ", "Ver"}], " ", "tambi\[EAcute]n", " ", RowBox[{"FullSimplify", "."}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"Simplify", "[", RowBox[{ SuperscriptBox[ RowBox[{"Cos", "[", "x", "]"}], "2"], "+", SuperscriptBox[ RowBox[{"Sin", "[", "x", "]"}], "2"]}], "]"}], " "}]], "Input", CellChangeTimes->{{3.7311928491962*^9, 3.7311928579611998`*^9}, { 3.7311930025202*^9, 3.7311930030702*^9}, {3.731233424125*^9, 3.7312334871832*^9}, {3.7312347357304*^9, 3.7312347794035997`*^9}, { 3.7312348274723997`*^9, 3.7312348384812*^9}},ExpressionUUID->"c67a7358-722f-4338-80b0-d9962c6788e0"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ "Para", " ", "simplificar", " ", "funciones", " ", "trigonom\[EAcute]tricas"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"TrigReduce", "[", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], " ", RowBox[{"Cos", "[", "x", "]"}]}], "]"}], "\[IndentingNewLine]", RowBox[{"TrigExpand", "[", RowBox[{"Cos", "[", RowBox[{"2", "x"}], "]"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.7311928227072*^9, 3.7311928449592*^9}, 3.7311929368272*^9, 3.7311930646032*^9, {3.731234846043*^9, 3.731234866557*^9}},ExpressionUUID->"663fe9f3-35d1-4fb8-b70a-dd694dd0f376"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"El", " ", StyleBox["Mathematica", FontSlant->"Italic"], StyleBox[" ", FontSlant->"Italic"], "es", " ", "por", " ", "dem\[AAcute]s", " ", RowBox[{"melindroso", ".", " ", "No"}], " ", "va", " ", "a", " ", "cancelar", " ", "la", " ", "ra\[IAcute]z", " ", "cuadrada", " ", "de", " ", "una", " ", "expresi\[OAcute]n", " ", "al", " ", "cuadrado", " ", "as\[IAcute]", " ", "porque", " ", RowBox[{"s\[IAcute]", "."}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "Pero", " ", "pueden", " ", "indicarle", " ", "qu\[EAcute]", " ", "cosas", " ", RowBox[{"asumir", ".", " ", "Comparen"}], " ", "los", " ", "tres", " ", "resultados", " ", "siguientes"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Simplify", "[", SqrtBox[ SuperscriptBox["x", "2"]], "]"}], " ", "\n", RowBox[{"Simplify", "[", RowBox[{ SqrtBox[ SuperscriptBox["x", "2"]], ",", " ", RowBox[{"x", " ", "\[Element]", " ", "Reals"}]}], "]"}], " ", RowBox[{"(*", " ", RowBox[{"El", " ", "s\[IAcute]mbolo", " ", "\"\\"", " ", RowBox[{"es", " ", "[", "Esc", "]"}], RowBox[{"elem", "[", "Esc", "]"}]}], " ", "*)"}], "\n", RowBox[{"Simplify", "[", RowBox[{ SqrtBox[ SuperscriptBox["x", "2"]], ",", " ", RowBox[{"x", " ", ">", " ", "0"}]}], "]"}], " "}]}]], "Input", CellChangeTimes->{{3.7311928662102003`*^9, 3.7311928753062*^9}, { 3.7311929752712*^9, 3.7311930422852*^9}, {3.7311930776652*^9, 3.7311931257142*^9}, {3.7312335098958*^9, 3.7312336044952*^9}},ExpressionUUID->"3b63bc71-8961-4104-9354-1383bceff509"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Un", " ", "gr\[AAcute]fico", " ", "simple"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"Plot", "[", RowBox[{ RowBox[{"Sin", "[", SuperscriptBox["x", "2"], "]"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", "0", ",", " ", RowBox[{"2", "\[Pi]"}]}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.7311655838900003`*^9, 3.7311656809374*^9}, { 3.7311657121948*^9, 3.7311657264708*^9}, {3.7311675944846*^9, 3.7311676520116*^9}, {3.7311690340076*^9, 3.7311690469948*^9}, { 3.7311838145322*^9, 3.7311841299332*^9}, {3.7311874419172*^9, 3.7311875634941998`*^9}, {3.7311880628742*^9, 3.7311880866512003`*^9}, { 3.7312336186758003`*^9, 3.7312336296387997`*^9}},ExpressionUUID->"baec48e4-bf84-41fc-9f0b-\ e090e69dad74"], Cell[BoxData[ RowBox[{ RowBox[{"RandomReal", "[", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], "]"}], " ", RowBox[{"(*", RowBox[{ RowBox[{ "Un", " ", "n\[UAcute]mero", " ", "real", " ", "pseudo", " ", "random", " ", "entre"}], " ", "-", RowBox[{ "1", " ", "y", " ", "1.", " ", "A", " ", "ver", " ", "si", " ", "adivinan", " ", "cu\[AAcute]l", " ", RowBox[{"ser\[AAcute]", "."}]}]}], " ", "*)"}]}]], "Input", CellChangeTimes->{{3.7311880981702003`*^9, 3.7311881081892*^9}, { 3.7311882931802*^9, 3.7311883078642*^9}, {3.7311931774892*^9, 3.7311931811152*^9}, {3.7312336522702*^9, 3.7312336853302*^9}},ExpressionUUID->"4924e4ae-298c-4991-a1a5-6e6f42b1778a"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ "Una", " ", "lista", " ", "de", " ", "1000", " ", "n\[UAcute]meros", " ", "random", " ", "graficados", " ", "con", " ", "el", " ", "comando", " ", "ListPlot"}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"tabla", " ", "=", " ", RowBox[{"Table", "[", RowBox[{ RowBox[{"RandomReal", "[", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", " ", "1", ",", " ", "1000"}], "}"}]}], "]"}]}], ";"}], " ", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"Alternativamente", " ", "tabla"}], " ", "=", " ", RowBox[{"RandomReal", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", "1000"}], "]"}]}], ";"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"ListPlot", "[", "tabla", "]"}]}]}]], "Input", CellChangeTimes->{{3.7312337052412*^9, 3.7312338314334*^9}},ExpressionUUID->"82f049e6-ffa9-47f4-a981-6be700b741bd"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{ "La", " ", "definici\[OAcute]n", " ", "de", " ", "una", " ", "funci\[OAcute]n", " ", "cuya", " ", "variable", " ", "no", " ", "tiene", " ", "atributos", " ", RowBox[{"determinados", ".", " ", "Es"}], " ", "lo", " ", "m\[AAcute]s", " ", RowBox[{"usual", ".", " ", "Notar"}], " ", "el", " ", "guion", " ", "bajo", " ", "y", " ", "el", " ", "s\[IAcute]mbolo"}], " ", StyleBox[":=", FontWeight->"Plain"]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"funcion", "[", "x_", "]"}], ":=", " ", SuperscriptBox["x", "2"]}], ";"}], " ", "\[IndentingNewLine]", RowBox[{"funcion", "[", "y", "]"}], "\[IndentingNewLine]", RowBox[{"funcion", "[", "4", "]"}]}]}]], "Input", CellChangeTimes->{{3.7311883124751997`*^9, 3.7311883565112*^9}, { 3.7311884712522*^9, 3.7311884737122*^9}, {3.7311932031842003`*^9, 3.7311932336602*^9}, {3.7312338452464*^9, 3.7312338579168*^9}},ExpressionUUID->"48660189-dacc-48e8-b790-1f2fc18ca073"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ "Una", " ", "funci\[OAcute]n", " ", "que", " ", "s\[OAcute]lo", " ", "se", " ", "eval\[UAcute]a", " ", "cuando", " ", StyleBox["x", FontSlant->"Italic"], StyleBox[" ", FontSlant->"Italic"], "tiene", " ", "el", " ", "atributo", " ", "de", " ", "ser", " ", "un", " ", "entero"}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"uncion", "[", "x_Integer", "]"}], ":=", " ", RowBox[{"x", "+", SqrtBox["2"]}]}], " ", ";"}], "\n", RowBox[{"uncion", "[", "\[Pi]", "]"}], "\[IndentingNewLine]", RowBox[{"uncion", "[", "1", "]"}]}]}]], "Input", CellChangeTimes->{{3.7311883597422*^9, 3.7311884197892*^9}, { 3.7311932525632*^9, 3.7311932633262*^9}, {3.7312338726942*^9, 3.7312338983642*^9}},ExpressionUUID->"ea39819d-712c-4d3d-ad28-6c61145d7d95"], Cell[TextData[{ StyleBox["\[FilledSquare] Algunos shortcuts \[UAcute]tiles: ra\[IAcute]z, \ potencia y cociente.\n\n", FontSize->18], "Ctrl + 2", Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{"\[Rule]", " "}]}], TraditionalForm]],ExpressionUUID-> "44b3baf6-69f6-41fb-a6cf-ff7cf75091a8"], Cell[BoxData[ FormBox[ SqrtBox["\[Placeholder]"], TraditionalForm]],ExpressionUUID-> "bd5f07db-ba55-45e0-9dfa-26591a7e9964"], StyleBox[" \n\nCtrl + 6 ", FontSize->18], Cell[BoxData[ FormBox[ RowBox[{"\[Rule]", " ", SuperscriptBox["\[Placeholder]", "\[Placeholder]"]}], TraditionalForm]], ExpressionUUID->"604143cc-9171-4efb-bec2-c7433d1fc429"], "\n", StyleBox["\nCtrl + 7 ", FontSize->18], Cell[BoxData[ FormBox[ RowBox[{"\[Rule]", " ", FractionBox["\[Placeholder]", "\[Placeholder]"]}], TraditionalForm]], ExpressionUUID->"5482e533-baa6-4a30-931a-51ec14dba09b"], "\n\nLa flechita es ->[espacio]." }], "Text", CellChangeTimes->{{3.7311841723702*^9, 3.7311843956612*^9}, { 3.7311932843082*^9, 3.7311933314681997`*^9}, 3.7312458765396*^9}, FontSize->18,ExpressionUUID->"941c29a9-91b6-429a-b371-2960aa3ae000"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Primer ejemplo: problema 3.\n\n", Cell[BoxData[ GraphicsBox[{ {RGBColor[0.87, 0.94, 1], AbsoluteThickness[2], ArrowBox[{{-1.5, 0}, {1.5, 0}}], ArrowBox[{{0, 1.5}, {0, -1.5}}]}, {RGBColor[0, 0, 1], AbsoluteThickness[2], LineBox[NCache[{{Rational[-1, 2], 0}, { 0, Rational[-1, 2] 3^Rational[1, 2]}}, {{-0.5, 0}, { 0, -0.8660254037844386}}]]}, { {RGBColor[0, 1, 0], DiskBox[NCache[{Rational[-1, 2], 0}, {-0.5, 0}], 0.05]}, {RGBColor[1, 0, 0], DiskBox[NCache[{0, Rational[-1, 2] 3^Rational[1, 2]}, { 0, -0.8660254037844386}], 0.05]}}, { {GrayLevel[1], InsetBox[ StyleBox["\<\"\[ScriptL]\"\>", StripOnInput->False, FontSize->40], {-0.42320508075688773, -0.5330127018922193}]}, {GrayLevel[1], InsetBox[ StyleBox["\<\"\\!\\(\\*SubscriptBox[\\(m\\), \\(1\\)]\\)\"\>", StripOnInput->False, FontSize->30], NCache[{Rational[-1, 2], 0.25}, {-0.5, 0.25}]]}, {GrayLevel[1], InsetBox[ StyleBox["\<\"\\!\\(\\*SubscriptBox[\\(m\\), \\(2\\)]\\)\"\>", StripOnInput->False, FontSize->30], NCache[{0.33, Rational[-1, 2] 3^Rational[1, 2]}, { 0.33, -0.8660254037844386}]]}, {GrayLevel[1], InsetBox[ StyleBox["\<\"\[ScriptX]\"\>", StripOnInput->False, FontSize->30], {0.2, -1.35}]}, {GrayLevel[1], InsetBox[ StyleBox["\<\"\[ScriptY]\"\>", StripOnInput->False, FontSize->30], {1.35, 0.2}]}}}, AspectRatio->Automatic, Axes->False, Background->GrayLevel[0], ImageSize->400, PlotRange->{{-1.6500000000000001`, 1.6500000000000001`}, {-1.6500000000000001`, 1.6500000000000001`}}, Ticks->False]], "Output", CellChangeTimes->{3.7310996831682*^9},ExpressionUUID-> "4cdb0b43-d0e3-4305-9e52-a763ef34e7d9"], "\n", StyleBox["\nDesplegar este grupo de celdas desde la flecha de la derecha, \ como muestra la figura\nsiguiente:", FontSize->30], "\n\n", Cell[BoxData[ GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJzs3Q2cJFddL/wOiSSSgMiLRGEkvMiLooIbFBEVEGUELgZE4M4iIrKCz5oF FDQ8G5LlEUVcXKMi1xtJbtaoCLKSGFjfgmsuKhu4wgZQhFXYABq5cXU1aAIB znNqumemuqa6uqq7uk/17Pf7+fwIO1Vddaq6urv6/PtU3e/5L376j96h1+v9 5Bnxf57+wz/9uJ/4iR9+xfffNf7jB3b95I+9cNeOF3zvrpfteOGOn3jU80+N f3zoKb3eL92x1zst/v8wgexhIt3LL8Vkx+ehZG148QV7wsdOhNX/pt8fIt0L AAAAUM8v/OL1rU277bbbsv/0REQapLHUfY+yNbO0vCvs2bMn7Nm+bcJlPCXm lpiPxzwkyTaoHYlUBwAAAKhH7UhEEqex1H2PsvWS1Y0uO3y8f4Ad3R+WlyZZ zmkxvxuTHaNvHPx7vtuhdiRSHQAAAKAetSMRSZzGUvc9ytZLVju65ujaEXY8 XHnepMs6N+am0B9/9Ni5b4fakUh1AAAAgHrUjkQkcRpL3fcoWzM/enDtCJum dpTl1THZcfpHMWfNdRvUjkSqAwAAANSjdiQiidNY6r5H2YrZFvatjzs6Gi55 9DTLuk/MB2Nuj3neXLdD7UikOgAAAEA9akcikjiNpe57lC2Ypd1h41Pt+rB7 ovsd5fO80K8dZTWks+e2HWpHItUBAAAA6lE7EpHEaSx136NsvSztOBiOrx1g R/eFbVMvM7tW3bUx2fG6Z27boXYkUh0AAACgHrUjEUmcxlL3PcpWy1LYcXC9 chSO7tvW0nKfEHNLzE0xD5/LtqgdiVQHAAAAqEftSEQSp7HUfY+yxbLtgnB4 rXR0/HC4YFtbyz4t5o0x2TH7W4N/z3Zb1I5EqgMAAADUo3YkIonTWOq+R9la 2bbv6PqxdfzgjrDU6vIfEvPJ0B9/tDzzbVE7EqkOAAAAUI/akYgkTmOp+x5l K2Vb2CgdHQ8HdyzNYB0XxmTH7aGYu850e9SORKoDAAAA1KN2JCKJ01jqvkfZ Qtm2L6yXjo7uD8tLs1jP2THvjbk95kUz3R61I5HqAAAAAPWoHYlI4jSWuu9R tkqWwvL+jevVHd23bYbrenbo144+HHPOzNajdiRSHQAAAKAetSMRSZzGUvc9 yhbJ0o5w8PjaUXU07Ns2y/WdFfP2mOz4/fmZrUftSKQ6AAAAQD1qRyKSOI2l 7nuUrZGlHQfDWuno+OELwraZr/MxMTfH3BTzqJmsQ+1IpDoAAABAPWpHIpI4 jaXue5StkG3hgsPrlaNwcMfSHNZ5WszrY7Jj+K2hPxap3XWoHYlUBwAAAKhH 7UhEEqex1H2PsgWybV9Yv9PR0f1heWle635IzNGYW2Ke0fry1Y5EqgMAAADU o3YkIonTWOq+R1n0LIXl/euVo3B037Y5r/9lMbfHvCvm7FaXrXYkUh0AAACg HrUjEUmcxlL3PcqCZ2lHOLh2ubpwNOzbNu82ZPWirG6U1Y9e1uqy1Y5EqgMA AADUo3YkIonTWOq+R1nsLO04GNbvdHT4grAtSTvOC/3r1mXXr3tIa8tVOxKp DgAAAFCP2pGIJE5jqfseZZGzLVxweL1yFA7uWErUjjNi3hqTHc+vjzmtleWq HYlUBwAAAKhH7UhEEqex1H2PssDZti+s3+no+MGwYyllex4Vc1PMzTGPaWWZ akci1QEAAADqUTsSkcRpLHXfoyxqlsLy/vXKUTh+cEdYSt6mn4/Jjum3x5w1 9fLUjkSqAwAAANSjdiQiidNY6r5HWdAs7QgH1y5Xl/R6dfmcE/PhmNtjnj31 8tSORKoDAAAA1KN2JCKJ01jqvkdZzCztOBg2Skepr1eXz4tCv3b03pizp1qW 2pFIdQAAAIB61I5EJHEaS933KIuYpbBjY9BRR65Xt5a7xhyKyY7tC6daltqR SHUAAACAetSORCRxGkvd9yiLmEeHSzZudRSu392F69XlsxxzS8wnYx4y8XLU jkSqAwAAANSjdiQiidNY6r5HWcQMjzs6un+5Q+OOspwW81sx2fH9xsG/my9H 7UikOgAAAEA9akcikjiNpe57lMXM8P2ODoe9y10be/TwmJtCf/zREyZahtqR SHUAAACAetSORCRxGkvd9ygLmqXlsPdwVj06Hg5ftifs6lztKMuemOwYvzbm rMaPVzsSqQ4AAABQj9qRiCROY6n7HmVxs7S8K+zZsyssL6VvS3nOjnl/zO0x z2v8eLUjkeoAAAAA9agdiUjiNJa671FktnlO6NeOPhhzn0aPVTsSqQ4AAABQ j9qRiCROY6n7HkVmm+xadX8Ukx3rr270WLUjkeoAAAAA9agdiUjiNJa671Fk 9nlszL/F3BTz8NqPUzsSqQ4AAABQj9qRiCROY6n7HkVmn9Nifj0mO95/a/Dv 8Y9TOxKpDgAAAFCP2pGIJE5jqfseReaTh8R8POaWmKfUeozakUh1AAAAgHrU jkQkcRpL3fcoMr9cEJMd8++KuevY+dWORKoDAAAA1KN2JCKJ01jqvkeR+eXs mHfH3B7zorHzqx2JVAcAAACoR+1IRBKnsdR9jyLzzTNibo35cMwDK+dVOxKp DgAAAFCP2pGIJE5jqfseReabs2KuismO/ddVzqt2JFIdAAAAoB61IxFJnMZS 9z2KzD+PiblpkEeNnE/tSKQ6AAAAQD1qRyKSOI2l7nsUmX9Oi7kkJjv+3xr6 Y5E2z6d2JFIdAAAAoB61IxFJnMZS9z2KpMlDQv+eR7eE/j2QNs+jdiRSHQAA AKAetSMRSZzGUvc9iqTLj8fcHvOumLM3TVc7EqkOAAAAUI/akYgkTmOp+x5F 0uUeoV83yupHL9s0Xe1IpDoAAABAPWpHIpI4jaXuexRJm6eE/nXrjob+dew2 pqkdiVQHAAAAqEftSEQSp7HUfY8iaXNazO/GZK+F1w/+3Z+mdiRSHQAAAKAe tSMRSZzGUvc9iqTPuTE3xdwc85j1v6sdiVQHAAAAqEftSEQSp7HUfY8i3cir Y7LXw9tjzlr9m9qRSHUAAACAetSORCRxGkvd9yjSjdwn5sMxt8c8e/Vvakci 1QEAAADqUTsSkcRpLHXfo0h38oLQrx29N+bscPHOnwj/eOi94VU/9pKZrXNp eVfYs2dPzK6wvFT82yC7lsNS4XHbtu8ZnmfP9rAt+f6Tky0AAABAPWpHIpI4 jaXuexTpTrJr1V0bHtN7V7iwd+/w7m/8pvCfT3xKuP7rHx72xOlPiDmt1fUt hR0Hj/dfiMcPhh1L28L2PXvCZYePD79Ijx8Ol63Vj5aWw644zzVHi6/ko+Ga XP1JZB4BAAAA6lE7EpHEaSx136NIl/K83uPCtb0nhNt7p2YvjqG8K+YlMWe0 tr7zwpVrZaLrrwwX7LkmbCoJrTl+OFywvBx2XXY4HB81T5xycMdS8n0oJ08A AACAetSORCRxGkvd9yjSlTw25uO9U7IXxcjcHPPstta5tDusf/ofPTqoG2Xj hzauRZcfX3T08KBulI1Dys2TH6d0/Mrzku9HOXkCAAAA1KN2JCKJ01jqvkeR LiQbS3RtTKiR98fco4V1Lu04ODSG6Og1m+9btO2Cw5vnKdz/KL8ctSOZZwAA AIB61I5EJHEaS933KNKFPCTm9phQM09oYZ3nXZkbL3T4srB9W8l85125UTs6 ek35PI++ZP1ad9fvds06mV8AAACAetSORCRxGkvd9yjShTwnJjTIhVOvcyns 3rhgXdi/XF7zWVqf6Xg4fMG28mWt15eOhyvPKzx+edf6te3WsmvEukSaBgAA AKhH7UhEEqex1H2PIl3IC2JCg7x62nUu7QgH1wYUHd03dJ26jSyFHWszHT8Y diyVL2vbvqOl82zbPnwvpDXZGKfide9EJgkAAABQj9qRiCROY6n7HkW6kHNj QoM8Y9p15q5Fd3TfiPFEvfPCleulox0jaj258UvX796YZ9v2cM1qSel4OHxZ btzRZYP7Jx0/HPYafyRTBgAAAKhH7UhEEqex1H2PIl3IWTEfjAk18smY+0y5 vvy16IrXmVvPtn3j72OUG790/MrzBn9fCsv7j4Z+3WhXWM6PV1paDrsG9aPR 9SiRegEAAADqUTsSkcRpLHXfo0hX8ryYW2JCRW7vtXGvo14478rx16LbqC8d Dfu2jVhW7l5HB3es1ZfWxitdH3aXLXtpd1hd8tFLwqM7sN9lcQMAAADUo3Yk IonTWOq+R5GuJBt7tCfmaEwoSTbe6Ndjzp56XdvCvo0BRSOvRbdxr6Mrw3kj lrVtY0G5OtG2sH31GnXby++jtFY7GrlukXoBAAAA6lE7EpHEaSx136NIl5LV j54T88aYj5xz//C5r31YOPrV54Qr4r9f0Jv+WnWrWavdhPx15orZuNdRVX1p Y2jSvvI6Ucljlvdm16w7Gq7ZPuo+SyL1AgAAANSjdiQiidNY6r5HkS4mqxH9 8nOeHz79m28Nv7ryvHBOm8svvc5cIbn60tF9I2o8pfc6qs627ZeFw/ExR68Z MSZJpEEAAACAetSORCRxGkvd9yjS1bz4gj3hYyfC6n/bXG75deaGs7Tj4Hp9 6crzRixrvQaVDU0aUYNaz1JY3rUnXHM0qxvtCdtH3T9JpEEAAACAetSORCRx Gkvd9yjS1cymdpS7zlzFfYzO27hg3ej60sYF68K+qlrQ0nLYtScbb3Q8HL5M 3UjaCwAAAFCP2pGIJE5jqfseRbqaWdWOsvE/e/bE7FoecR+j7Npyg3n2jL62 3NLyrrHz9LZtD3suOxyOHz8cLtuzKyyPqEOJTBIAAACgHrUjEUmcxlL3PYp0 NbO6Zt28slpb6l+krrJOJTJpAAAAgHrUjkQkcRpL3fco0tUsdO1o2/Zw2eHj /brR9m3p2yNbMgAAAEA9akcikjiNpe57FOlqFrd2tC1sz8YbZbLa0Z495TEW SaYMAAAAUI/akYgkTmOp+x5FupqFrR1t2xeO1nnxH70kPDp1W2WhAwAAANSj diQiidNY6r5Hka5mcWtH20ePNTLuSFoMAAAAUI/akYgkTmOp+x5FupqFrR2J zCkAAABAPWpHIpI4jaXuexTpatSORKoDAAAA1KN2JCKJ01jqvkeRrkbtSKQ6 AAAAQD1qRyKSOI2l7nsU6WrUjkSqAwAAANSjdiQiidNY6r5Hka5G7UikOgAA AEA9akcikjiNpe57FOlq1I5EqgMAAADUo3YkIonTWOq+R5GuRu1IpDoAAABA PWpHIpI4jaXuexTpatSORKoDAAAA1KN2JCKJ01jqvkeRrkbtSKQ6AAAAQD1q RyKSOI2l7nsU6WrUjkSqAwAAANSjdiQiidNY6r5Hka5G7UikOgAAAEA9akci kjiNpe57FOlq1I5EqgMAAADUo3YkIonTWOq+R5GuRu1IpDoAAABAPWpHIpI4 jaXuexTpatSORKoDAAAA1KN2JCKJ01jqvkeRrkbtSKQ6AAAAQD1qRyKSOI2l 7nsU6WrUjkSqAwAAANSjdiQiidNY6r5Hka5G7UikOgAAAEA9akcikjiNpe57 FOlq1I5EqgMAAADUo3YkIonTWOq+R5GuRu1IpDoAAABAPWpHIpI4jaXuexTp atSORKoDAAAA1KN2JCKJ01jqvkeRrkbtSKQ6AAAAQD1qRyKSOI2l7nsU6WrU jkSqAwAAANSjdiQiidNY6r5Hka5G7UikOgAAAEA9akcikjiNpe57FOlq1I5E qgMAAADUo3YkIonTWOq+R5GuRu1IpDoAAABAPWpHIpI4jaXuexTpatSORKoD AAAA1KN2JCKJ01jqvkeRrkbtSKQ6AAAAQD1qRyKSOI2l7nsU6WrUjkSqAwAA ANSjdiQiidNY6r5Hka5G7UikOgAAAEA9akcikjiNpe57FOlq1I5EqgMAAADU o3YkIonTWOq+R5GuRu1IpDoAAABAPWpHIpI4jaXuexTpatSORKoDAAAA1KN2 JCKJ01jqvkeRrkbtSKQ6AAAAQD1qRyKSOI2l7nsU6WrUjkSqAwAAANSjdiQi idNY6r5Hka5G7UikOgAAAEA9akcikjiNpe57FOlq1I5EqgMAAADUo3YkIonT WOq+R5GuZja1o6WwvGt72NaB7ROZNgAAAEA9akcikjiNpe57FOlqZlI7WtoR Dh4/Gq7ZtRyWSufJakt7wp49e8Ku5aXk+0CkKgAAAEA9akcikjiNpe57FOlq ZlE7WtpxMBzPXnjHD4e9pbWh88KVx/uvzaOXPDr5PhCpCgAAAFCP2pGIJE5j qfseRbqamdSOlneFa472X3vHD+4ojD3KxhxdE/qTj4eDO4w7km4HAAAAqEft SEQSp7HUfY8iXc1s7nfUC9v2rRePwo6ltb9ndaPLwuHBmKPjh/eG5aX21iky iwAAAAD1qB2JSOI0lrrvUaSrmVXtqLdt3/rYoivPi/9eWg679mzUjcLRa9zr SBYiAAAAQD1qRyKSOI2l7nsU6WpmVjvK39Pomj1hz2WHw1rZ6Pjhy8Ke7duS b7tInQAAAAD1qB2JSOI0lrrvUaSrmV3taCnsOHi88Eo8Hg5ftsd4I1moAAAA APWoHYlI4jSWuu9RpKuZVe1oaXlXuOxwrnZ09JqwZ88u9zeShQsAAABQj9qR iCROY6n7HkW6lPt89TnhtNNOW/3/xdpR9vds+uTLXwrLu/YM142i41eel3y7 RSYJAAAAUI/akYgkTmOp+x5FupRnPfcF4cdffmF4/PJTwsWv/ZXV2tGFP7cv POoxjw0veukFYfvzXzThsreF7XsuC4c3bmwUrhn84/jBHWGpA9su0jQAAABA PWpHIpI4jaXuexTpUrLa0Yc/fWu4+s/fGw7+5QdWa0fX/O/3hTe9/c/Dh/7x lvDcH/3xCZab1Y2uCUcHr7njhy8Le3Yth207DobV6tHxg2GH69XJAgYAAACo R+1IRBKnsdR9jyJdyjn3f2A4evz21ZpRMdnfH/CghzRc5nDd6Og1e8Ku5aX+ tKUd4WC/eBQO7lhKvu0iTQMAAADUo3YkIonTWOq+R5EuJbun0bXv/XBp7ejQ +4+u3wupXvJ1o+Ph8GV7wvZt+elLYcfBwXXrDl8QtnVg+0WaBAAAAKhH7UhE Eqex1H2PIl3Lq/a+vrR2tPcNVzRazrbt+brRrrBccl26pbXr1sU59y8beySL FQAAAKAetSMRSZzGUvc9inQt3/Pk80prR+c96zkNlrMt7BtcqO744b2ldaPV LC2H/evzXbZxPTuRBQgAAABQj9qRiCROY6n7HkW6lnve6+xw5MZ/G6obffjT t4avvPd9GiznvHBlf0BRuH53dT1oY3xSCEcveXTy7RepGwAAAKAetSMRSZzG Uvc9inQxb3r7oaHa0Tve9f6Gy+jfy+joNcV7HJVl7b5Ix8PBHcYdyeIEAAAA qEftSEQSp7HUfY8iXcyLL9gzVDt65WsuabyMpeVdNepGa8nqR+X3RBLpagAA AIB61I5EJHEaS933KNLFPOKRjxqqHT1++SnJ2yTStQAAAAD1qB2JSOI0lrrv UaSLOf2MM8L1H71ptW6U3fvobne/R/I2iXQtAAAAQD1qRyKSOI2l7nsU6Wp+ 7Td/b7V2lN37KHVbRLoYAAAAoB61IxFJnMZS9z2KdDXPeu4LVmtH2b2PUrdF pIsBAAAA6lE7EpHEaSx136NIV3PO/R8Yjh6/PZz7rY9J3haRLgYAAACoR+1I RBKnsdR9jyJdzWmnnRbe9I5D4cyzzkreFpEuBgAAAKhH7UhEEqex1H2PIl3O 45efkrwNIl0NAAAAUI/akYgkTmOp+x5FupzTzzgjeRtEuhoAAACgHrUjEUmc xlL3PYqIyGIGAAAAqEftSEQSp7HUfY8iIrKYAQAAAOpROxKRxGksdd+jiIgs ZgAAAIB61I5EJHEaS933KCIiixkAAACgHrUjEUmcxlL3PYqIyGIGAAAAqEft SEQSp7HUfY8iIrKYAQAAAOpROxKRxGksdd+jiIgsZgAAAIB61I5EJHEaS933 KCIiixkAAACgHrUjEUmcxlL3PYqIyGIGAAAAqEftSEQSp7HUfY8iIrKYAQAA AOpROxKRxGksdd+jiIgsZgAAAIB61I5EJHEaS933KCIiixkAAACgHrUjEUmc xlL3PYqIyGIGAAAAqEftSEQSp7HUfY8iIrKYAQAAAOpROxKRxGksdd+jiIgs ZgAAAIB61I5EJHEaS933KCIiixkAAACgHrUjEUmcxvbs2SMiItI4AAAAQD1q RyKSOAAAAAAAdIjakYgkDgAAAAAAHaJ2JCKJAwAAAABAh6gdiUjiAAAAAADQ IWpHIpI4AAAAAAB0iNqRiCQOAAAAAAAdonYkIokDAAAAAECHqB2JSOIAAAAA ANAhakcikjgAAAAAAHSI2pGIJA4AAAAAAB2idiQiiQMAAAAAQIeoHYlI4gAA AAAA0CFqRyKSOAAAAAAAdIjakYgkDgAAAAAAHaJ2JCKJAwAAAABAh6gdiUji AAAAAADQIWpHIpI4AAAAAAB0iNqRiCQOAAAAAAAdonYkIokDAAAAAECHqB2J SOIAAAAAANAhakcikjgAAAAAAHSI2pGIJA4AAAAAAB2idiQiiQMAAAAAQIeo HYlI4gAAAAAA0CFqRyKSOAAAAAAAdIjakYgkDgAAAAAAHaJ2JCKJAwAAAABA h6gdiUjiAAAAAADQIWpHIpI4AAAAAAB0iNqRiCQOAAAAAAAdonYkIokDAAAA AECHqB2JSOIAAAAAANAhakciMs9EZ8XcM/c3AAAAAAA6RO1IROaV6GtjPhnz 7zF3G/wdAAAAAIAOUTsSkXklujYm+z+3xtx98HcAAAAAADpE7UhE5pHoEYO6 UZafzk0DAAAAAKBD1I5EZB6J/nRQN/q7mFNz0wAAAAAA6BC1IxGZdaJ7x3wx 5raYbyxMBwAAAACgQ9SORGTWiZ45GHP0ypLpAAAAAAB0iNqRiMw60fNjro25 Y8l0AAAAAAA6pOu1o+hLYr4s5i4x22IeF/PEmOWY74n5jphzB9fEOrXt9c87 0Smp2zCP7YjOjPmBmIe0vN77DI6Ts1PvgxHte3zMV8xo2afHPCbmp2IuiPn+ mDs1eHz2Gjujwfx3innwYH9/TfZaLbQl+9tXZs/F4Hl5yOA1m+XRMY8Y1JIA AAAAAOiQLteOslpQzLHBta6+OPhvVf4l5pqYK2J+blBn+pI221TSxlNivi3m pYN1vrhJDWuwjf895kDMp2Juj3lXzENn2e4Z7IeHxrw25gMxt8T835iXVWzz uwfP2edjHtVSG7I64hdyx8MnYvZldYvU+2fQvtcO2nU8q6m0uNwHxLwt5taS 18R/DGpJI18H0ZfHfDD3mH+N+euYP4y5IWZnzBti7jCYP6tPHR4cq/l13TZ4 Dk6LOVTj9ZrlugAAAAAAQKd0uXYU+v3Ul9Xsgx6Vf4q5d9vtyrXvf5Ss86kN Hn/WoM5SXMaFs2rzjPbDq0u24d9GzPuthfl2t9SGbCxaWY3xMzHnJN4/Zw9q K2tt+vUWlpmN7bmoUDP6h5jfifk/MZ/L/T2rR545Yjk/UuN1lNXkzhjM/zMV 8/3wYJ6/rvn6fG0AAAAAAKBTFqB2dIeY+8a8bETf82/HfHXMN8c8LeZ5MS+M eXNunmyMS9l9Vtpo3/tL2vT6hsu4X8yRwjJeMYv2ziq9/virCwvb8C8j5n1A Yb7vb7EdWf3ojwt1kyxPTrx/dhbak43ZmXhsWa9/zb+/yC3v09m2F+Z5WMz7 cvNcOWJZ3x5z04jXV7Yffz1me27+bFzR/sJ82Riv18TcYzBPdq3J74r51RHL vT7m0YNlAgAAAADQIV2vHYWN/ursOmd/X+h//lBvcB2tEY/5cG7evTNq14N6 /XvL5GsV/3uC5TyysG07ZrUvZ5ls23Pb8Hcj5snqgW8bzHNkFnW9Xv/eOvn9 +b2J98tVJfWTN024rDNi/iy3nKMxSyPmvVtv47qPWV4yYr6sHvRTJW18VkU7 rszN96MV8/1aYZnZOLAvzc0DAAAAAECHLErtKPT7oIvXh3vdmPn/W27e7Fpm j51h296WW9cnJlxGvo8/aa1jiv2wK7cN11bM96W9/n2e7jWjdtyxcKx8R+L9 8qmSusyJCZaTje96R24Z/57VycY85gW5+bNrz428pmKvfy+mtXmza+yNvHdX 9E25eZ9YMV+xJvUXhXkAAAAAAOiQBasdvbzQB/3cGo/5w9z8f5ONr5hR216c W8/nY75kgmXk2/oNs9yXM3yOnpDbhv2J2/KZXFu2JWzHl5XUjdZy94bLelbh 8a+p8ZivKjzmlpgHjpg3X+P6YtVxHN0zN++3VMz3gsL631mYBwAAAACADlmw 2tEPFPqgR15PK/eYZxYe8+Nj5v/6mIti/iTmDwZjJp42ruYUfUdhPQ8aLOs1 g2X9Tsx9xyzj13OPf0CNbcvG7mT39/n/Yl4S830xXzGD/X6XmKfG/EzMG2O+ q2Ler8ltwxtKpp89qDl8XcxTejXv+ZPVWGKeEfNzMb9RVavIPeZfc215aGHa XXv9+0x95bjntoX9V6yd5PPwBsvJxlJ9rPD4yjFHuccW78t1xYj5bi3M91UV yzwzf7xXzPe0wjLfVZgHAAAAAIAOWbDa0ZMKfdCvqPGYcwqP+aeYM0rmy64F lo1r+lyvvI//z7N6Q8V6zi3M/4GYfxzUjn588LcTMa/LajEjlvGa3OO/rmJd 2f1usuv33VbSzqxesr2l/f30mDeX1BOyPH3EY+6Rm+fywrSs9vHvheX8R8zp I5aV3eNqe69fwys+L9mYmG8f0/5/zs1/38Hfsvv6HC4sKxsnlo1Jq7wG4oT7 MKuv3DTYh9nz+1+FdZ/XYFkvLjz29l7FNeUKj31L4bGf7RXGFPX690YqPs/n VizzS3LzfU3FfMW66g2FeQAAAAAA6JAFqx09sdAH/ds1HnNGSX/4zpL59uWm Z9f0enLMQ3v9cTZrf39PzJ1GrOdHCuv43Xy/fvSzuWmvHbGMC3LzfHPFNu3P zbe31x/rs7M3XOMZeU+bmvv62bllZct9d8yHcn/L6iFnljwuX094c8n07Jp2 xTrQvUe04SWF5+QvY47m/vZ3VbWT6BO5ec8Z/C2rX/1NyTGR3QfoN2ZwzP7Y YPm/MPj37sJ6L26wrPcWHntjg8f+dsk2f0Nhnq8pmecZFcu8Q26+keOnoocV lvl3hXkAAAAAAOiQBasdfXehD/rPaz6uOD7nLYXp+evaZTWE5cL0vbnpfzai ZrK3sI5HFabnx+P8zYh2viw3z+NGzJMf35TVsk7JTcvXnt6X9e1PuJ9P721c G+0jMXfLTXt7bh2bxjf1+uO31qa/fcTyX1rYV5uugdfrX1PuXwbTr+8NanaD 5b8n99gnVGxHvs704Nzfs+vm3TT4e3ZsZGPBSu//08Ix+8HBeh4QyusoR/PP YcVyzur1x1rlH/vBBu24ovDYLN9WcWyt5aUVyzwtN99jKua7f2GZ7y7MAwAA AABAhyxY7ag47ugvaj6ueJ209+Sm3Snm07lpryx5fHYtry/k5tlXMs+rCus4 q2Se/DXUlkqm58fZPHnEtrx5VO2m17//Ub6+sGPC/Zy/79KLCtPy47DeMuLx a234sxHTs5rDf+SWs6tknrflpj+tMO2a3LRfrdiOD+bme3Rh2h/3+nWjR416 fAvH67cN1n1z4e+3FI6V766xrAeV1HWa1I7eWPL44rijx5bMs7timXfMzfc9 FfOdXVjmbxXmAQAAAACgQxasdvQDhT7oP675uH8pPO7Pc9N+Mvf3rMY06t47 78/N98mS6T+Um37ziGUcyM3zgpLp+fE4m64VFi31+vfmWZvnYYXpWR0sfz+d 359gHz+usK++sjA9P+bnT0YsY612VBxfkp8nPybo+wrT8tfLy+o7X1qYfmNu +pUV6/g/ufl+JPf3B/b69/sZOaampeP1Nwbr/o3c3x7R69+nqKqWUras4tid LB9q0JZi7eh4rzAurde/nmBxHZtqqYXjbW2+p1TM92WFZf58YR4AAAAAADpk wWpHzy/0Qf9izcfdXHjcz+Wm/UXu7++tWMYfFJZx58L0x+em/f2IZbw4N8/v lUx/eW76c0umF8c2vXDw92wcz7fGvKkw/doJ9vH/yj3+0yXTb8hNv6Bkev4e ODdUrCd/757iNQL/MDftAyWPzY8T++GKdfxlbr63D/6WXTvwSMyJXsm1B1s8 VrMxYGvj3bLr42XXNPyVmH8rqc9kbbnjmOVl+/U/C4+7qUF7irWjt5bM8z0l bfupimXmr8P4tIr57lJY5osL80zuxJFw4NJLw6WNcigcm2qli+5EOHJgbV8c CEdOpG4PMDfHDm28Fx46ud8JN7T0nniy7tutuN2d2aaOfl7n98/QuVVH21vi 2KGNtm+Vw3aIY3hyndl33bTlXzvAjHT082ALnNPAPCxY7eglhT7oC2s+7l8L j3tybtr1ub+/s2IZBwrLeExh+nfkpr1/xDK+MTdP1qbiuI+fzk1/Ucnj/76k b/8fYj5T8vcs/2OCffzO3OM3XRMt+s6YP+r161inlkzP3wPnaMV6rh1V/4k+ lJu2qf4V/beYP435yQbbkuX3extjlg7P+FhdGfGcjMrIa77llnm48JjsOoqn 1WxP8X5cm65n2Csfd1R1v6Ovzs23aZxcbr4vLyzzOYV5Jnfj/rD93HPDuY2y Enaf1N95bgz7t6/ti+1h/42p20Nbsu/zB5zYUuW6izfeCy++LnVrOqKl98ST dd9uxe3uzDZ17/N6td9498rmc6vlS8INHWzvKNddvNH2rXLYDnEMT64z+66b tvxrBxbE4n3v697nwVY5p4F5WLDa0asLfdC/VOMxp/SGr/OW3XPo9Nz0/H11 DlYs508K6/7BwvRvzU0bVTs6tTd836Ti/WZ256a9rOTxN5X07WdjVrI61LFe f2zJG2LeGnMo5pET7OP8+KqPTfD4M3KP/6eK+Q7m5nt8YVr+ungjr3tXoy35 dRTzyd6YsT5THqt/mltXdvx9qtcf43Z5zDtibi20Z+R9m3LLfG7JdtyvZnvy 1yLMrle3acxVdG7J8kfWZ6Ovy8337RXz3b2wzCcV5pncRLWjjazsXrRzrjY4 D9pyBr+X2r1ybtjuCaWKPrESakdT2Yrb3Zlt6tjndfysyT5nSs+pzr86nOha eyts+f5vx/DkOrPvumnLv3ag6xb2e1/HPg+20DkNzMOC1Y5+o9AH/Zs1HvNV hce8sjD9V3LT3lSxnL8oLOdxhen5MUWbrrOWm++fR/W3D+oKa9N+tuSxry20 4Y9msI/z173LxjOd0vDx+XrCrRXz5Wt2Dy5MO5Sb1rh+lVtOvt73D73hGmJp fa6lfZjdl2qtRvg3vcI9owbzZPdcOpFry401lpvVHo8WtuGZNduUH1P06hHz PLCkdvS6imXmr3F3n4r5vqawzCcW5plcvna0vDPsHXu9ur1h5/LwucHyzr0n 2fgj50FbzYmrz18/nhfrOwRzp0+shNrRVLbidndmm7r1eZ3/rMmP4d64tle3 2ltly/d/O4Yn15l9101b/rUDHbe43/u69Xkw/pzGNesgb8FqR9cU+qDfUeMx P5Gb/79i7lGYnr8O3t6K5fzv3Hyfi/nywvQH5aZ/vGI5a/WC/4j5ksK0/DXW Nl1vLvrewvZ/d8V6To+59wT7+MWFdXzjiPm+dtDeRxb+/qTC4+804vFX5eZ5 WmHazxWWcfaIZTy61x/f8+AR09+VW8YjYu4bc2nub7dlf5/BcZofH/edFfMV r4P4zTWWXTwGfik37Ttj9vT6488ujPmW3LS1e2llr4F7jVj2nXrD4+Ky/FlF W35kMM9ne4XrLxbme3xhmU8tzDO5fO1o+/4w/hRkcA6wd2dYHhp/dDKdD3Tr vI3p3bh/+4J+h2Du9ImVUDuaylbc7s5sU7c+r2+4ZDn3u5urSu4d2a32Vtny /d+O4cl1Zt9105Z/7UDHLe73vm59How/pwHyFqx29KFCH3Tl9cx6/fus5Md2 vLxknm/JTT9UsayP5Oa7smT6A/I1iRHLuG9unreVTP+93PSy+/xk2/PFcXWJ Xv86fe+OuXmCfXyPQS1g5NicwfLfO5j+msK0RxWeo28Y8fibc/O8qjD9QYVl /GDJMu7Y648lyv7x4hHb8je5Zdwr9/f/N/f3j4+qpUx4jJ7ZG76/1pdUzPur he2sdX+qbL7cY/4l5sExR3r9+2G9KOZhvf49qbLpWR3pLrl//8KYZRfHNWW1 pi8dMe//HMzzu2OW+YLCMn+8MM/kGteOBk4cCQeG6kfLYedVx6ZqyuLo1nkb 01vc7xDMnT6xEmpHU9mK292ZberW53W+z/j8q8t+cNOt9lbZ8v3fjuHJdWbf ddOWf+1Axy3u975ufR6MP6cB8haldtTrX6/rtkIf9EfHPCZ/PbrsmnOlYyN6 G9ejuz3mniXTH5Cr2WTzfP2IefJt2zReJ3p6bvp/L5mev15caX989L7cPCsj 5vnvg+kTXdMuVxPIkt1j6c6F6T+Um75cmFa8Z86msU+9fn0qVG1rb3hc0t8V azDRT+WmP7zk8ecU1vFVhelvzk27vjdifNQE++5nC+t9aMW8V5bUaUZe+y33 uGx80N8WHrevl7t/U/T9hWVnyca63X3Msn+n5HFlY+C+q7dRl/2mMcu8trC8 PyjMM7lJa0eZE0fC5Ts3fm9y7soVJ8nvTbp13sb0Fvc7BHOnT6yE2tFUtuJ2 d2abuvV5Pb7PuFvtrbLl+78dw5PrzL7rpi3/2oGOW9zvfd36PPBeBs0sUO3o eSV92tn1tb5uxPw/Wqh/PKBi2dlYmf8czPuGkumX5JY16l4xX1to2/8smee3 BtM+GnNqYVpW6/hMoZ//K0qW8czcPGVjl7Ia1qd7/Xv7VPbpV+yPbExP/hp9 f9Dr3zfqzjHfF/Nvg79/IL8dvf54ov2F/XBhyfK/rzBPdg+ouxTmuctg+Wvz /GbM3WLuGrN9UC/J/v7OkuVndcY3Fdbx0MI8312Y/oe9ijFCNfZZtn+ya+19 sbd5256Vm+9evf619rbn9mM+2bifXxwku+7c0oj1fX3MrbnHHerl6mO94ftv reWNNbbjkSWPW63vxazEPK3Xvy/X2r2j/qRiWdn9k15ask+y121WRz0zpKwd hax8tC+s5K5ze8XY4lH+ure5HDgS6v9a5Vg4NOJ+TNX3Xco/7tB6nevEkQOb lnOg8gJ8Tc7b2tje7FaUxWXkrhE4uN/nxrWFKxc0+l5WY9q03oa1+bKxZ6Pa 1Fia42Jtm/buzI+531vjOGjnea21VVM8902es/x6xt6/rHK9bb3Oikbs89w6 2lK5zxv1ic3vOBl1/Leyj8e2t/57Ymv7dor3stxCJvwsaa5bx1Q7292tbRql wed1K8dUidz7bv6e0iu7y5Y///OLSd87yvuMytvU6PU0q+ehdFWO4Ul1Yd9N fl7qtTMfMzwvGXvuV34uWraPSvdx3flabXMd892u9r4bFHX/e9/E7y8zfR12 4POg0TlN/fsdtfJ9t4XjtJvPO1tF12tHg77q95b0P+frQntiXhHzzb3+fW3y Y1JuGNX/XljPE3sb45qyPvtvinlqzCt7G/eAycYn3XHE47+n0K5sfNK9wkYt 5oLctB8qPPbbY/5vybZtup9Tr1+fedtgerZPdvf697nJ7jP02lw94uen3O9Z neZPcm25NVcvWBvr8q25+bOxMG8p2Ybs3lBfn5uvWBOqqoMtxfxVbp7/LBwH 2bXhijWhs3vDda+1PK8w3zeXzJPVm0bet2fEfrp3r39duM+WLC+fbBzVnUds e1V+rWLdT+8Nj8XLrl/3A2GjtlRc1vfV3KbsHmH/XqNt/9QbMU6q13/9VD02 O5b+JSSuHYVwQ7hkOXfeUFE86n8W7w07c/OvZ3ln2Dv2XHPt/GN3rl41nLXz lvLFXBcuXp/34nDdoE3588fh88hR5/j1ztum396wfh6SPzdbv0bg3sE5bp3v 6GvnM7tXSvdbnTatf9fNjpNN1yyc/PdPKY+L/Pf3spT9Fq2V57Xejpn6uW/y nDX67Vjlett6neV3RcU+X7s3a0f2ea02t3mcjDn+W9nHY9tb4z2xQ+9l03+W NNCpY6ql7e7UNo1T/9ic7piqakLuPGtU1s+/5nh+MeV7x6bPjNX9WN6m/nE1 5n1o1s9DybocwxPo0L6b5LzUa6eN845x5nBeMvbcr/xctGwfZft4o2YwaPuI +er9zm6W56vz3a72vhtsWJTvfY3fX+byOuzA50Hb5zRtft9t4Tjt5vPOVrEA taP/1hu+f8yoZPWdrI6U1Zmy625d1OuP0Tmrwbq+otevQd1UsvysBnW3isdm dY63xmyL+cle/95MWbuz+w6t1XOycUV7Yk4rPPa3e8N1mbV8eMS6svrRBYN1 lD0uq/lMPIamsK4fiPlkbtnZtmTjsB5UmO+xI56n2/M1i8H2lz1/f1yxrT/S G74/UlZne03MV5fM/10jlv/ZwXFx95iX9crH/GTXrhtbZyys71BhGVlNLaup /O3guc/GbGX3J7q41x/rlF2n7v0xx2N+P+bFvX79Lxuv9VeDv//t4Hh7V8z9 xqz/cb3+OLbi8391yfY9s8F2fVnMSwbtKNuf2f2/vrbi8dl1CbPxSdcN9sPe wXOfbWc2himr0/1wSF47OhGuuyjXJ3z+1SXnnv1zvM3nBCVZ2T3iczVbxqhz 8bJzxrLfhAyfb1995MCYNmXn+GXfbcadB7WxvaH/O5eq85Bz+9+/Dl0x5lw9 O6cZs5xim8qatHEudUm46vLieVT2uH0Nxx2lPy6a1Y5ael5r7Zp2nvsmz9ms akeTv85Wd0SzfT7t7+jaeL3N8zipffy3uI9L2zvmPbFT72VtfJbU1KljqqXt 7tQ21THm2Gzp87G6CW32s7S136Z/7xj6zLiizn6Myxr1Hj2P52F90x3DW2Xf NTsv9dqZ+vmvJcF5Sem+aXYuurzz8tVj5dihMW1f3hkuL/9wnNP56ny3q93a UfpzmclqRzXeX+b2OuzA50Gb5zRtf99t4Tjt5vPOVtH12lHY6IvOxndk43Me P+iDz/ItMQ+N+cpeoR4z5bqya21l15f76V7/2l8P7o0YbzRmOd8wWE52PbRs /NKma9Dl5r3jYL2PGmxjNm5kbP0nOiPm22J+flDH+Nk298VgHV8a88JBDafy vkC9fv3t4YOaRrYt9ypMz6459/xevyb1NYN9lD2vXz5muXcZ1FlWxj0Xvf79 nrIa3p0Hx0Z2Hb/sWnGnDKafHvMdvf712bJ9fk7MfdemN9w3pw+Oj/v1Nq7B Nvf0+tfM2zbYrmw/5et9a/mNCZedPU8vivnBXn+s0/N6hWsMTpnJTV07Gr5m cNkyThy5fPgcLzsfLIzlHRqTUPa5euyqoWUMjYtey9DvQpbDzquKC8mfb6+E nWvrLLRn+Jw2frfZ1Jjq86BWtjc7Ny6crwxv88Z588pK7pxl0zlQXM6+leHt KRtLXfhNTdn4sfVzqeWVsJKte+03NLWvTzCD/TTlcdHk2gXtPK+19kxLz32z 52w2taNpXmcl+7zY/uLvFkd+p592n2+0d9w+n99xUmNdu4df+/tK9k077a16 T2xr37b0XtbKZ0mtZ6dbx1Qr292xbaplzLHZ0udjpRavWdfWfmvjvSP/mbH+ fG96jy78Lnz5onDdpkXN6XlYW5djeMvsuybnOF470z7/9czkvGSic7+yc9H+ OIbyfdyf1j+GC/MV9t/yRddtqvvM73x1vtvVZp98F85lmnzvq//+Ms/XYQc+ D1o7p5nB990WjtNuPu9sFYtSOxKR+un1x8HdVlI/+l+9MWOZEmRyLdSOTlx9 fu5c+JJww9DUY+Gq9fOzwTlraR/xgaHP1pV9w7/Hyq9j9fcnmxfRP5fJfz5v GgOVP9/OnaMUFrZp7P+m8TRV50HtbO/wuXF/OcOLGfHbreI50InrwkVry1k9 9xnxG7+x+674W62K30DW0qXjos49U1t6Xuto67kPzZ6z2dSOpnmd5ff54Lvd pvb398Xwd8Crml9Pfuw+H3FNkE3bPsfjpDDmc3X/bG70UJs375u22lvxntjW vm3pvayt94yxOnZMtbLdHdumeiqOzRY/H+sa/z47h/OLVt47Nv9+u/w9Orsf xXA/5kXFDvB5Pg+O4S217+qf43jttPUeVq3t85Jpzv2K56JZv25xPG3cx5vG DJTMVxwbUfldd8bnq3Pdrja/G3ToXCbU+d7X4P1lrq/DjnweDEx1TjOj77ut 1Y469byzVagdiWzN9PrXxBt1jcdPjBtDNsdMroXa0dBn8ODay+uOXbH+vWdt 3PxI8bN138rGZ3D+J8/5c7zlS4pntsPLOLDpNy/rDR0+3676DWjhfGb4+1rV eVA723vsivz3qtHLOXao8LvETf2tVfuj2J6rw/kVx8LQudTKFRN838k3vEvH RY3vEC21t47WnvvQ7DmbWe1o0tdZbp+P+33m8G8ZV0LTn3TV3edZn8fQd5ji ts/xOBn6zjLit7v9NuX38fnh6vxsrbV39Htia/u2pfeytt4zxunaMdXGdndt m+qp6mdp7/Oxrun6WVrab228dxS2pfo9utCvWjz+5vg8OIa31r6rfY7jtdPa e1ills9Lpjv3Gz4XHVmnya+v9nyzanMdc9yu0OJ3gw6dyxSXU6t2VPX+MtfX YTc+D9ZMc04zq++7rdaOOvO8s1WoHYlszQyuB1h2X6csH0jdvlwmN+PaUf68 4PziCWmJUfMPjW1aG+PeuD9v+Hy7eszw8Djk4fPTeudBk2/viXD1+WvLL/md 4fAShr5XVt2btLIdhwrXOBhTO6o8X6+zvk4dF+O/Q7TV3vHafe6bPGezqh1N +job+m1hyXU0isvJ/9a12fUAmuzz4ee2uO3zO06iGy7Z+A3bSlVdcO2ewlmG f3PaXntHvSe2t2/rGvde1tZ7RrXuHVPTb3f3tqmeGvdpHrf+Gp+PdbXVzzLV fmvhvaO4LePeo4eOvxmep1RzDG+1fVf3HMdrp733sEot7J/2zv2Gz0VHP+/5 +aqO7fx8w6/D+Z2vzne7Vqe29N2gO+cyfU1rR9N+78208zrswufBhsnPaWb3 fbfN2lF3nne2CrUjka2bwb2e3perGX0m5s0xD0rdtlwmN9Nr1uXPC0Zck7iY 3SPqNYXrG/fX1fR+O8PXiB57up7/DjQ0vrjOedA023tDuKTi94qV+3/MCdPq tQBK2rFpPPiY2lHzvo+hVnTsuBj3HaLF9o7V7nPf5Dmb1f2OJn2d3XDJcqPj bfL+lWb7fKi9Q+uZ53FS6KuY6LtNm+0d9Z7Y1r4taf2k72UtvWeM2ZDuHVNT b3cHt6mW+v0s03w+1tVOP8t0+236947N2zKq7y0381zOU6o5hrfavqt3juO1 0+Z7WOX6W9g/7Z37DddORjenunaSa1nuNTA83/zOV+e7XatLaeW7QZfOZfqa 1o6afO+d7euwC58HGyY/p5nd9902a0fded7ZKtSORLZ2otNjvim7z1HMKanb U5LJtVA7yp8zj66xTJDCeeeRA4Uxy8Xk7rl5oHTgc/48unBtvUb7ZtR5UEvb mx/XXHLt6c2bNf57Zdm9QSszpnY04U8f291Pq9o4LsZ9h2izvWO0/Nw3ec5m Uzua9HU2/Hu0Wl0QI2u9YzTd5/n5h7Z9jsdJaN5XsVmb7R3xntjavt0w/XtZ O+8ZtbejM8fUlNvdyW2qY3w/Sxufj3VN3s/S3n6b/r1j87aMXc6czlMqOYa3 3L6rd97itdPme1iV6fdPm+d+dWsn+fmq+rDrjZ+Y6fnqXLdrsJRWvht06Fxm rUUNa0d13rbn8zrswOdBzsTnNAm/77a6rNCd918Wg9pR7f73J8f8UOp2iGzB TG7q2tHwb4lG/xZ92nPFTHbf2EuH7qE5KqX3Z12U2lHT52TMOVB2TrPpNy9D GdyztME167pTO1rdwimPiw7Vjlp+7he3djTBNRkmfS9r/Ljc9iXsT5z+9TiH 2lFr+7avrfeyNt4zqndtV4+pKba7s9s0TvV7SXvHVD1dqB219VneZl/NXJ4H x/CW23fzrh2dtK+dWWxXqTbP/erWTuqes9Z5b57x+epct2uwlM7VjjKz/t7X fNvn9zrswOdBzsTnNAm/77a5rC69/7IY1I7GJ9oV8/mYy1O3RWQLZnLT1o6G 7otadQ+Mtc/OBhnVX5e/N+GlezePXV/Lyu4wvIh51o6m2N42f4tTvGdxcVz/ atauNZ7bP3OrHXXhuGhSO2qxvaXbYNxRf+8v+rijGR8noe1xR9O2dw7jjlp8 L9tY3+TvGbW3o4vH1CTb3fVtGqmin2UWx9QY7dSOpttvsxg7MdVnxryeB8fw ltt3zWtHXjuz7Lvs7rijqnPRaWssKccdzXK7BktpvXa0CN/7Gm77XF+HHfg8 yDmpxx117P2XxaB2NDrRqTG/FvPFmItSt0dki2ZyU9aOjl2V/81P8d4mE5xP N5a/3+qlm36DNPq+qTWurXvdRVPc72ia7W3vGsD5e42u/vaq6n6i+fO4mdaO unZcNLnf0azauybd9Z+bXEOler3tvM4W+35Hsz5Oho/ZsfcViN9vNn8Hb7O9 s7/fUZvvZSMe1Og9Y8yGLNAxVXe7F2mb8kb3s8z+mNqsrftKT7Pfpn/vqLst QzPP5TylmmN4q+27eseg186qlt7DqrSxf2Zzv6PZ1ljS3e9ovrWjyb8bdOlc pq/N2tF8X4dd+DzY0MX7HU33HbarzztbhdpReaK7xPxRzK0xz07dHpEtnMlN Uzs6cSTsy/3eYnnnVeFYYZb8+fTKvorP1OoV5c4H136/MbpNB3L316y6b+pF 11UuKFx3Ua7tQ+ec9b4/TLO9+XPsJu2sOlevXk6hD7/kN0Dt1Y66dlyM/w7R TnvraOu572vynOW3sfrezePW287rbOieyyXvLXWXM16z10n+u0Jx2+d3nBRe rytXVO6foe83uS/t7bW3Xn/35Pu2rfey9t4zqnXtmGpju7u2TXW1c2yO+3ys a/J+lvb2WxvvHfW2ZWjmuZynVHMMb7V9V/cY9Npp7z2s9jom3D/tnfvNr8Yy v/PV+W5Xpq3vBt05l+lrr3Y079dhFz4PNrT1e5hpv++29x22q887W4Xa0eZE 58R8KObTMd+auj0iWzyTm7R2lJ2T7R0ec7Sv5CRu+LNyZ7h8zH3H1+43mGXj /pbDn887rzpW3bT8OfzQ97X8eXR2fn/5yPPOE0cuz419L46nqvj+0Mr2Fn/L UredU3yvPHaocI/Hzd8z2qwddeu4GP8doq3ntY52nvu+Js/Z0O9FK777jl9v S6+zY1fk7oW7EnZXXOen+vU6Xt19vun6BIVtn+dxMny90PL33/58+Rr/8PtA e+2t+zvISfdtW+9l7b1njNOtY6qd7e7WNtXVQr9Fjc/HuqapHbW231p476i3 LUMzz+U8ZRzH8Nbad3WPQa+d9t7DKrWxf1o795tjjWWO56vzrh219d2gS+cy xe2aW+2olddhNz4P1kxzTtPm9932vsN29Xlnq1A7Gk70qEHNKKsdnZO6PSIn QSbXuHZUfn/Kld2Hyj+nN41NGjWmt7/cje+bw985hq6Nt7J75Ljg7Fxz4/O5 +Fk+3Ke9ds3l4in+8DLKzkEqzrNb2t64wblzm3rtLDsHyv8OJ2vL5q8zg99w 5X+bNeK8ps3aUbeOi8I550XXbV5GW89rHS0995kmz9nQ97rsu++lxdd0/1gZ v962XmfHwlX5dZU+v5vbNP43nyVK9nmxj+rEkQObXyfFbZ/ncZJt+77C9RKK O7lY41/ZN/zdrLX2VvWptLNv23ova+s9Y6yOHVOtbHfHtqmeeuN4pv18rGua fpb29lsL7x21tmVo5rmcp4zlGN5S+672Mei109p7WLU29k9b537zrLHM8Xx1 zrWj1r4bdOlcJtT43hcmG9c4+9dhRz4PBqY6p2nx+25732G7+ryzVagdbSR6 1uAaddm16u6Suj0iJ0kml68dld7jr5jdud9WVX1ebjh2qHD/ytL1DC93Uy2q cM45qq1Dv3Xc9H1k+Fpay8tr66pYRulvo6rPs1vZ3ux84/Jifa6inSPOgU4c 2VdYT7Edo+4tuvnaw63WjtraT60cF8O/TcsvY2gsWCvPax3tPPeZRs/Z0O9F 1869y46VeH6/s+paXm29zkp+H7Zpn29+Tsb9lnHkPj8w/Nytfq/NrWvt+8by ysrIe/Jk5nechM2/786+R+fXUxgbWvZb2HbaW/We2M6+be29rKX3jPE6dky1 st0d26ZaKsbxtPj5WNdU/Syhxf3WwntHW/3f830eHMNbad81OQa9dsY8/1lN Z/1xY64HVqWF/dPOud+cayxzO1+d73a1992gS+cy9b731R7XONf34a58HvRN d07T3vfdNo/Tbj7vbBVqR/1Er4z5YswbYk5N3R6RkyiTy9eOGqf8d4ebZd83 R31+bk722VtWi8p+e1J6DlGW7LvKpoXkz6PPD/sObK6DDSU7lyz9PdOY8+yW tnfzdQFHPAeV50DHwqFNv3cZ1Y58mzffy7Tt2lF3jotQuN7ERoavcdDS81pr 17Tx3Dd9zjb3C5W/5g+EI1eP7sto73W21qaaz2/F7w/ryX7rOKatcR0Hrrpk 4z2zdKfO8TgJdY//st/gtdnece+Jbezb9t7LWnnPqPfsdOqYame7u7VN41X/ VrytY6quaWtHbe63ad872ur/nv/z4BjeKvuu+TmO187I53/o+2DZe0997ZyX THvuN+cay9zOV1NsVxvfDdaW1ZFzmRrf++q/Tuf5Ptylz4MWzmla+r7b5nHa zeedreJkrx1Fd4y5MuYLMS9O3R6RkzCTm6R2tP77nCa/S1u7v+Xoc8a13y9W j2GqXsb679tKF1I8jy6Oi1/L4LcqI8/rx51nt7e9a78DLD1HXt3WGufqxw5V tmPtdzKHjlXfv7X92lF7+2m642J1CfFYKHn8+VeXXnNi6ue11q6Z/rlv/pwN rklZdi68ts4TYUxfRluvs1yrqp7ftfejqXd49favvk6ydeTfM0fu1DkeJ2Ft /5R/Z+qvZ9xv3adtb533xBb2bUvvZRv7bJr3jLq6dUy1s93d2qZqY47NFo+p OqavHWXa22/TvHe01/8d5v48OIa3xr5rfo7jtTPy+W+xdtRv1rTnJdOe+827 xtJGm+tIsV1tfDdY05VzmfHf+xq9Tuf2Ptytz4NWzmna6Ovob3wrx2k3n3e2 ipO5dhTdI+ZdMbfEPDl1e0RO0kxu6BoFNTPVb/vXzhk3p/79g0cvo/p8vPw8 On8/zn7q9rPWqZ+1sb1lbdzY1nr3cx/djvwuW71W/Yh9mW9DK930Nds3++Oi 4vFjxsNM+7zWMc1zP/FztnouXLEP89Mrx/dN8zorGrHPp3o/GqFk+9c3M/+e OXanzu84Wf/ONNV6Jm1vg/fEqfft9O9ldZbVTi0yp1PHVEvb3altqrPsUcdm m8dUtfHvyfM/v5j0vaPR50vlZ8b47Wn7eShtl2O4mQ7su8nPS712Su9DdOna dQenrx0NGj+785Kx5375dVedb9adr4X35lbOVxNu11TfDarWO+nxMdvvfc3f X+bxPtytz4M2z2mm7+tYX9BUx2k3n3e2ipO1dhQ9JObvYz4R842p2yNyEoda 6v4GK70m5y35ezWe7wK6C2/xn/vFeZ0BANDXP69sq3YEUG7xv+9Ccydj7Sj6 rph/i3lvzFembo/ISR5qWZw+7fx46cpxzUP3DHX93K1g8Z/7xXmdAQCQORGu Pj+7ttpF4Trds8AMLf73XWjuZKsdRTtibo95a8yXpm6PiFDP4vRpH7sid63e UfdUzcZc5+8vubKvwf2n6KrFf+4X53UGAEDWRXv56n07VvbN4FrAADmL/30X mjtZakfRHWL2xmT/eE3MKanbJCKroZYF6tM+dtXwfRfX7q+az9C9IFfCbtfO 3RoW/rlfoNcZAMBJr38v9+Wde2dwT1OAgoX/vgvNnQy1o+jMmKtiPhfzw6nb IyJDoZZF6tPO7ru4d/icamTiuVTlfVBZLIv+3C/S6wwA4GTXv9/7AT/qB+Zi 0b/vQnNbvXYUfVXMX8ccj3ls6vaIyKZQy6L1afe/xw2N1R7Kcti5N/tdjnOp rWeRn/tFe50BAAAwP4v8fRea28q1o+gRMZ+K+WjMg1K3R0RKQy3HwqH1cdAL dA5y4kg4UBzDvZoDrvm71S3kc7+grzMAAADmZyG/70JzW7V2FH1fzGdi/jzm bqnbIyIjAwAAAABAh2zF2lH0kzFfiPlfMXdM3R4RqQwAAAAAAB2ylWpH0Wkx l8Z8MeYVKdsiIrUDAAAAAECHbJXaUXTXmD+N+a+YZ6Rqh4g0DgAAAAAAHbIV akfR/WM+HHNTzCNTtEFEJg4AAAAAAB2y6LWj6Ntibo65IWZp3usXkakDAAAA AECHLHLtKNoec1vMO2LuPM91i0hrAQAAAACgQ1ZrQFnN59prQ7j00hB++qdD eOYzV3P48c/t/y2bduutmx9XMK/aUXRKzKtisn/8csyp81iviMwkAAAAAAB0 xY03hnd/1w+FcM97htDrhXCnO4XwsIeF8NSnrubmsx/Q/1s27e53D+HlLw/h Yx9bfWiq2lF0RsybYj4f8//Men0iMvMAAAAAAJDaP/9zCM94Rginnho+c+e7 hXDRRSEcO7ZptvX6UDbt4otDOPvsEO5whxCe/vTwa3v+cNP8s64dRV8R81cx /x6zPMt1icjcAgAAAABAStn15+51rxCWlkK48srwi7/wFyNn3TS26HOfC+FN bwrhfvfr15yyZeW0WTvK7l8U8z25f39dzMdjjsU8rK31iEjyJHQiHDlwabj0 0iwHwpETaVsz3qK1FwAAAADovFe+sj9u6LzzQvjXf139U9m159aMnHbiRPjI Nzyuv6wLLwzhi19c/XPLtaO3xDx98P+fOBhr9O5s7FFb6xCRTiShG8P+7eeG c8/Nsj3svzFta8ZbtPZuOHbo0nBAsQsAAAAAuuUVrwjhtNNCeP3rh/48Ue1o bVq2rFNPDeGlL139W1u1o+x6dDG3xXx7zI8N7m30u9m9jtpYvoh0KgktWi1m 0dobsqLR6jip3Svnhu0L0WAAAAAAOEn86q+G0OuFcPnlmyZNVTvKvPGN/WW/ 7nWt1I4G16r7WMynY34zJvvjz8ScMu2yRaSTSWjRrgG3aO2NLb76/EGtS+0I AAAAADrj936vf225n/3Z0slT144yr351CKecEj53xRXZv6bqR45+L+YLMbfG 3B5zQcw9Y+4w7bJFpJNhC7tx/3a1IwAAAADokk98IoQzzwzhx35s5Cyt1I4y 2TqydfV6S2HCPuToSTH/OhhrlOUzg39/MebamEdMumwR6WzYwtSOAAAAAKBj nva0EO53vxD+679GztJa7Siu44v3vW8Ivd7vhwn6jwfXqvvHXN0oqxd9KuYP Y75hkmWKyEKELUztCAAAAAA65B3vCKv3IXr72ytna612FH3u93+/v85e70mh Yf9xdDhXM/pkzBtj7t10OSKycGnBsXDo0rX7AA3n0LGqx9W/f9CxQ8Vl5+Y/ dmjj7yUrzD+2uj3jltXkfkf5eXM5cCSMu01SeXvL9/GBEY1YW8bencvrtaPl nXvHPm6adocTR8KBsucHAAAAAAjhs58N4f73D+G888bO2mbt6Lbbbguh13tb zD/EnBFq9h0PrlX3uZh/j3lVNgap7mNFZOEzhbU6w+6wMqhPFLOyu6pmc2PY v31t3u2hdFjMoJaze6W47OWwc++gBnLdxRt/v/i6TYu47uKNx5VMLs5csawa 7Q1rdZu9YedyyT5Z3hn2jqhxjWpvf3nl+7hfD9pcp8kvoyxlY5CmbXe4cX/Y fu74/QMAAAAAJ6U3vzmEO9whhI99bOysM6gd3S/mCzHPDTX6jaO7xLwj5nkx p9V5jIhsqUwoqxuNqDOU1pDKxqGMqcVk41h2r1QuN6udHLqiK7Wjfi1tc52r JCu7R9Zh8u3Nam/jl7ccdl4+PC6oWe2onXarHQEAAABAhcc/PoQnPanWrK3X jrK+4F7vHTF/GWr0G0en15lPRLZsJnPsqqG60dr4oqHs3RmW8/WNq44VFlJV izkRjlyef3xxHRt1q5WVXH0pYe3oxJHLh2tpWZ2lsE/y15DLppeVYUrrPmvj ftZTGIcUp+d3b5Nr1rXVbtesAwAAAIARPvrREE45JYSrr641+4xqR08d3Pfo YSF9v7SIdDsTOXH1+cNjf46VzXQkHMjXj86/unDPnIpazFBtqn99uuF1jBgr k6x2dCxctV5f6be3bHzOiSMHhmpqK/s230eoWDtarflsut9Qdv+j4XFf51+9 uVhz4/7tldepa7PdAAAAAMAIL395CPe5Twif/3yt2WdUOzo15pMxvxLS90uL SLczkXxNYvmSG0bPmB+Lsqn+MboWc+yKlVzt5PKRY1iOHSqMv0lVOzp2xXo7 qtq7Ku6TfWs1r8J4oWJ7s+mXj1zYiXDdRcuVz8PY2lGL7QYAAAAARlhaCmH3 7tqzz6R2lKXXe3XMP4d0/dEishiZSH7c0fo1zjbVhsYZVYs5Ea4+f2PM0UXX VS01P24mXe0oX+sqG/+zqdUV8+fbu3zRdZX7dOh5KNm4cbWjNtsNAAAAAJT4 xCfC6rXirr229kNmWDt6/OC6dQ8I8++LFpHFyWQK9zsqvSdP6YXs8kbVYm4I l6wv+/wwrkQxrn4y+9pRvtY14t5PxezOjasqjBfKt7f8OnN12zuudtRuuwEA AACAEr/zOyGcemoIt9xS+yEzrB2dGfP5mB8M6fqkRaT7mVB2v6HC9eKKWRuP FHOg9GJoI2oxJ64O56/Xoy4JYysUY+ons68d5f8+QQrrybd37NieqWpH7bYb AAAAACixc2cIj3hEo4fMrHaUpdf765g3hDT90SKyGJnCsXAoqw3t3RmWx9QZ lnfuLRmHNKIWc+P+sH3tsdv3hzEjb7Z07Wi69qodAQAAAEByD394v37UwIxr R78ScySk6Y8WkcXI9E4cCQfWr2u2d/O17HLjkIbLR1tx3NFy2Lm3xrXfKq7t l6Z2NH27AQAAAIASd75zCG94Q6OHzLh29CMxnw1p+qNFZDHSsuxadrn6QmFM 0soVx3Lzzv9+R+OuAVe9rDr3O1oO094GaH61o3bbDQAAAAAUfPazIfR6Ibzl LY0eNuPa0VNX29TrnRXm2xctIouTCeTrQwdC6a2M1mc9Eg7sXhlR36hXi7no usoVhOsuWq6sn9xwyXJF/aTJska1d3gdK/uOhDHlrkrzqx21224AAAAAoOBT nwqrdZp3vrPRw2ZcO/q2Qe3ovmG+fdEisjiZwHBtZ+dVx6rnzo3lWR4a3DK6 FnPsio160/LOy0fWp04cuXz4Gnlj6ifLO68Ko1o7flmj23viuos2xlct7wyX VxbU4vYd2hibdaAw7zxrR222GwAAAAAoOHIkrNZpbmh20Z8Z144ePKgdPSLM ty9aRBYnEzl2Ve5adCu7w6UHysesZLWGvTuX1+tMw2OIRtdi4gpydZz+vXiK t9cZXvbo+slQfeTclbD70kOF+lF/HNX4ZVW098SRsG/l3FyNau+IfXIsHLr0 0rB7ZaM9++ZUO1q+6LrN7Wmx3QAAAABAwbXXhtU6TTb+qIEZ147uPqgdPSHM ty9aRBYnkynUHLIxK3svzd3naJDd+XlW9hXGD1XUYrJ6zuWFeyXtrlh2Rf0k nLguXJQfT7RaP8ova++gTrUcdu4cdX29ce3Nall7h8ctle6T3WFlaJuKdax2 a0dD92/KtSc/Zqitdq9en/DSmtcyBAAAAICTwcGDYbVO8+lPN3rYjGtHdxnU jr43zLcvWkQWJxPLxv2U1m/Kko1NKg4cGlOLWa1F7B2uH23OuHrP6oLCkQPD tY/S5ew9EI5cXVWLGdPe1fUU6jAVyWphm3ZJaLd2FI5dUbrdw9cObKfd4cb9 Yfu5VfsHAAAAAE4y73lPWK3T/O3fNnrYjGtH9xvUjr4lzLcvWkQWJ1Pp3/+m ou6Q1YyycSjlxYYxtZiwPpaltEa1uuxx9Z71lq5ec+3S3Sujl5ONk6msxdRo 7+D6d1X7ZPW6cJeOqL+ElmtHq9td0pbzry5cl276dqsdAQAAAEDBxz8eVus0 73pXo4fNuHb0yEHt6IFhvn3RIrI4acFa3aEkIwsNxcdVX+OsX6MqX3b+umzD 42lKF1Tdxvz0TW2v396qfXJgzMXc8ttaufvGtreiLSPuTzVNu12zDgAAAAAK brklrNZp3va2Rg+bce3oewe1oy8P8+2LFpHFSSc1qZ/ccMnyeu3o/KsVLAAA AACADjnjjBDe+MZGD5lx7eg5MZ+POSWk6ZMWke6nk/LXbVu54tjoGU8cCfvW r2e3HMYNOwIAAAAAmKv73z+E3bsbPWTGtaNXxRwLafqjRWQx0knHrsjdlyi7 H1HZNday67Xt3RmW1+fb5zppAAAAAEC3rKyE8LjHNXrIWg3oM5/5XDj8nn8K f/lXn1pPC7Wja2PeFNL0R4vIYqSbjl0Vdi5vjD06d3ln2Fu8B8/uXH3p3JWw e+zNgQAAAAAA5uwNbwjhzDNDuP322g/J147eeejGsO+X37v6t7WMe1zeUO2o 1zs15paY80O6PmkR6X466kQ4cmDvcP1oZFbC7ksPhWOpmwwAAAAAUHTDDSH0 eiH89V/Xfki+BlRWP6rzuDWF2tE3rbal19sW5t8XLSKLkw7L6keXDl+XbijL YefebAySuhEAAAAA0FFf+EIIX/ZlIfzyL4+c5UN/c/PQdemyOlFesX40So3a 0a6Y/4w5LaTrkxaR7qf7ThwJB4rXq1vNAfc3AgAAAAC679nPDuGRjxw5uVg7 yu5xVLRWP7p8/wdGLqdG7eg9MW8L6fqjRWQxAgAAAADALP3Zn4XVa8W9731T LSarH33ko8dHTq+sHfV6jxhcr+57Q/p+aRHpdgAAAAAAmLUHPSiEF75wpqsY Uzv69ZhjMXcI6fulRaTbAQAAAABg1l73uhDufOcQbrllZqsYWTvq9c6K+Y+Y 3SF9n7SIdD8AAAAAAMzazTeHcOaZIVx44cxWUVE7+pmYz8ScHdL3SYtI9wMA AAAAwDy89rUhnH56CB/5yEwWX1Y7+uwHPxhCr/fZmJeH9P3RIrIYAQAAAABg Hj73ufD/t3c/K1FFcQDHfwtjiBZBm6BHkHLjpoIIwU3PUZTtfIRcmriupULk IhKfwHFT0CZsIfYERe10Ef5Jjz9n7sJIQuU6h4nPFz4wc5n53Xu258BMGR0t ZXLyUsafdnZ0MDFRSsRGulLq70cDw0GSJEmSJEmSNKjW1kqJKGVxsfXRf50d LSz07xXxsNTfiwaGhyRJkiRJkiRpkE1P93+7rtttdewfZ0erq717/J6aOn5X ex8aGC4vAAAAAAAYoP39mTI+vlE6nZ2ysvKqrbkv5z/1Xy8vv+7NHhv7urO9 PVPq70MDAAAAAADwLxGd1E3f0p0W595O39OHdLX6OgEAAAAAADibiOvNGc+v 9KyFeU+aWR/TjerrAwAAAAAA4HwiRtJsOkzv0q0LzLiZ3jYzZnsza68LAAAA AACAi4t4lH6kvbSU7p3hO3fTm7SbfvZm1F4HAAAAAAAA7Tj+f6KIx+lzyiux md6nufS8Mddc22w+8yU9TdeqPz8AAAAAAACXI+L+iXOi9bTVWD9xnvSg+nMC /50jM1AxEQ== "], {{0, 297}, {1679, 0}}, {0, 255}, ColorFunction->RGBColor], BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{1679, 297}, PlotRange->{{0, 1679}, {0, 297}}]], "Input",ExpressionUUID-> "6019e03b-d339-4975-8644-9538ea1ea5b6"] }], "Chapter", CellFrame->{{0, 0}, {0, 0.5}}, CellChangeTimes->{{3.7310896562732*^9, 3.7310896723052*^9}, { 3.7310929577434*^9, 3.7310929620646*^9}, {3.7311558834132*^9, 3.7311559004296*^9}, {3.7311900163182*^9, 3.7311900290462*^9}, { 3.7311901735931997`*^9, 3.7311903425242*^9}, {3.7311904268732*^9, 3.7311904345931997`*^9}, {3.7311904773782*^9, 3.7311905335432*^9}, { 3.7311906196252003`*^9, 3.7311906348262*^9}, {3.7311933841191998`*^9, 3.7311933852622004`*^9}, 3.775569125667297*^9, 3.7755691934649887`*^9},ExpressionUUID->"5cf578f3-9a65-466f-a3b6-\ f0e47de816ba"], Cell[CellGroupData[{ Cell[TextData[{ "Se trata del sistema de dos masas que se mueven cada una sobre un eje, \ unidas por una barra de longitud \[ScriptL]", StyleBox[".", FontSlant->"Italic"], " Elegimos como coordenada el \[AAcute]ngulo \[Phi] que forma el vector ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox[ StyleBox[ OverscriptBox[ StyleBox["r", FontWeight->"Bold"], " "], FontWeight->"Bold"], "21"], "=", " ", RowBox[{ SubscriptBox[ StyleBox["r", FontWeight->"Bold"], "2"], "-", SubscriptBox[ StyleBox["r", FontWeight->"Bold"], "1"]}]}], TraditionalForm]],ExpressionUUID-> "f60eb531-d3e9-4480-a60d-be200e60b571"], " con el eje x." }], "Subchapter", CellChangeTimes->{{3.7310896794072*^9, 3.7310897208803997`*^9}, { 3.7310898236387997`*^9, 3.7310898255418*^9}, 3.7310904816296*^9, { 3.731155890258*^9, 3.7311558936784*^9}, {3.7311844263512*^9, 3.7311844726692*^9}, {3.7312350673622*^9, 3.7312350760492*^9}}, FontSize->24,ExpressionUUID->"41c0ffb3-534c-415e-9813-c3aabebbd088"], Cell[BoxData[ GraphicsBox[{ {RGBColor[0.87, 0.94, 1], AbsoluteThickness[1], ArrowBox[{{-1.5, 0}, {1.5, 0}}], ArrowBox[{{0, 1.5}, {0, -1.5}}]}, { {RGBColor[0, 1, 0], Opacity[0.6], DiskBox[NCache[{Rational[-1, 2], 0}, {-0.5, 0}], 0.05]}, {RGBColor[1, 0, 0], Opacity[0.6], DiskBox[NCache[{0, Rational[-1, 2] 3^Rational[1, 2]}, { 0, -0.8660254037844386}], 0.05]}}, {GrayLevel[1], AbsoluteThickness[4], ArrowBox[NCache[{{Rational[-1, 2], 0}, { 0, Rational[-1, 2] 3^Rational[1, 2]}}, {{-0.5, 0}, { 0, -0.8660254037844386}}]]}, {GrayLevel[1], AbsoluteThickness[1], Dashing[{Small, Small}], LineBox[NCache[{{Rational[-1, 2], 0}, { Rational[-1, 2], -1.5}}, {{-0.5, 0}, {-0.5, -1.5}}]]}, {RGBColor[1, 1, 0], AbsoluteThickness[2], ArrowBox[{{-0.5000000000000002, -1.}, {-0.45002083072932203`, \ -0.9987502603949663}, {-0.4001665833531724, -0.9950041652780258}, \ {-0.3505618675264006, -0.9887710779360422}, {-0.3013306692049388, \ -0.9800665778412416}, {-0.25259604074547726`, -0.9689124217106448}, \ {-0.2044797933386608, -0.9553364891256061}, {-0.15710219254454916`, \ -0.9393727128473791}, {-0.11058165769134937`, -0.921060994002885}, \ {-0.06503446588876982, -0.9004471023526769}, {-0.02057446139579716, \ -0.8775825618903728}}]}, { {GrayLevel[1], InsetBox[ StyleBox["\<\"\\!\\(\\*SubscriptBox[\\(r\\), \\(1\\)]\\)\"\>", StripOnInput->False, FontSize->30], NCache[{Rational[-1, 2], 0.25}, {-0.5, 0.25}]]}, {GrayLevel[1], InsetBox[ StyleBox["\<\"\\!\\(\\*SubscriptBox[\\(r\\), \\(2\\)]\\)\"\>", StripOnInput->False, FontSize->30], NCache[{0.33, Rational[-1, 2] 3^Rational[1, 2]}, { 0.33, -0.8660254037844386}]]}, {GrayLevel[1], InsetBox[ StyleBox["\<\"\[ScriptX]\"\>", StripOnInput->False, FontSize->30], {0.2, -1.35}]}, {GrayLevel[1], InsetBox[ StyleBox["\<\"\[ScriptY]\"\>", StripOnInput->False, FontSize->30], {1.35, 0.2}]}, {RGBColor[1, 1, 0], InsetBox[ StyleBox["\<\"\[Phi]\"\>", StripOnInput->False, FontSize->25], NCache[{Rational[-1, 2] + (Rational[1, 2] 2^Rational[-1, 2]) (-1 + 3^Rational[ 1, 2]), -1.1159258262890681`}, {-0.24118095489747932`, \ -1.1159258262890681`}]]}}}, AspectRatio->Automatic, Axes->False, Background->GrayLevel[0], ImageSize->400, PlotRange->{{-1.6500000000000001`, 1.6500000000000001`}, {-1.6500000000000001`, 1.6500000000000001`}}, Ticks->False]], "Output", CellChangeTimes->{ 3.731099700148*^9},ExpressionUUID->"e2c3dd99-f597-4540-8e8e-9d653486a56d"] }, Open ]], Cell[TextData[{ "El lagrangiano es (\[DownExclamation]revisen!):\n\n", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{ RowBox[{ RowBox[{"\[ScriptCapitalL]", "(", RowBox[{"\[Phi]", ",", " ", FractionBox["d\[Phi]", "dt"]}], ")"}], " ", "=", " ", RowBox[{ RowBox[{ FractionBox["1", "2"], SuperscriptBox[ RowBox[{ SuperscriptBox["\[ScriptL]", "2"], "(", FractionBox["d\[Phi]", "dt"], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["m", RowBox[{"1", " "}]], SuperscriptBox["cos", "2"], " ", "\[Phi]"}], " ", "+", " ", RowBox[{ SubscriptBox["m", "2"], SuperscriptBox["sin", "2"], "\[Phi]"}]}], ")"}]}], " ", "+", " ", RowBox[{ SubscriptBox["m", RowBox[{"2", " "}]], "g", " ", "\[ScriptL]", " ", "cos", " ", "\[Phi]"}]}]}], ","}], FontColor->GrayLevel[0], Background->RGBColor[0.87, 0.94, 1]], TraditionalForm]], FontColor->GrayLevel[0.5],ExpressionUUID-> "fd205f7c-a07b-408a-b828-c728c1aa5157"], "\n\ny la ecuaci\[OAcute]n de movimiento:\n\n", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{ RowBox[{ StyleBox[ RowBox[{ RowBox[{"[", RowBox[{ SubscriptBox["m", "1"], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["m", "2"], "-", SubscriptBox["m", "1"]}], ")"}], " ", SuperscriptBox["sin", "2"], "\[Phi]"}]}], "]"}], FractionBox[ RowBox[{ SuperscriptBox[ StyleBox["d", FontSlant->"Plain"], "2"], "\[Phi]"}], SuperscriptBox["dt", "2"]], RowBox[{"+", RowBox[{"(", RowBox[{ SubscriptBox["m", "2"], "-", SubscriptBox["m", "1"]}], ")"}]}], " ", "sin", " ", RowBox[{"(", RowBox[{"2", "\[Phi]"}], ")"}], " ", SuperscriptBox[ RowBox[{"(", FractionBox["d\[Phi]", "dt"], ")"}], "2"]}], FontColor->GrayLevel[0]], StyleBox[ RowBox[{"+", " ", RowBox[{"(", RowBox[{"g", "/", "\[ScriptL]"}], ")"}]}], FontColor->GrayLevel[0]], StyleBox[" ", FontColor->GrayLevel[0]], SubscriptBox[ StyleBox["m", FontColor->GrayLevel[0], Background->RGBColor[0.87, 0.94, 1]], "2"], StyleBox["sin", FontColor->GrayLevel[0]], StyleBox[" ", FontColor->GrayLevel[0]], StyleBox["\[Phi]", FontColor->GrayLevel[0]]}], StyleBox[" ", FontColor->GrayLevel[0]], StyleBox["=", FontColor->GrayLevel[0]], StyleBox[" ", FontColor->GrayLevel[0]], StyleBox[ RowBox[{ StyleBox["0", FontColor->GrayLevel[0]], "."}]]}], Background->RGBColor[0.87, 0.94, 1]], TraditionalForm]],ExpressionUUID-> "0eaabd1d-7473-44bb-82b0-87806d91d645"], "\n\nIntroduciendo la relaci\[OAcute]n \[Mu] = ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["m", "1"], "/", SubscriptBox["m", "2"]}], TraditionalForm]],ExpressionUUID-> "fb8540b3-4594-4bfa-80e2-8a22b467e78f"], " y el tiempo adimensional \[Tau] = ", Cell[BoxData[ FormBox[ RowBox[{ SqrtBox[ RowBox[{"g", "/", "\[ScriptL]"}]], "t"}], TraditionalForm]], ExpressionUUID->"cf0e4e65-7ce7-4bd7-97e9-6c9e16e4db04"], ", queda una ecuaci\[OAcute]n que depende de un \[UAcute]nico \ par\[AAcute]metro:\n\n", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"[", RowBox[{"\[Mu]", "+", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Mu]"}], ")"}], " ", SuperscriptBox["sin", "2"], "\[Phi]"}]}], "]"}], RowBox[{"\[Phi]", "''"}]}], " ", "+", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Mu]"}], ")"}], " ", "sin", " ", RowBox[{"(", RowBox[{"2", "\[Phi]"}], ")"}], " ", SuperscriptBox[ RowBox[{"\[Phi]", "'"}], "2"]}], "+", " ", RowBox[{"sin", " ", "\[Phi]"}]}], " ", "=", " ", "0."}], Background->RGBColor[0.87, 0.94, 1]], TraditionalForm]], FontColor->GrayLevel[0],ExpressionUUID-> "8c8248c1-f8e8-4bab-87fb-3b5412af4420"], "\n\nAqu\[IAcute] las derivadas de \[Phi] son respecto a la variable \[Tau]. \ Si las masas son iguales, ", Cell[BoxData[ FormBox[ RowBox[{"\[Mu]", " ", "=", " ", "1"}], TraditionalForm]],ExpressionUUID-> "f87551f9-7e3d-47c2-86ae-bb4dcec1d08e"], ", resulta la ecuaci\[OAcute]n del p\[EAcute]ndulo. \n\nAl haber \ introducido el tiempo \[Tau], la escala de tiempo caracter\[IAcute]stica del \ problema es 2\[Pi], salvo casos extremos.\n\nPara explorar las soluciones \ posibles ya no es necesario variar por separado ", Cell[BoxData[ FormBox[ SubscriptBox["m", "1"], TraditionalForm]],ExpressionUUID-> "a044dd56-d11e-4a15-b3c0-95b9227ebadb"], ", ", Cell[BoxData[ FormBox[ SubscriptBox["m", "2"], TraditionalForm]],ExpressionUUID-> "b8360ec6-b749-4cf5-af7c-f7215a9413f3"], ", ", Cell[BoxData[ FormBox["g", TraditionalForm]],ExpressionUUID-> "a7b08209-0235-4624-9f37-118bf096842f"], " y \[ScriptL]. Todo lo que importa es \[Mu], la relaci\[OAcute]n entre las \ masas." }], "Subchapter", CellChangeTimes->{{3.7310916222022*^9, 3.7310920927525997`*^9}, { 3.7310921693796*^9, 3.7310924018894*^9}, {3.7310926136842003`*^9, 3.7310926724852*^9}, {3.7310927678814*^9, 3.7310928171521997`*^9}, { 3.7310928479664*^9, 3.7310929406096*^9}, {3.731092986311*^9, 3.7310929871066*^9}, {3.7310935713887997`*^9, 3.7310936214944*^9}, { 3.7310939831546*^9, 3.731093984075*^9}, {3.731099821882*^9, 3.7310998729926*^9}, {3.7311539669482*^9, 3.7311539691976*^9}, { 3.7311540012452*^9, 3.7311540430256*^9}, {3.7311845060652*^9, 3.7311845275872*^9}, {3.7311893885212*^9, 3.7311894178602*^9}}, FontSize->24,ExpressionUUID->"2f180f7e-a0f9-4ab7-b7ea-22e9ea48c02d"], Cell[CellGroupData[{ Cell[TextData[{ "La soluci\[OAcute]n num\[EAcute]rica de la ecuaci\[OAcute]n de movimiento: \ \n\nEl comando esencial es ", StyleBox["NDSolve", FontWeight->"Bold"], ". Si buscan en la ayuda, van a encontrar numerosos ejemplos de aplicaci\ \[OAcute]n a problemas f\[IAcute]sicos, incluidos problemas de \ mec\[AAcute]nica.\n\nLo m\[AAcute]s concreto es proponer condiciones \ iniciales y resolver directamente. Va un ejemplo de prueba (pr). " }], "Subchapter", CellFrame->{{0, 0}, {0, 0.5}}, CellChangeTimes->{{3.7310929888538*^9, 3.73109309509*^9}, { 3.7310931357047997`*^9, 3.7310933533808002`*^9}, {3.7310999806837997`*^9, 3.731099982825*^9}, {3.7311000313042*^9, 3.731100036656*^9}, { 3.7311002104252*^9, 3.7311002359351997`*^9}, {3.7311894545452003`*^9, 3.7311894549632*^9}}, FontSize->24,ExpressionUUID->"43a29b54-1a66-469a-8eb8-b5b643bf2ded"], Cell["\<\ La celda de abajo es la primera celda que tienen que ejecutar s\[IAcute] o s\ \[IAcute] para poder seguir adelante. Recuerden: con el cursor dentro de la celda, tecleen Enter del teclado num\ \[EAcute]rico o Shift + Enter para ejecutar.\ \>", "Text", CellChangeTimes->{{3.7311002389782*^9, 3.7311002442042*^9}, { 3.7311540687139997`*^9, 3.7311540764323997`*^9}, {3.7311657701774*^9, 3.7311658054706*^9}, 3.7311845700552*^9, {3.7312351335568*^9, 3.731235166867*^9}}, FontSize->18,ExpressionUUID->"f061db74-98fa-43fb-89ea-e6f2c820b8fe"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ "\[CapitalAAcute]ngulo", " ", "inicial", " ", "de", " ", "prueba"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Phi]0pr", " ", "=", " ", FractionBox[ RowBox[{"5", "\[Pi]"}], "6"]}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"Velocidad", " ", "angular", " ", "inicial", " ", "de", " ", RowBox[{"prueba", ":", " ", RowBox[{ "lo", " ", "leo", " ", "as\[IAcute]", " ", "\"\\""}]}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Phi]p0pr", " ", "=", " ", "0"}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "Un", " ", "valor", " ", "de", " ", "\[Mu]", " ", "de", " ", "prueba"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Mu]pr", " ", "=", " ", "2"}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", " ", RowBox[{"(*", " ", RowBox[{ RowBox[{ "Un", " ", "tiempo", " ", "m\[AAcute]ximo", " ", "de", " ", "prueba", " ", "hasta", " ", "el", " ", "cual", " ", "integrar", " ", "las", " ", "ecuaciones"}], ";", " ", RowBox[{ "elegido", " ", "en", " ", "realidad", " ", "despu\[EAcute]s", " ", "de", " ", "algunos", " ", "tanteos", " ", RowBox[{"preliminares", "."}]}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"tmaxpr", " ", "=", " ", "20"}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"La", " ", "cosa", " ", "en", " ", RowBox[{"s\[IAcute]", "."}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "Notar", " ", "el", " ", "uso", " ", "del", " ", "doble", " ", "\"\<=\>\"", " ", "para", " ", "significar", " ", "\"\\"", " ", "entre", " ", RowBox[{"expresiones", ".", " ", "Un"}], " ", "solo", " ", "\"\<=\>\"", " ", RowBox[{"asigna", "."}]}], " ", "*)"}], " ", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{"Por", " ", "ejemplo"}], ",", " ", RowBox[{ "\"\\"", " ", "le", " ", "asigna", " ", "a", " ", "\"\\"", " ", "el", " ", "valor", " ", RowBox[{"\"\<1\>\"", "."}]}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{ "Un", " ", "doble", " ", "\"\<=\>\"", " ", "significa", " ", "\"\\"", " ", "sin", " ", RowBox[{"asignaci\[OAcute]n", ".", " ", "\"\\""}], " ", "puede", " ", "ser", " ", "cierta", " ", "o", " ", "falsa"}], ",", " ", RowBox[{ "pero", " ", "no", " ", "le", " ", "asigna", " ", "a", " ", "\"\\"", " ", "el", " ", "valor", " ", RowBox[{"\"\<1\>\"", "."}]}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"sol", " ", "=", " ", "\[IndentingNewLine]", RowBox[{"NDSolve", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"\[Mu]pr", " ", "+", " ", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Mu]pr"}], ")"}], " ", SuperscriptBox[ RowBox[{"Sin", "[", RowBox[{"\[Phi]", "[", "t", "]"}], "]"}], "2"]}]}], ")"}], " ", RowBox[{ RowBox[{"\[Phi]", "''"}], "[", "t", "]"}]}], " ", "+", " ", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Mu]pr"}], ")"}], " ", RowBox[{"Sin", "[", RowBox[{"2", RowBox[{"\[Phi]", "[", "t", "]"}]}], "]"}], " ", SuperscriptBox[ RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "t", "]"}], "2"]}], "+", " ", RowBox[{"Sin", "[", RowBox[{"\[Phi]", "[", "t", "]"}], "]"}]}], " ", "\[Equal]", " ", "0"}], ",", " ", RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{"Ec", ".", " ", "de"}], " ", "movimiento"}], ",", " ", RowBox[{"copiada", " ", "de", " ", "m\[AAcute]s", " ", RowBox[{"arriba", " ", "[", "revisen", "]"}]}]}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Phi]", "[", "0", "]"}], " ", "\[Equal]", " ", "\[Phi]0pr"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "0", "]"}], " ", "\[Equal]", " ", "\[Phi]p0pr"}]}], " ", RowBox[{"(*", " ", RowBox[{"Condiciones", " ", "iniciales"}], " ", "*)"}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", "\[Phi]", ",", " ", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", "tmaxpr"}], "}"}]}], " ", RowBox[{"(*", " ", RowBox[{ RowBox[{ "La", " ", "funci\[OAcute]n", " ", "para", " ", "la", " ", "que", " ", "va", " ", "a", " ", "resolver", " ", "y", " ", "en", " ", "qu\[EAcute]", " ", "variable", " ", "e", " ", RowBox[{"intervalo", ".", " ", "Aqu\[IAcute]"}], " ", "es", " ", "la", " ", "funci\[OAcute]n", " ", "\[Phi]"}], ",", " ", RowBox[{ "de", " ", "la", " ", "variable", " ", "t", " ", "en", " ", "el", " ", "intervalo", " ", "entre", " ", "0", " ", "y", " ", "tmaxpr"}]}], " ", "*)"}], "\[IndentingNewLine]", "]"}]}]}]}]], "Input", CellChangeTimes->{{3.7310933168054*^9, 3.7310935639944*^9}, { 3.7310936512194*^9, 3.7310937854728003`*^9}, {3.7310939391446*^9, 3.7310939392538*^9}, {3.7310939949084*^9, 3.7310940111822*^9}, { 3.731094060884*^9, 3.7310940836348*^9}, {3.7310942751556*^9, 3.7310942882460003`*^9}, {3.7310963787258*^9, 3.7310964225601997`*^9}, { 3.7310965286104*^9, 3.7310965311084003`*^9}, {3.7311000600444*^9, 3.731100187144*^9}, {3.7311540826043997`*^9, 3.7311541610278*^9}, { 3.7311548737584*^9, 3.7311549014158*^9}, {3.731167110516*^9, 3.7311671110299997`*^9}, {3.7311849160792*^9, 3.7311849255572*^9}, { 3.7311849652662*^9, 3.7311849741242*^9}, {3.7311897327382*^9, 3.7311897376401997`*^9}, {3.7312351793442*^9, 3.7312352346636*^9}, { 3.7312352840078*^9, 3.7312352922318*^9}, {3.7314181076672*^9, 3.7314184099966*^9}},ExpressionUUID->"61e50612-bb55-4ecd-a422-69f81336b06b"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Si todo sali\[OAcute] como es debido, deber\[IAcute]a aparecer justo arriba \ el siguiente cuadrito\n\n", Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{"\[Phi]", "\[Rule]", TagBox[ TemplateBox[{RowBox[{ StyleBox[ TagBox["InterpolatingFunction", "SummaryHead"], "NonInterpretableSummary"], StyleBox["[", "NonInterpretableSummary"], DynamicModuleBox[{Typeset`open$$ = False}, PanelBox[ PaneSelectorBox[{False -> GridBox[{{ PaneBox[ ButtonBox[ DynamicBox[ FEPrivate`FrontEndResource[ "FEBitmaps", "SquarePlusIconMedium"]], ButtonFunction :> (Typeset`open$$ = True), Appearance -> None, Evaluator -> Automatic, Method -> "Preemptive"], Alignment -> {Center, Center}, ImageSize -> Dynamic[{ Automatic, 3.5 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ Magnification])}]], GraphicsBox[{{{}, {}, { Directive[ Opacity[1.], RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1]], LineBox[CompressedData[" 1:eJwB0QMu/CFib1JlAgAAADwAAAACAAAAStFeOa+/lj4a0DjGpvEEQFp+433D 3dQ/ggAXf0vSBEA+lvq2a77lP8wbZEeMZQRAT/QI4wkn8D+i/p0LZ60DQDc0 cm9ZVPU/PXETDnmSAkD2vGVz/fH6P6u35xLxsQBArkFwQdgXAECTvOGKCMn7 P03J8gTc7gJAv7u5+V5d8z9IHOSKnbgFQDpHAnxYL+c/Fw6ZlmZSCEBG/kre HYXVP1EkE95ZJAtAjycy9BQXrL9f2VCrVMYNQEhfwRC2H9u/5Kx+nYYtEEAj RbOH1T/qv05/NwP4kxFAby/GxA029b8iIdIrbeISQGwcv7kawPy/LFVPcvdM FEAS9d1KiSoBwOTuA5rgsBVAPzM7RlzaAsAGWJqEzfwWQHtaxi6a3APAXlMT jc9kGECWkQnT/YkEwCAebljVtBlAwCRAbujdBMAYe6tB8CAbQE8NMcfs7gTA vT0gDGqGHEDNXzqAqbYEwM3Pdpnn0x1AyRUVsCo7BMAT9K9Eej0fQPfxQoF2 VgPA4nNlWYhHIEAbc0tO2wUCwJCgDgED7SBAopMp6xcGAMBZFqk3iKAhQNRU gTqBL/m/13O0Tw9IIkAb5g7ri0Lxv3Aasfag/SJA32ciENpq47/gc0kO4q8j QK8H3bQpIsq/BbVSByVWJEDP+NtyY7PDP0U/TY9yCiVAbfaj4VbR4T86sbj4 wbIlQAwDdOFkcO8/Bta/0sBXJkDJPb8NVHT3P+1DuDvKCidAE3dqXcHc/j+J mSGG1bEnQG1fLSV3qQFAQDh8X+tmKEDccNr/ui8DQKy+RxoDEClAwNbE4BoX BEDv965FyrUpQM54B/kDogRATXoHAJxpKkB9LaoFqOkEQGDk0JtvEStAbA3H /uPpBECOl4vGTccrQCrkw0mFoQRAkv3hYdt5LEDw04UbMggEQEtLqd5qIC1A 8PdXZMAcA0Af4mHqBNUtQErHkYCJjAFAqGCL16B9LkCzZIEQgHP+PwiSUDXs Ii9AI9zqgwOI9z+DDAciQtYvQAStxJ7DU+4/WjcX+Mw+MEDrCdPZVvDgPwCN oyZ+mTBAgR5gbQ8nwD8RvH0Nh/IwQLWXIWuagdC//F4Q5ZBFMUCFJP1ejl/k v3WmGwSgnzFAIqcpj77D8b/IYd8TsPMxQJFx+XLrtvm/qcEba8VOMkD9fAdl 5TsAwPX6pXoyqDJAG/6yYmZHAsAcqOh6oPsyQMtxUZcdfgPA0PmjwhNWM0C6 /ADfO1MEwF+/F/uHqjNAN6Hye2fEBMAyFFD6//8zQMCwWOGx8ATAS6K5zg== "]]}}}, { DisplayFunction -> Identity, AspectRatio -> 1, Axes -> {False, False}, AxesLabel -> {None, None}, AxesOrigin -> {0, 0}, DisplayFunction :> Identity, Frame -> {{True, True}, {True, True}}, FrameLabel -> {{None, None}, {None, None}}, FrameStyle -> Directive[ Opacity[0.5], Thickness[Tiny], RGBColor[0.368417, 0.506779, 0.709798]], FrameTicks -> {{None, None}, {None, None}}, GridLines -> {None, None}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> Dynamic[{ Automatic, 3.5 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ Magnification])}], Method -> { "DefaultBoundaryStyle" -> Automatic, "ScalingFunctions" -> None}, PlotRange -> {{0., 20.}, {-2.6175267796698733`, 2.617993877991478}}, PlotRangeClipping -> True, PlotRangePadding -> {{ Scaled[0.1], Scaled[0.1]}, { Scaled[0.1], Scaled[0.1]}}, Ticks -> {Automatic, Automatic}}], GridBox[{{ RowBox[{ TagBox["\"Domain: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox[ RowBox[{"{", RowBox[{"{", RowBox[{"0.`", ",", "20.`"}], "}"}], "}"}], "SummaryItem"]}]}, { RowBox[{ TagBox["\"Output: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox["\"scalar\"", "SummaryItem"]}]}}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> { "Columns" -> {{2}}, "Rows" -> {{Automatic}}}, BaseStyle -> { ShowStringCharacters -> False, NumberMarks -> False, PrintPrecision -> 3, ShowSyntaxStyles -> False}]}}, GridBoxAlignment -> {"Rows" -> {{Top}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, BaselinePosition -> {1, 1}], True -> GridBox[{{ PaneBox[ ButtonBox[ DynamicBox[ FEPrivate`FrontEndResource[ "FEBitmaps", "SquareMinusIconMedium"]], ButtonFunction :> (Typeset`open$$ = False), Appearance -> None, Evaluator -> Automatic, Method -> "Preemptive"], Alignment -> {Center, Center}, ImageSize -> Dynamic[{ Automatic, 3.5 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ Magnification])}]], GraphicsBox[{{{}, {}, { Directive[ Opacity[1.], RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1]], LineBox[CompressedData[" 1:eJwB0QMu/CFib1JlAgAAADwAAAACAAAAStFeOa+/lj4a0DjGpvEEQFp+433D 3dQ/ggAXf0vSBEA+lvq2a77lP8wbZEeMZQRAT/QI4wkn8D+i/p0LZ60DQDc0 cm9ZVPU/PXETDnmSAkD2vGVz/fH6P6u35xLxsQBArkFwQdgXAECTvOGKCMn7 P03J8gTc7gJAv7u5+V5d8z9IHOSKnbgFQDpHAnxYL+c/Fw6ZlmZSCEBG/kre HYXVP1EkE95ZJAtAjycy9BQXrL9f2VCrVMYNQEhfwRC2H9u/5Kx+nYYtEEAj RbOH1T/qv05/NwP4kxFAby/GxA029b8iIdIrbeISQGwcv7kawPy/LFVPcvdM FEAS9d1KiSoBwOTuA5rgsBVAPzM7RlzaAsAGWJqEzfwWQHtaxi6a3APAXlMT jc9kGECWkQnT/YkEwCAebljVtBlAwCRAbujdBMAYe6tB8CAbQE8NMcfs7gTA vT0gDGqGHEDNXzqAqbYEwM3Pdpnn0x1AyRUVsCo7BMAT9K9Eej0fQPfxQoF2 VgPA4nNlWYhHIEAbc0tO2wUCwJCgDgED7SBAopMp6xcGAMBZFqk3iKAhQNRU gTqBL/m/13O0Tw9IIkAb5g7ri0Lxv3Aasfag/SJA32ciENpq47/gc0kO4q8j QK8H3bQpIsq/BbVSByVWJEDP+NtyY7PDP0U/TY9yCiVAbfaj4VbR4T86sbj4 wbIlQAwDdOFkcO8/Bta/0sBXJkDJPb8NVHT3P+1DuDvKCidAE3dqXcHc/j+J mSGG1bEnQG1fLSV3qQFAQDh8X+tmKEDccNr/ui8DQKy+RxoDEClAwNbE4BoX BEDv965FyrUpQM54B/kDogRATXoHAJxpKkB9LaoFqOkEQGDk0JtvEStAbA3H /uPpBECOl4vGTccrQCrkw0mFoQRAkv3hYdt5LEDw04UbMggEQEtLqd5qIC1A 8PdXZMAcA0Af4mHqBNUtQErHkYCJjAFAqGCL16B9LkCzZIEQgHP+PwiSUDXs Ii9AI9zqgwOI9z+DDAciQtYvQAStxJ7DU+4/WjcX+Mw+MEDrCdPZVvDgPwCN oyZ+mTBAgR5gbQ8nwD8RvH0Nh/IwQLWXIWuagdC//F4Q5ZBFMUCFJP1ejl/k v3WmGwSgnzFAIqcpj77D8b/IYd8TsPMxQJFx+XLrtvm/qcEba8VOMkD9fAdl 5TsAwPX6pXoyqDJAG/6yYmZHAsAcqOh6oPsyQMtxUZcdfgPA0PmjwhNWM0C6 /ADfO1MEwF+/F/uHqjNAN6Hye2fEBMAyFFD6//8zQMCwWOGx8ATAS6K5zg== "]]}}}, { DisplayFunction -> Identity, AspectRatio -> 1, Axes -> {False, False}, AxesLabel -> {None, None}, AxesOrigin -> {0, 0}, DisplayFunction :> Identity, Frame -> {{True, True}, {True, True}}, FrameLabel -> {{None, None}, {None, None}}, FrameStyle -> Directive[ Opacity[0.5], Thickness[Tiny], RGBColor[0.368417, 0.506779, 0.709798]], FrameTicks -> {{None, None}, {None, None}}, GridLines -> {None, None}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> Dynamic[{ Automatic, 3.5 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ Magnification])}], Method -> { "DefaultBoundaryStyle" -> Automatic, "ScalingFunctions" -> None}, PlotRange -> {{0., 20.}, {-2.6175267796698733`, 2.617993877991478}}, PlotRangeClipping -> True, PlotRangePadding -> {{ Scaled[0.1], Scaled[0.1]}, { Scaled[0.1], Scaled[0.1]}}, Ticks -> {Automatic, Automatic}}], GridBox[{{ RowBox[{ TagBox["\"Domain: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox[ RowBox[{"{", RowBox[{"{", RowBox[{"0.`", ",", "20.`"}], "}"}], "}"}], "SummaryItem"]}]}, { RowBox[{ TagBox["\"Output: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox["\"scalar\"", "SummaryItem"]}]}, { RowBox[{ TagBox["\"Order: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox["3", "SummaryItem"]}]}, { RowBox[{ TagBox["\"Method: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox["\"Hermite\"", "SummaryItem"]}]}, { RowBox[{ TagBox["\"Periodic: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox["False", "SummaryItem"]}]}}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> { "Columns" -> {{2}}, "Rows" -> {{Automatic}}}, BaseStyle -> { ShowStringCharacters -> False, NumberMarks -> False, PrintPrecision -> 3, ShowSyntaxStyles -> False}]}}, GridBoxAlignment -> {"Rows" -> {{Top}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, BaselinePosition -> {1, 1}]}, Dynamic[Typeset`open$$], ImageSize -> Automatic], BaselinePosition -> Baseline], DynamicModuleValues :> {}], StyleBox["]", "NonInterpretableSummary"]}]}, "CopyTag", DisplayFunction->(#& ), InterpretationFunction->("InterpolatingFunction[{{0., 20.}}, <>]"& )], False, Editable->False, SelectWithContents->True, Selectable->False]}], "}"}], "}"}]], CellChangeTimes->{{3.7312352714446*^9, 3.7312352924814*^9}},ExpressionUUID-> "36917deb-9d71-48fb-99ef-ad5eaca79d6e"], "\n\nEs la soluci\[OAcute]n de NDSolve, y la hemos asignado a la variable \ \"sol\".\n\nLa soluci\[OAcute]n est\[AAcute] dada en t\[EAcute]rminos de una \ funci\[OAcute]n num\[EAcute]rica, de la que no se dan otros detalles que su \ intervalo de definici\[OAcute]n y el tipo de salida que arroja, en este caso, \ un escalar.\n\nPara extraer de aqu\[IAcute] la funci\[OAcute]n \[Phi](t) hay \ que seleccionar la parte adecuada de \"sol\". Paso por paso nos vamos \ abriendo camino en la lista {{...}} hasta llegar a la funci\[OAcute]n \ propiamente dicha:" }], "Subchapter", CellChangeTimes->{{3.7311002522548*^9, 3.731100439532*^9}, { 3.7311542353084*^9, 3.7311542413536*^9}, {3.7311658184568*^9, 3.7311659397748003`*^9}, {3.731165996451*^9, 3.7311659981836*^9}, { 3.7311846110402*^9, 3.7311846253702*^9}, {3.7312352997986*^9, 3.7312353044458*^9}}, FontSize->24,ExpressionUUID->"0b9c32f4-c8e3-4512-880f-59486011539e"], Cell[BoxData[{ RowBox[{"sol", "[", RowBox[{"[", "1", "]"}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"sol", "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"sol", "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}], " ", RowBox[{"(*", " ", RowBox[{"Con", " ", "este", " ", "nos", " ", RowBox[{"quedamos", "."}]}], " ", "*)"}]}]}], "Input", CellChangeTimes->{{3.731093866955*^9, 3.7310939183448*^9}, { 3.731154227901*^9, 3.7311542321502*^9}},ExpressionUUID->"89aaeb0d-4710-4dec-aff4-49dc94f6c01b"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ La operaci\[OAcute]n de seleccionar partes de una lista se hace mediante los \ dobles corchetes. Lo \[UAcute]nico que nos interesa es el \[UAcute]ltimo \ resultado. Es decir, en general nos bastar\[IAcute]a con escribir:\ \>", "Subchapter", CellChangeTimes->{{3.7311004623744*^9, 3.7311004854351997`*^9}, { 3.7311005880892*^9, 3.7311006115108*^9}, {3.7311542677756*^9, 3.7311542681344*^9}}, FontSize->24,ExpressionUUID->"14a72643-a6b1-4dfb-95e2-64acd5555a33"], Cell[BoxData[ RowBox[{ RowBox[{"Phi", " ", "=", " ", RowBox[{ RowBox[{ RowBox[{"sol", "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}]}], ";"}]], "Input", CellChangeTimes->{ 3.7311006213564*^9},ExpressionUUID->"ca63bb95-0d54-4b75-ba48-ee45a3cc9ff1"] }, Open ]], Cell[CellGroupData[{ Cell["El gr\[AAcute]fico de la soluci\[OAcute]n \[Phi](t):", "Subchapter", CellChangeTimes->{{3.7310941227967997`*^9, 3.7310941284918003`*^9}, { 3.7311006377394*^9, 3.731100646727*^9}, {3.7311659893062*^9, 3.7311659935338*^9}}, FontSize->24,ExpressionUUID->"735c7a1f-dea0-4ec4-abf5-9a2f1b749d1b"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"Phi", " ", "=", " ", RowBox[{ RowBox[{ RowBox[{"sol", "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}]}], ";"}], " ", RowBox[{"(*", " ", RowBox[{ "Repito", " ", "la", " ", "definici\[OAcute]n", " ", "por", " ", "las", " ", "dudas", " ", "de", " ", "que", " ", "se", " ", "olviden", " ", "de", " ", "ejecutar", " ", "la", " ", "celda", " ", "anterior"}], " ", "*)"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Plot", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Phi", "[", "t", "]"}], ",", " ", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", "tmaxpr"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"AbsoluteThickness", "[", "3", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"Background", "\[Rule]", "Black"}], ",", "\[IndentingNewLine]", RowBox[{"AxesStyle", "\[Rule]", "White"}], ",", "\[IndentingNewLine]", RowBox[{"TicksStyle", "\[Rule]", RowBox[{"Directive", "[", RowBox[{"White", ",", " ", "16"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", "600"}], ",", " ", "\[IndentingNewLine]", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", " ", "\"\<\[Phi]\>\""}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"LabelStyle", "\[Rule]", "20"}], ",", "\[IndentingNewLine]", RowBox[{"ImageMargins", "\[Rule]", "40"}]}], "\[IndentingNewLine]", "]"}]}], "Input", CellChangeTimes->{{3.7310940268368*^9, 3.7310940333596*^9}, { 3.7310941312530003`*^9, 3.7310942708606*^9}, {3.7311006527964*^9, 3.7311007923724003`*^9}, {3.7311542876605997`*^9, 3.731154309432*^9}, { 3.7312353688182*^9, 3.7312353972176*^9}},ExpressionUUID->"cdbff3ed-7a58-4b57-a760-3445301282a3"], Cell["\<\ Lo \[UAcute]nico importante en la sintaxis del Plot son las comas. Los cortes \ de l\[IAcute]nea no tienen ning\[UAcute]n efecto, salvo facilitar la lectura. \ Todas las opciones despu\[EAcute]s de \"{t, 0, tmaxpr}\" pueden omitirse y \ permutarse. \ \>", "Text", CellChangeTimes->{{3.7311543334316*^9, 3.7311544249779997`*^9}, { 3.7311660182346*^9, 3.731166023135*^9}},ExpressionUUID->"354c4176-7501-49ee-940d-67da4b1fd514"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Phi", "[", "t", "]"}], ",", " ", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", "tmaxpr"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.7311895807562*^9, 3.7311895834572*^9}},ExpressionUUID->"9f3f5b30-dfe0-4973-b551-27b17a0c089d"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "La animaci\[OAcute]n. \n\nPrimero probamos graficar las cosas en un \ instante ", Cell[BoxData[ FormBox["t", TraditionalForm]],ExpressionUUID-> "3de6dbcc-7ebe-4210-9c9c-1f251d058ddb"], " fijo. Elegido un ", Cell[BoxData[ FormBox["t", TraditionalForm]],ExpressionUUID-> "2dd2252a-c778-416e-9cf6-c3fbd9971099"], " de prueba, la celda de abajo combina varios gr\[AAcute]ficos: los ejes, \ las masas y la barra entre las masas." }], "Subchapter", CellChangeTimes->{{3.731094365837*^9, 3.7310943771012*^9}, { 3.7310944214172*^9, 3.7310944777256002`*^9}, {3.7310947778822002`*^9, 3.7310948661484003`*^9}, {3.7311008153542*^9, 3.731100825388*^9}, { 3.7311544383234*^9, 3.7311544423571997`*^9}}, FontSize->24,ExpressionUUID->"d4438861-2645-45aa-b5bb-bae4755c6426"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Un", " ", "valor", " ", "de", " ", "tiempo", " ", "de", " ", RowBox[{"prueba", ".", " ", "Tiene"}], " ", "que", " ", "estar", " ", "entre", " ", "0", " ", "y", " ", "tmaxpr"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "Cambien", " ", "luego", " ", "este", " ", "valor", " ", "para", " ", "obtener", " ", "gr\[AAcute]ficos", " ", "a", " ", "distintos", " ", "tiempos"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"tpr", " ", "=", " ", "3.75"}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{"Para", " ", "ese", " ", "valor", " ", "del", " ", "tiempo"}], ",", " ", RowBox[{ "la", " ", "configuraci\[OAcute]n", " ", "del", " ", "sistema", " ", "queda", " ", "dada", " ", "por", " ", "el", " ", "valor", " ", "de", " ", "\[Phi]", " ", "que", " ", "arroja", " ", "la", " ", "funci\[OAcute]n", " ", RowBox[{"Phi", "[", "tpr", "]"}]}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{"Conocido", " ", "\[Phi]pr"}], " ", "=", " ", RowBox[{ RowBox[{"Phi", "[", "tpr", "]"}], " ", "deber\[IAcute]a", " ", "poder", " ", "graficar", " ", "la", " ", "configuraci\[OAcute]n", " ", "del", " ", "sistema"}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Phi]pr", " ", "=", " ", RowBox[{"Phi", "[", "tpr", "]"}]}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "El", " ", "comando", " ", "Show", " ", "combina", " ", "varios", " ", "gr\[AAcute]ficos", " ", "que", " ", "comparten", " ", "la", " ", "misma", " ", "regi\[OAcute]n", " ", "del", " ", "plano"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{ "Empiezo", " ", "por", " ", "graficar", " ", "un", " ", "par", " ", "de", " ", "ejes"}], ",", " ", RowBox[{ "y", " ", "luego", " ", "agrego", " ", "las", " ", "masas", " ", "y", " ", "la", " ", "barra"}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"Show", "[", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", "Ejes", " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ejes", " ", "=", " ", RowBox[{"Graphics", "[", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"AbsoluteThickness", "[", "2", "]"}], ",", " ", "LightBlue", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"1.5", ",", " ", "0"}], "}"}]}], "}"}], "]"}], ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "1.5"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1.5"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"White", ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{"\"\<\[ScriptX]\>\"", ",", " ", "30"}], "]"}], ",", RowBox[{"{", RowBox[{"0.2", ",", RowBox[{ RowBox[{"-", "0.95"}], "\[Times]", "1.5"}]}], "}"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"White", ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{"\"\<\[ScriptY]\>\"", ",", " ", "30"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.99", " ", "1.5"}], ",", "0.22"}], "}"}]}], "]"}]}], "}"}]}], "}"}], "\[IndentingNewLine]", "]"}]}], ",", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"Masas", " ", "y", " ", "barra"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"Graphics", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"AbsoluteThickness", "[", "2", "]"}], ",", " ", "Blue", ",", " ", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"Sin", "[", "\[Phi]pr", "]"}]}], ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]pr", "]"}]}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Green", ",", " ", RowBox[{"Disk", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"Sin", "[", "\[Phi]pr", "]"}]}], ",", " ", "0"}], "}"}], ",", " ", "0.05"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Red", ",", " ", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]pr", "]"}]}]}], "}"}], ",", " ", "0.05"}], "]"}]}], "}"}]}], "}"}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"Retoques", " ", RowBox[{"opcionales", "."}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", RowBox[{"1.6", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}]}], "}"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Background", "\[Rule]", " ", "Black"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", " ", "400"}]}], "\[IndentingNewLine]", "]"}]}]}]], "Input", CellChangeTimes->{{3.7310944144742002`*^9, 3.7310944512181997`*^9}, { 3.7310944962946*^9, 3.7310947727654*^9}, {3.731094844165*^9, 3.731094926943*^9}, {3.7311008450802*^9, 3.7311009024392*^9}, { 3.7311544504792*^9, 3.7311546003554*^9}, {3.731166049974*^9, 3.7311660595378*^9}, {3.7311660940861998`*^9, 3.7311661202866*^9}, { 3.7311846869402*^9, 3.7311846903022003`*^9}, 3.7311848837172003`*^9, { 3.7311896686422*^9, 3.7311896695052*^9}, {3.7312354302082*^9, 3.7312356830846*^9}, {3.731235729815*^9, 3.731235750811*^9}},ExpressionUUID->"0692414a-1332-4a67-8c5b-f1c84ec3bd43"], Cell[TextData[{ "OK. Si result\[OAcute] para un ", StyleBox["t", FontSlant->"Italic"], " dado, tiene que funcionar para un ", StyleBox["t", FontSlant->"Italic"], " cualquiera. M\[AAcute]s que nada, lo de arriba sirvi\[OAcute] para ajustar \ los tama\[NTilde]os de los discos, la extensi\[OAcute]n de los ejes, etc." }], "Text", CellChangeTimes->{{3.7311677133996*^9, 3.7311677687416*^9}, { 3.7311847081212*^9, 3.7311847099042*^9}, 3.7311896175982*^9, { 3.7312357240366*^9, 3.731235725507*^9}},ExpressionUUID->"7d12eb58-1388-4691-a8c9-e12a085e18d1"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "En lugar de andar cambiando el valor de ", Cell[BoxData[ FormBox[ RowBox[{"tpr", " "}], TraditionalForm]],ExpressionUUID-> "68d58234-d0fb-4370-a84a-edf1c8df31a1"], "una y otra vez, lo m\[AAcute]s pr\[AAcute]ctico es usar el comando ", StyleBox["Manipulate", FontWeight->"Bold"], ", que nos permite variar el tiempo y graficar la configuraci\[OAcute]n de \ las masas de manera interactiva." }], "Subchapter", CellChangeTimes->{{3.7310948088542*^9, 3.7310948088698*^9}, { 3.7310949324342003`*^9, 3.7310949823194*^9}, {3.7311009089630003`*^9, 3.7311009168878*^9}}, FontSize->24,ExpressionUUID->"17d936da-2009-4a9a-9182-3bbb69cf60af"], Cell[BoxData[ RowBox[{"Manipulate", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Phi]pr", " ", "=", " ", RowBox[{"Phi", "[", "t", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Show", "[", "\[IndentingNewLine]", " ", RowBox[{"ejes", ",", " ", RowBox[{"(*", " ", RowBox[{ "El", " ", "gr\[AAcute]fico", " ", "de", " ", "los", " ", "ejes", " ", "se", " ", "defini\[OAcute]", " ", "m\[AAcute]s", " ", RowBox[{"arriba", ".", " ", "Ahora"}], " ", "lo", " ", "uso", " ", RowBox[{"directamente", "."}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Graphics", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"AbsoluteThickness", "[", "2", "]"}], ",", " ", "Blue", ",", " ", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"Sin", "[", "\[Phi]pr", "]"}]}], ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]pr", "]"}]}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Green", ",", " ", RowBox[{"Disk", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"Sin", "[", "\[Phi]pr", "]"}]}], ",", " ", "0"}], "}"}], ",", " ", "0.05"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Red", ",", " ", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]pr", "]"}]}]}], "}"}], ",", " ", "0.05"}], "]"}]}], "}"}]}], "}"}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", " ", RowBox[{"1.6", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}]}], "}"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Background", "\[Rule]", " ", "Black"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", " ", "400"}]}], "\[IndentingNewLine]", "]"}]}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "Abajo", " ", "est\[AAcute]", " ", "contenida", " ", "la", " ", "informaci\[OAcute]n", " ", "sobre", " ", "la", " ", "variable", " ", "que", " ", "se", " ", "contrala", " ", "con", " ", RowBox[{"Manipulate", ".", " ", "El"}], " ", "tiempo", " ", "t", " ", "va", " ", "desde", " ", "0", " ", "hasta", " ", "tmaxpr", " ", "y", " ", "el", " ", "paso", " ", "por", " ", "defecto", " ", "es", " ", RowBox[{"\"\\"", ".", " ", "El"}], " ", "\"\<.\>\"", " ", "luego", " ", "del", " ", "\"\<1000.\>\"", " ", "es", " ", "para", " ", "que", " ", "no", " ", "use", " ", "n\[UAcute]meros", " ", "de", " ", "precisi\[OAcute]n", " ", RowBox[{"infinita", "."}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", "tmaxpr", ",", " ", FractionBox["tmaxpr", "1000."], ",", " ", RowBox[{"Appearance", "\[Rule]", " ", "\"\\""}], ",", " ", RowBox[{"AnimationRate", "\[Rule]", " ", "2"}]}], "}"}]}], " ", "\[IndentingNewLine]", "]"}]], "Input", CellChangeTimes->{{3.7310949963196*^9, 3.7310950465596*^9}, { 3.7311009225671997`*^9, 3.731100955302*^9}, {3.7311546421809998`*^9, 3.7311546914614*^9}, {3.7311547318216*^9, 3.7311547828682003`*^9}, { 3.7311572357860003`*^9, 3.7311572495818*^9}, 3.731166146094*^9, { 3.7311671475346003`*^9, 3.7311671506926003`*^9}, {3.7311677900506*^9, 3.7311678593456*^9}, {3.7311848494302*^9, 3.7311848538992*^9}, { 3.7311849815052*^9, 3.7311849839782*^9}, {3.7311896525982*^9, 3.7311896964342003`*^9}, {3.7312357661146*^9, 3.731235901383*^9}},ExpressionUUID->"41ef6b99-e2ff-4547-9c5b-cb19e2a258a9"], Cell[TextData[{ "\[DownExclamation]Cautivador! Pueden mover el tiempo usando el mouse, \ apretar el bot\[OAcute]n Play, o ingresar un tiempo cualquiera en el cuadrito \ debajo de la barra. En tal caso usen el ", StyleBox["Enter", FontWeight->"Bold"], " ", StyleBox["normal", FontWeight->"Bold"], " para forzar el cambio." }], "Text", CellChangeTimes->{{3.7311009590928*^9, 3.731100976326*^9}, { 3.7311546735880003`*^9, 3.731154687572*^9}, {3.7312360688156*^9, 3.7312361054890003`*^9}},ExpressionUUID->"64485fe9-68e4-48b4-beb3-\ 4f3602fc4d90"], Cell["\<\ Si le dan Play, al llegar al final del recorrido temporal la \ animaci\[OAcute]n vuelve a t = 0. Ser\[IAcute]a raro que justo el tiempo \ tmaxpr fuera igual a un m\[UAcute]ltiplo entero del per\[IAcute]odo del \ movimiento. De manera que, en general, la animaci\[OAcute]n no se cerrar\ \[AAcute] sobre s\[IAcute] misma, sino que tendr\[AAcute] un salto desde la \ configuraci\[OAcute]n en tmaxpr hasta la configuaci\[OAcute]n en t = 0. Si quieren hacer un gif prolijo, esos saltos son indeseables. Es necesario \ que la animaci\[OAcute]n termine justo un paso antes de completarse un per\ \[IAcute]odo del movimiento.\ \>", "Text", CellChangeTimes->{{3.7310950899386*^9, 3.7310956269722*^9}, { 3.7310956851078*^9, 3.7310957701458*^9}, {3.7310959279906*^9, 3.7310960648316*^9}, {3.7310962597*^9, 3.731096345289*^9}, { 3.7311009918968*^9, 3.7311010511138*^9}, {3.7311547092592*^9, 3.7311547209606*^9}, {3.7311661924516*^9, 3.7311661957432003`*^9}, { 3.73116622762*^9, 3.731166236204*^9}, {3.7311850243442*^9, 3.7311850251482*^9}}, FontSize->18,ExpressionUUID->"914fb612-fc74-4269-aa87-1ca2c470fb28"] }, Open ]], Cell[TextData[{ "Podr\[IAcute]amos calcular el per\[IAcute]odo del movimiento de manera anal\ \[IAcute]tica (lo veremos m\[AAcute]s adelante en la materia). En lugar de \ eso, vamos a incluir dentro de ", StyleBox["NDSolve", FontWeight->"Bold"], " un comando que vigile los cruces por cero del \[AAcute]ngulo \[Phi]. Ese \ comando, que sirve tambi\[EAcute]n para muchas otras cosas, es ", StyleBox["WhenEvent", FontWeight->"Bold"], ". Ya que \[Phi] s\[IAcute] o s\[IAcute] cruza por cero (\[DownQuestion]por \ qu\[EAcute]?), esto servir\[AAcute] para medir el intervalo entre pasos \ sucesivos.\n\nCada vez que sea cierto que Sin[\[Phi](t)/2] = 0, lo que \ implica que \[Phi](t) es un multiplo entero y par de 2\[Pi], ", StyleBox["WhenEvent", FontWeight->"Bold"], " va a \"sembrar\", v\[IAcute]a ", StyleBox["Sow", FontWeight->"Bold"], ", el valor de t correspondiente. Cuando el c\[AAcute]lculo est\[EAcute] \ completo, el comando ", StyleBox["Reap ", FontWeight->"Bold"], "va a \"cosechar\" la lista de esos valores. La diferencia temporal entre \ estos sucesivos cruces por 0 deber\[IAcute]a ser constante e igual al per\ \[IAcute]odo del movimiento.\n\n", StyleBox["En realidad hay que hacer una salvedad. La barra puede rotar \ (siempre en el mismo sentido) u oscilar como un p\[EAcute]ndulo. Si oscila, \ el per\[IAcute]odo es igual a dos veces el intervalo entre pasos sucesivos \ por \[Phi] = 0 (\[DownQuestion]por qu\[EAcute]?). Si rota, el per\[IAcute]odo \ es igual al intervalo entre dos pasos sucesivos. Para cubrirnos en ambos \ casos, definimos T = 2 veces el intervalo entre pasos sucesivos, lo que es \ redundante para el movimiento de rotaci\[OAcute]n. Hay maneras de corregir \ esto.", FontSize->18] }], "Subchapter", CellFrame->{{0, 0}, {0, 0.5}}, CellChangeTimes->{{3.7310950899386*^9, 3.7310956269722*^9}, { 3.7310956851078*^9, 3.7310957701458*^9}, {3.7310959279906*^9, 3.7310960648316*^9}, {3.7310962597*^9, 3.731096345289*^9}, { 3.7311009918968*^9, 3.7311011767504*^9}, 3.731154848229*^9, { 3.7311549233532*^9, 3.7311551174764*^9}, {3.7311564500668*^9, 3.7311564589435997`*^9}, {3.7311662786616*^9, 3.7311663636236*^9}, { 3.7311850503132*^9, 3.7311851478772*^9}, {3.7312361959298*^9, 3.7312361987146*^9}, {3.7312369355228*^9, 3.7312370129038*^9}, { 3.731237055374*^9, 3.7312370754004*^9}}, FontSize->24,ExpressionUUID->"7134e300-dc09-4987-87d2-58f165ba0d2a"], Cell[CellGroupData[{ Cell[TextData[{ "He aqu\[IAcute] entonces el ", StyleBox["NDSolve", FontWeight->"Bold"], " que nos devuelve la soluci\[OAcute]n de la ecuaci\[OAcute]n de movimiento \ y la lista de tiempos en los que \[Phi] cruza por cero.\n\n", StyleBox["(Notar que el tiempo tmax tiene que ser lo suficientemente largo \ para que haya varios pasos por la vertical. Si en la primera elecci\[OAcute]n \ no funciona, tendr\[AAcute]n que cambiarlo.)", FontSize->18] }], "Subchapter", CellFrame->{{0, 0}, {0, 0.5}}, CellChangeTimes->{{3.7310950899386*^9, 3.7310956269722*^9}, { 3.7310956851078*^9, 3.7310957701458*^9}, {3.7310959279906*^9, 3.7310960648316*^9}, {3.7310962597*^9, 3.731096345289*^9}, { 3.7311009918968*^9, 3.7311011767504*^9}, 3.731154848229*^9, { 3.7311549233532*^9, 3.7311551386806*^9}}, FontSize->24,ExpressionUUID->"585316a5-eeaf-4156-b69c-860fb8ab91de"], Cell[BoxData[{ RowBox[{ RowBox[{"\[Phi]0pr", " ", "=", " ", FractionBox[ RowBox[{"5", "\[Pi]"}], "6"]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Phi]p0pr", " ", "=", " ", "0"}], ";"}], " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Mu]pr", " ", "=", " ", "2"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"tmaxpr", " ", "=", " ", "50"}], ";"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"sol2", " ", "=", "\[IndentingNewLine]", RowBox[{"Reap", "[", " ", RowBox[{"(*", " ", RowBox[{ "El", " ", "cosechador", " ", "de", " ", "lo", " ", "que", " ", "siembra", " ", "Sow", " ", "m\[AAcute]s", " ", "abajo"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NDSolve", "[", " ", RowBox[{"(*", " ", RowBox[{ "El", " ", "mismo", " ", "sistema", " ", "de", " ", "ecuaciones", " ", "y", " ", "condiciones", " ", "iniciales", " ", "que", " ", "antes"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"\[Mu]pr", " ", "+", " ", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Mu]pr"}], ")"}], " ", SuperscriptBox[ RowBox[{"Sin", "[", RowBox[{"\[Phi]", "[", "t", "]"}], "]"}], "2"]}]}], ")"}], " ", RowBox[{ RowBox[{"\[Phi]", "''"}], "[", "t", "]"}]}], " ", "+", " ", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Mu]pr"}], ")"}], " ", RowBox[{"Sin", "[", RowBox[{"2", RowBox[{"\[Phi]", "[", "t", "]"}]}], "]"}], " ", SuperscriptBox[ RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "t", "]"}], "2"]}], "+", " ", RowBox[{"Sin", "[", RowBox[{"\[Phi]", "[", "t", "]"}], "]"}]}], " ", "\[Equal]", " ", "0"}], ",", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Phi]", "[", "0", "]"}], " ", "\[Equal]", " ", "\[Phi]0pr"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "0", "]"}], " ", "\[Equal]", " ", "\[Phi]p0pr"}], ",", "\[IndentingNewLine]", RowBox[{"WhenEvent", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", RowBox[{ RowBox[{"\[Phi]", "[", "t", "]"}], "/", "2"}], "]"}], " ", "\[Equal]", " ", "0"}], ",", " ", RowBox[{"Sow", "[", "t", "]"}]}], "]"}]}], " ", RowBox[{"(*", " ", RowBox[{ "WhenEvent", " ", "para", " ", "detectar", " ", "los", " ", "pasos", " ", "por", " ", "la", " ", "vertical", " ", "en", " ", "combinaci\[OAcute]n", " ", "con", " ", "el", " ", "sembrador", " ", "Sow"}], " ", "*)"}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", "\[Phi]", ",", " ", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", "tmaxpr"}], "}"}]}], " ", "\[IndentingNewLine]", "]"}], "\[IndentingNewLine]", "]"}]}]}], "Input", CellChangeTimes->{{3.7310957991436*^9, 3.7310958959021997`*^9}, { 3.7310960055718*^9, 3.7310960158064003`*^9}, {3.7310960853964*^9, 3.7310960859424*^9}, {3.7310963548986*^9, 3.7310963607516003`*^9}, 3.7310965000408*^9, {3.7310965720966*^9, 3.7310965825038*^9}, { 3.731096630987*^9, 3.7310966310962*^9}, {3.7311551514779997`*^9, 3.7311551883529997`*^9}, {3.7311671718556004`*^9, 3.7311671725046*^9}, { 3.7311851968282003`*^9, 3.7311852011772003`*^9}, {3.7312371096214*^9, 3.7312371651879997`*^9}},ExpressionUUID->"258f9772-57ba-4e16-a669-\ b6db5d3f6b83"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Si todo sali\[OAcute] bien, el resultado de la celda de arriba deber\ \[IAcute]a tener esta forma:\n\n", Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"\[Phi]", "\[Rule]", TagBox[ TemplateBox[{RowBox[{ StyleBox[ TagBox["InterpolatingFunction", "SummaryHead"], "NonInterpretableSummary"], StyleBox["[", "NonInterpretableSummary"], DynamicModuleBox[{Typeset`open$$ = False}, PanelBox[ PaneSelectorBox[{False -> GridBox[{{ PaneBox[ ButtonBox[ DynamicBox[ FEPrivate`FrontEndResource[ "FEBitmaps", "SquarePlusIconMedium"]], ButtonFunction :> (Typeset`open$$ = True), Appearance -> None, Evaluator -> Automatic, Method -> "Preemptive"], Alignment -> {Center, Center}, ImageSize -> Dynamic[{ Automatic, 3.5 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ Magnification])}]], GraphicsBox[{{{}, {}, { Directive[ Opacity[1.], RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1]], LineBox[CompressedData[" 1:eJwB0QMu/CFib1JlAgAAADwAAAACAAAAnIW2B5tvrD5UzzjGpvEEQPBdXF00 Feo/W6YiFqUkBEDOO7mkBi77P9Gf6i9imABAZDHLW8wwBECwkw0nJl7vP0XB TstvqQpAPZuvZknDhj8alh9oPtcQQPBMmk4eyfC/GlLMUc4dFEAA3BkOfOAA wKF7LwaTqhdAJjyUnDk8BMBaI53txCYbQNZS1+2X7gTAnFE/PABnHkDuR9ci i+sDwLP2yyq49iBAx/OdQHfA/7/chxLr9JsiQJ/r4kyZMuu/H1jeROg4JEA3 EdCPNEO3PyVfBQT2+CVAi0pllQDr8j9vqcZ2CJsnQICLwPv7aQFAfSrjTjVg KUCwBsCc1mMEQKTqhMAYHStAxOCsX4/nBEAP7sDlALwsQDhtYEvqtgNAPihY cAN+LkArQzqbGXD+P9jSRFcFETBA0zVZmSAB6D/zLAsplvQwQGCQcRdgFdG/ miaURwLUMUC6y1l8Ab/2v+RB6r9wpDJANj/bygo2AsCP+O1qbIYzQOS7s68A nQTA3NC+b2pZNEDUdb/0f9gEwLZIUsFDKDVA8AapwdhpA8DyW5NFqgg2QMMz BUJUgfy/0JChIxPaNkClOssAGwDkvxBhXTQJvTdAB6SFLREk2D/c0NuR2ps4 QB4s7569Cvk/SmInSa5rOUBBDM/FJ54CQBqPIDMPTTpAWBrS06+3BECM3eZ2 ch87QIwcQzPnxgRAi8tvB7HtO0BIh9TjQSIDQOxUpsp8zTxAfuztBlK9+j/v /6nnSp49QP0W9MQ84OA/VEZbN6aAPkB9LMq3n/Pdv1uu2eADVD9AxGMpnu/T +b/4Wo1rnhFAQKrlY1qfvgLAc6wEgAGCQEDxjqaJI78EwL+OYsHl6kBA+ksR N6DABMC7PheckFxBQIOboKSXugLAfj4tHSnMQUD/18rEi0P4vxLPKctCNEJA REBynILw2b9XLX0SI6VCQM8NTGJS3OI/bRy3hoQOQ0Dx6pMcxAP8P0lbUqHT dUNAaOAIyUYbA0DWZ0RV6eVDQEi9hYbX0wRANAUdNoBOREDwx7yBT6cEQENw TLDdv0RAn5CsEANZAkAYK93QKC9FQIFNFla0HvY/vnZUHvWWRUAa4ppHo7TT PxWQIgWIB0ZAv5g/7wok5r89OtcYnHBGQO5F2UzVnP2/FrLixXbiRkCK+w0A ep4DwLV5Txk/UkdAHfRkpmXqBMAm0qKZiLpHQDzccM/EbgTAR/hMs5grSEDG W8HQ/ZEBwDmv3fkplUhAp1L4quhj878+GeT4//9IQKQb9h94HMS/HEa84A== "]]}}}, { DisplayFunction -> Identity, AspectRatio -> 1, Axes -> {False, False}, AxesLabel -> {None, None}, AxesOrigin -> {0, 0}, DisplayFunction :> Identity, Frame -> {{True, True}, {True, True}}, FrameLabel -> {{None, None}, {None, None}}, FrameStyle -> Directive[ Opacity[0.5], Thickness[Tiny], RGBColor[0.368417, 0.506779, 0.709798]], FrameTicks -> {{None, None}, {None, None}}, GridLines -> {None, None}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> Dynamic[{ Automatic, 3.5 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ Magnification])}], Method -> { "DefaultBoundaryStyle" -> Automatic, "ScalingFunctions" -> None}, PlotRange -> {{0., 50.}, {-2.616500719197897, 2.61799387799139}}, PlotRangeClipping -> True, PlotRangePadding -> {{ Scaled[0.1], Scaled[0.1]}, { Scaled[0.1], Scaled[0.1]}}, Ticks -> {Automatic, Automatic}}], GridBox[{{ RowBox[{ TagBox["\"Domain: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox[ RowBox[{"{", RowBox[{"{", RowBox[{"0.`", ",", "50.`"}], "}"}], "}"}], "SummaryItem"]}]}, { RowBox[{ TagBox["\"Output: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox["\"scalar\"", "SummaryItem"]}]}}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> { "Columns" -> {{2}}, "Rows" -> {{Automatic}}}, BaseStyle -> { ShowStringCharacters -> False, NumberMarks -> False, PrintPrecision -> 3, ShowSyntaxStyles -> False}]}}, GridBoxAlignment -> {"Rows" -> {{Top}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, BaselinePosition -> {1, 1}], True -> GridBox[{{ PaneBox[ ButtonBox[ DynamicBox[ FEPrivate`FrontEndResource[ "FEBitmaps", "SquareMinusIconMedium"]], ButtonFunction :> (Typeset`open$$ = False), Appearance -> None, Evaluator -> Automatic, Method -> "Preemptive"], Alignment -> {Center, Center}, ImageSize -> Dynamic[{ Automatic, 3.5 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ Magnification])}]], GraphicsBox[{{{}, {}, { Directive[ Opacity[1.], RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1]], LineBox[CompressedData[" 1:eJwB0QMu/CFib1JlAgAAADwAAAACAAAAnIW2B5tvrD5UzzjGpvEEQPBdXF00 Feo/W6YiFqUkBEDOO7mkBi77P9Gf6i9imABAZDHLW8wwBECwkw0nJl7vP0XB TstvqQpAPZuvZknDhj8alh9oPtcQQPBMmk4eyfC/GlLMUc4dFEAA3BkOfOAA wKF7LwaTqhdAJjyUnDk8BMBaI53txCYbQNZS1+2X7gTAnFE/PABnHkDuR9ci i+sDwLP2yyq49iBAx/OdQHfA/7/chxLr9JsiQJ/r4kyZMuu/H1jeROg4JEA3 EdCPNEO3PyVfBQT2+CVAi0pllQDr8j9vqcZ2CJsnQICLwPv7aQFAfSrjTjVg KUCwBsCc1mMEQKTqhMAYHStAxOCsX4/nBEAP7sDlALwsQDhtYEvqtgNAPihY cAN+LkArQzqbGXD+P9jSRFcFETBA0zVZmSAB6D/zLAsplvQwQGCQcRdgFdG/ miaURwLUMUC6y1l8Ab/2v+RB6r9wpDJANj/bygo2AsCP+O1qbIYzQOS7s68A nQTA3NC+b2pZNEDUdb/0f9gEwLZIUsFDKDVA8AapwdhpA8DyW5NFqgg2QMMz BUJUgfy/0JChIxPaNkClOssAGwDkvxBhXTQJvTdAB6SFLREk2D/c0NuR2ps4 QB4s7569Cvk/SmInSa5rOUBBDM/FJ54CQBqPIDMPTTpAWBrS06+3BECM3eZ2 ch87QIwcQzPnxgRAi8tvB7HtO0BIh9TjQSIDQOxUpsp8zTxAfuztBlK9+j/v /6nnSp49QP0W9MQ84OA/VEZbN6aAPkB9LMq3n/Pdv1uu2eADVD9AxGMpnu/T +b/4Wo1rnhFAQKrlY1qfvgLAc6wEgAGCQEDxjqaJI78EwL+OYsHl6kBA+ksR N6DABMC7PheckFxBQIOboKSXugLAfj4tHSnMQUD/18rEi0P4vxLPKctCNEJA REBynILw2b9XLX0SI6VCQM8NTGJS3OI/bRy3hoQOQ0Dx6pMcxAP8P0lbUqHT dUNAaOAIyUYbA0DWZ0RV6eVDQEi9hYbX0wRANAUdNoBOREDwx7yBT6cEQENw TLDdv0RAn5CsEANZAkAYK93QKC9FQIFNFla0HvY/vnZUHvWWRUAa4ppHo7TT PxWQIgWIB0ZAv5g/7wok5r89OtcYnHBGQO5F2UzVnP2/FrLixXbiRkCK+w0A ep4DwLV5Txk/UkdAHfRkpmXqBMAm0qKZiLpHQDzccM/EbgTAR/hMs5grSEDG W8HQ/ZEBwDmv3fkplUhAp1L4quhj878+GeT4//9IQKQb9h94HMS/HEa84A== "]]}}}, { DisplayFunction -> Identity, AspectRatio -> 1, Axes -> {False, False}, AxesLabel -> {None, None}, AxesOrigin -> {0, 0}, DisplayFunction :> Identity, Frame -> {{True, True}, {True, True}}, FrameLabel -> {{None, None}, {None, None}}, FrameStyle -> Directive[ Opacity[0.5], Thickness[Tiny], RGBColor[0.368417, 0.506779, 0.709798]], FrameTicks -> {{None, None}, {None, None}}, GridLines -> {None, None}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> Dynamic[{ Automatic, 3.5 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ Magnification])}], Method -> { "DefaultBoundaryStyle" -> Automatic, "ScalingFunctions" -> None}, PlotRange -> {{0., 50.}, {-2.616500719197897, 2.61799387799139}}, PlotRangeClipping -> True, PlotRangePadding -> {{ Scaled[0.1], Scaled[0.1]}, { Scaled[0.1], Scaled[0.1]}}, Ticks -> {Automatic, Automatic}}], GridBox[{{ RowBox[{ TagBox["\"Domain: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox[ RowBox[{"{", RowBox[{"{", RowBox[{"0.`", ",", "50.`"}], "}"}], "}"}], "SummaryItem"]}]}, { RowBox[{ TagBox["\"Output: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox["\"scalar\"", "SummaryItem"]}]}, { RowBox[{ TagBox["\"Order: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox["3", "SummaryItem"]}]}, { RowBox[{ TagBox["\"Method: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox["\"Hermite\"", "SummaryItem"]}]}, { RowBox[{ TagBox["\"Periodic: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox["False", "SummaryItem"]}]}}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> { "Columns" -> {{2}}, "Rows" -> {{Automatic}}}, BaseStyle -> { ShowStringCharacters -> False, NumberMarks -> False, PrintPrecision -> 3, ShowSyntaxStyles -> False}]}}, GridBoxAlignment -> {"Rows" -> {{Top}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, BaselinePosition -> {1, 1}]}, Dynamic[Typeset`open$$], ImageSize -> Automatic], BaselinePosition -> Baseline], DynamicModuleValues :> {}], StyleBox["]", "NonInterpretableSummary"]}]}, "CopyTag", DisplayFunction->(#& ), InterpretationFunction->("InterpolatingFunction[{{0., 50.}}, <>]"& )], False, Editable->False, SelectWithContents->True, Selectable->False]}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{ "3.3428455269521837`", ",", "10.028534627349119`", ",", "16.714221051476557`", ",", "23.399904800155852`", ",", "30.085585873357363`", ",", "36.77126427101624`", ",", "43.45693999306614`"}], "}"}], "}"}]}]}]], "Output", GeneratedCell->False, CellAutoOverwrite->False, CellChangeTimes->{3.7311551920708*^9},ExpressionUUID-> "611dab78-1e02-44cc-a2e8-22e34e196170"], "\n\nVen que el resultado contiene dos partes: la soluci\[OAcute]n \ propiamente dicha, \[Phi](t), y una serie de tiempos en los que \[Phi] cruza \ por cero. La celda de abajo extrae cada cosa por separado:" }], "Subchapter", CellChangeTimes->{{3.7311552048817997`*^9, 3.7311552590861998`*^9}, { 3.7311664492724*^9, 3.7311664513627996`*^9}, {3.7311852147502003`*^9, 3.7311852256482*^9}, 3.7311899168392*^9, {3.7312371739519997`*^9, 3.7312371869052*^9}}, FontSize->24,ExpressionUUID->"e673cd50-a7ac-4eb6-802d-052a21e711a1"], Cell[BoxData[{ RowBox[{"Phi", " ", "=", " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{"sol2", "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"Tiempos", " ", "=", " ", RowBox[{ RowBox[{"sol2", "[", RowBox[{"[", "2", "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}]}], "Input", CellChangeTimes->{{3.7310961605108*^9, 3.7310961998182*^9}, { 3.7310965046906*^9, 3.7310965060478*^9}, 3.7312372024968*^9},ExpressionUUID->"c976fb29-0cbe-46e1-9a26-6594a8a614fb"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Verifiquemos que los sucesivos pasos por cero est\[EAcute]n equiespaciados\ \>", "Subchapter", CellChangeTimes->{{3.7310962137812*^9, 3.731096228185*^9}}, FontSize->24,ExpressionUUID->"8739149d-a517-40bd-9f6b-4c23166179e8"], Cell[BoxData[ RowBox[{"lista", " ", "=", " ", RowBox[{"Differences", "[", "Tiempos", "]"}]}]], "Input", CellChangeTimes->{{3.731237265131*^9, 3.731237275862*^9}},ExpressionUUID->"7169b827-182b-4e7a-8e70-5bebf396dd64"], Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{"lista", ",", " ", RowBox[{"PlotRange", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Min", "[", "lista", "]"}], "-", FractionBox[ RowBox[{ RowBox[{"Max", "[", "lista", "]"}], "-", RowBox[{"Min", "[", "lista", "]"}]}], "4"]}], ",", RowBox[{ RowBox[{"Max", "[", "lista", "]"}], "+", FractionBox[ RowBox[{ RowBox[{"Max", "[", "lista", "]"}], "-", RowBox[{"Min", "[", "lista", "]"}]}], "4"]}]}], "}"}]}], ",", " ", RowBox[{"Frame", "\[Rule]", " ", "True"}], ",", " ", RowBox[{"ImageSize", "\[Rule]", "500"}], ",", " ", RowBox[{"FrameTicksStyle", "\[Rule]", "16"}]}], "]"}]], "Input", CellChangeTimes->{{3.731166596818*^9, 3.7311667824848003`*^9}, { 3.7311899483571997`*^9, 3.7311899513962*^9}, {3.7312372950808*^9, 3.7312373045692*^9}},ExpressionUUID->"d7bc6ecf-bb95-48da-a5f0-db54cc3397dc"], Cell["\[DownExclamation]OK dentro del error! Miren la escala vertical.", \ "Text", CellChangeTimes->{{3.7310966177014*^9, 3.731096624743*^9}, { 3.7311899423052*^9, 3.7311899427502003`*^9}, {3.7312372874898*^9, 3.7312372918104*^9}},ExpressionUUID->"55043a09-7572-4f44-929f-93cbe70f009b"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Entonces para hacer la animaci\[OAcute]n alcanza con variar t entre 0 y el \ per\[IAcute]odo, obtenido como la diferencia de dos valores consecutivos \ dentro de la lista de tiempos Tiempos (y multiplicado por 2 para abarcar los \ casos de oscilaci\[OAcute]n y rotaci\[OAcute]n).\ \>", "Subchapter", CellChangeTimes->{{3.7310966462906*^9, 3.7310967088297997`*^9}, 3.7311012284406*^9, {3.7311552875418*^9, 3.7311553323526*^9}, { 3.7311852502432003`*^9, 3.7311852551832*^9}, 3.7312372207392*^9, { 3.731237340416*^9, 3.731237368888*^9}}, FontSize->24,ExpressionUUID->"3c66edac-fcdd-434d-bce4-8f315bb39c77"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"Periodo", " ", "=", RowBox[{"2", " ", "\[Times]", " ", RowBox[{ RowBox[{"Differences", "[", "Tiempos", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}]}], ";"}], " ", RowBox[{"(*", " ", RowBox[{ RowBox[{ "El", " ", "s\[IAcute]mbolo", " ", "\[Times]", " ", "es", " ", "redundante"}], ",", " ", RowBox[{ "pero", " ", "a", " ", "veces", " ", "ayuda", " ", "a", " ", "la", " ", RowBox[{"lectura", ".", " ", "Se"}], " ", "escribe", " ", RowBox[{"como", " ", "[", "Esc", "]"}], "*", RowBox[{"[", "Esc", "]"}]}]}], " ", "*)"}], "\n"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Ncuadros", " ", "=", " ", "100."}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[CapitalDelta]", " ", "=", " ", FractionBox["Periodo", "Ncuadros"]}], ";"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ejes", " ", "=", " ", RowBox[{"Graphics", "[", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"AbsoluteThickness", "[", "2", "]"}], ",", " ", "LightBlue", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"1.5", ",", " ", "0"}], "}"}]}], "}"}], "]"}], ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "1.5"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1.5"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"White", ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{"\"\<\[ScriptX]\>\"", ",", " ", "30"}], "]"}], ",", RowBox[{"{", RowBox[{"0.2", ",", RowBox[{ RowBox[{"-", "0.9"}], "\[Times]", "1.5"}]}], "}"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"White", ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{"\"\<\[ScriptY]\>\"", ",", " ", "30"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.9", " ", "1.5"}], ",", "0.2"}], "}"}]}], "]"}]}], "}"}]}], "}"}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Manipulate", "[", " ", RowBox[{"(*", " ", RowBox[{ "Ahora", " ", "el", " ", "tiempo", " ", "m\[AAcute]ximo", " ", "est\[AAcute]", " ", "elegido", " ", "igual", " ", "al", " ", RowBox[{"Per\[IAcute]odo", ".", " ", "El"}], " ", "paso", " ", "temporal", " ", "por", " ", "defecto", " ", "entre", " ", "cuadros", " ", "sucesivos", " ", "es", " ", RowBox[{"\[CapitalDelta]", "."}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Phi]pr", " ", "=", " ", RowBox[{"Phi", "[", "t", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Show", "[", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"ejes", ",", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Graphics", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"AbsoluteThickness", "[", "2", "]"}], ",", " ", "Blue", ",", " ", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"Sin", "[", "\[Phi]pr", "]"}]}], ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]pr", "]"}]}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Green", ",", " ", RowBox[{"Disk", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"Sin", "[", "\[Phi]pr", "]"}]}], ",", " ", "0"}], "}"}], ",", " ", "0.05"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Red", ",", " ", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]pr", "]"}]}]}], "}"}], ",", " ", "0.05"}], "]"}]}], "}"}]}], "}"}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"AspectRatio", "\[Rule]", " ", "Automatic"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", " ", RowBox[{"1.1", "\[Times]", " ", "1.5", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}]}], "}"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Ticks", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Background", "\[Rule]", " ", "Black"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", " ", "400"}]}], "\[IndentingNewLine]", "]"}]}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", RowBox[{"Periodo", "-", "\[CapitalDelta]"}], ",", "\[CapitalDelta]", ",", " ", RowBox[{"Appearance", "\[Rule]", " ", "\"\\""}], ",", " ", RowBox[{"AnimationRate", "\[Rule]", " ", "5"}]}], "}"}]}], " ", "\[IndentingNewLine]", "]"}]}], "Input", CellChangeTimes->{{3.7310967218724003`*^9, 3.7310967310608*^9}, { 3.7311553100690002`*^9, 3.731155339758*^9}, {3.7311668791654*^9, 3.7311668868445997`*^9}, 3.7311670325176*^9, 3.7311857748082*^9, 3.7312372225996*^9, {3.731237374059*^9, 3.7312374210158*^9}, { 3.7312375294188004`*^9, 3.7312375751696*^9}},ExpressionUUID->"1ec9e3c0-d840-4b73-bca5-\ 6c04630e90e6"], Cell["\<\ \[DownExclamation]Ahora la animaci\[OAcute]n es un loop cerrado! \ \[DownExclamation]Vaya que hay diferencia!\ \>", "Text", CellChangeTimes->{{3.731096770491*^9, 3.7310968072974*^9}, { 3.7311012948456*^9, 3.7311013009306*^9}, {3.7311554688512*^9, 3.7311554848515997`*^9}},ExpressionUUID->"f97d9f85-b0c9-4c87-8143-\ aae5d0983e7a"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Para exportar la animaci\[OAcute]n como un ", StyleBox["gif", FontWeight->"Bold"], " usando el propio ", StyleBox["Mathematica.", FontSlant->"Italic"], " \n\nPrimero creamos una tabla con todos los gr\[AAcute]ficos. En esencia, \ es sustituir en la celda de arriba ", StyleBox["Manipulate", FontWeight->"Bold"], " por ", StyleBox["Table", FontWeight->"Bold"], "." }], "Subchapter", CellChangeTimes->{{3.7311600013428*^9, 3.7311600681056004`*^9}}, FontSize->24,ExpressionUUID->"53374855-4acb-454b-8ca8-118025f22804"], Cell[BoxData[{ RowBox[{ RowBox[{"Ncuadros", " ", "=", " ", "200."}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"T", " ", "=", " ", "Periodo"}], ";"}], " ", RowBox[{"(*", " ", RowBox[{ RowBox[{ "Si", " ", "el", " ", "movimiento", " ", "fuera", " ", "de", " ", "rotaci\[OAcute]n"}], ",", " ", RowBox[{ "habr\[IAcute]a", " ", "que", " ", "dividir", " ", "el", " ", "Periodo", " ", "por", " ", "2"}], ",", " ", RowBox[{ "para", " ", "no", " ", "hacer", " ", "un", " ", "gif", " ", "el", " ", "doble", " ", "de", " ", "largo", " ", "de", " ", "lo", " ", "necesario"}]}], " ", "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[CapitalDelta]", " ", "=", " ", FractionBox["T", "Ncuadros"]}], ";"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"tgraficos", " ", "=", " ", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Phi]pr", " ", "=", " ", RowBox[{"Phi", "[", "t", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Show", "[", "\[IndentingNewLine]", RowBox[{"ejes", ",", " ", "\[IndentingNewLine]", RowBox[{"Graphics", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"AbsoluteThickness", "[", "2", "]"}], ",", " ", "Blue", ",", " ", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"Sin", "[", "\[Phi]pr", "]"}]}], ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]pr", "]"}]}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Green", ",", " ", RowBox[{"Disk", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"Sin", "[", "\[Phi]pr", "]"}]}], ",", " ", "0"}], "}"}], ",", " ", "0.05"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Red", ",", " ", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]pr", "]"}]}]}], "}"}], ",", " ", "0.05"}], "]"}]}], "}"}]}], "}"}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", RowBox[{"AspectRatio", "\[Rule]", " ", "Automatic"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", " ", RowBox[{"1.1", "\[Times]", " ", "1.5", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}]}], "}"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Ticks", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Background", "\[Rule]", " ", "Black"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", " ", "400"}]}], "\[IndentingNewLine]", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", RowBox[{"T", "-", "\[CapitalDelta]"}], ",", "\[CapitalDelta]"}], "}"}]}], " ", "\[IndentingNewLine]", "]"}]}], ";"}]}], "Input", CellChangeTimes->{{3.7310967396594*^9, 3.7310967568984003`*^9}, { 3.7311012536748*^9, 3.7311012767044*^9}, {3.7311553204776*^9, 3.7311554542274*^9}, {3.7311572069248*^9, 3.7311572204105997`*^9}, { 3.7311599368458*^9, 3.7311599427664003`*^9}, {3.7311599864955997`*^9, 3.7311599868406*^9}, {3.7311600790998*^9, 3.731160118392*^9}, { 3.7311669096236*^9, 3.7311669875861998`*^9}, 3.731167042257*^9, 3.7311853538892*^9, {3.7312376195032*^9, 3.7312376197693996`*^9}, { 3.7312376650456*^9, 3.7312376891896*^9}},ExpressionUUID->"dd9ad189-8011-4d6a-8046-\ 0ae6c1b36c33"], Cell[CellGroupData[{ Cell[TextData[{ "En efecto, todos los cuadros est\[AAcute]n en la lista ", StyleBox["tgraficos", FontWeight->"Bold"], ", y se pueden animar directamente:" }], "Subsection", CellChangeTimes->{{3.7311679310076*^9, 3.7311679363536*^9}, { 3.7311853857382*^9, 3.7311853998662*^9}, {3.7311856765022*^9, 3.7311856959862003`*^9}},ExpressionUUID->"1b404d34-b3f1-44a4-9193-\ 913cbb0e7fdb"], Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"tgraficos", "[", RowBox[{"[", "i", "]"}], "]"}], ",", " ", RowBox[{"{", RowBox[{"i", ",", " ", "1", ",", " ", RowBox[{"Length", "[", "tgraficos", "]"}], ",", " ", "1", ",", " ", RowBox[{"Appearance", "\[Rule]", " ", "\"\\""}], ",", " ", RowBox[{"AnimationRate", "\[Rule]", " ", "50"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.7311679414966*^9, 3.7311679573826*^9}, { 3.7311680086556*^9, 3.7311680200554*^9}, {3.7311853253332*^9, 3.7311853420882*^9}, {3.7312376498978*^9, 3.7312376746358*^9}, { 3.7312377073856*^9, 3.7312377075416*^9}},ExpressionUUID->"8d2f5c42-1770-4c85-bfcd-edbfa0b39db6"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Ahora exportamos el archivo gif, que aparecer\[AAcute] en el mismo directorio \ que el Notebook. Puede tomar hasta 1 minuto. \ \>", "Subchapter", CellDingbat->"\[WatchIcon]", CellChangeTimes->{{3.731160135792*^9, 3.7311601902052*^9}, { 3.7311602434168*^9, 3.7311602931492*^9}, {3.7312377273204*^9, 3.7312377315327997`*^9}}, FontSize->24,ExpressionUUID->"4c6b15bd-baae-4753-a208-f56b1771dcd6"], Cell[BoxData[{ RowBox[{ RowBox[{"SetDirectory", "[", RowBox[{"NotebookDirectory", "[", "]"}], "]"}], ";"}], "\n", RowBox[{ RowBox[{"Export", "[", RowBox[{ "\"\\"", ",", " ", "tgraficos", ",", " ", "\"\\"", ",", " ", RowBox[{"\"\\"", "\[Rule]", " ", RowBox[{"1", "/", "25"}]}]}], "]"}], ";"}]}], "Input", CellChangeTimes->{{3.731160194182*^9, 3.7311602022736*^9}, 3.7311603161518*^9, {3.7311604377896*^9, 3.7311604465727997`*^9}},ExpressionUUID->"bb89b7de-afa9-4f3e-8710-\ 04ba9d1262b0"], Cell["\<\ Mientras se hace el gif, aprovecho para decir que lo mejor suele ser \ exportar cada figura a un archivo, y luego hacer el gif en otro programa.\ \>", "Text", CellChangeTimes->{{3.7311602957644*^9, 3.7311603062406*^9}, { 3.7311854337511997`*^9, 3.7311854683782*^9}},ExpressionUUID->"fa3678cb-2c39-48cd-bcc3-b3fb9dce8094"], Cell["El tama\[NTilde]o en kB del gif generado: ", "Text", CellChangeTimes->{{3.7311855934272003`*^9, 3.7311856065102*^9}}, FontSize->18,ExpressionUUID->"45b40045-3466-482f-92d8-93a7080c7dac"], Cell[BoxData[ RowBox[{"Round", "[", RowBox[{ RowBox[{"FileByteCount", "[", "\"\\"", "]"}], "/", "1000"}], "]"}]], "Input", CellChangeTimes->{{3.7311854994561996`*^9, 3.7311855522522*^9}},ExpressionUUID->"f84b80ed-8824-4286-a8fa-322023c12692"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Segundo ejemplo: problema 1.\n\n", Cell[BoxData[ GraphicsBox[{ {RGBColor[0.87, 0.94, 1], AbsoluteThickness[1], ArrowBox[{{-1.5, 0}, {1.5, 0}}], ArrowBox[{{0, 1.5}, {0, -1.5}}]}, { {RGBColor[0, 1, 0], Opacity[1], DiskBox[{-0.95, 0}, 0.05]}, {RGBColor[1, 0, 0], Opacity[1], DiskBox[NCache[{-0.44999999999999996`, Rational[-1, 2] 3^Rational[1, 2]}, {-0.44999999999999996`, -0.8660254037844386}], 0.05]}}, {RGBColor[1, 0.5, 0], AbsoluteThickness[3], Arrowheads[0.03], ArrowBox[{{0.75, -0.25}, {0.75, -0.75}}]}, {GrayLevel[1], AbsoluteThickness[4], ArrowBox[NCache[{{-0.95, 0}, {-0.44999999999999996`, Rational[-1, 2] 3^Rational[1, 2]}}, {{-0.95, 0}, {-0.44999999999999996`, -0.8660254037844386}}]]}, {GrayLevel[1], AbsoluteThickness[1], Dashing[{Small, Small}], LineBox[{{-0.95, 0}, {-0.95, -1.5}}]}, {RGBColor[1, 1, 0], AbsoluteThickness[2], ArrowBox[{{-0.9500000000000002, -1.}, {-0.900020830729322, \ -0.9987502603949663}, {-0.8501665833531723, -0.9950041652780258}, \ {-0.8005618675264006, -0.9887710779360422}, {-0.7513306692049387, \ -0.9800665778412416}, {-0.7025960407454772, -0.9689124217106448}, \ {-0.6544797933386608, -0.9553364891256061}, {-0.6071021925445491, \ -0.9393727128473791}, {-0.5605816576913494, -0.921060994002885}, \ {-0.5150344658887698, -0.9004471023526769}, {-0.4705744613957971, \ -0.8775825618903728}}]}, { {GrayLevel[1], InsetBox[ StyleBox["\<\"\\!\\(\\*SubscriptBox[\\(m\\), \\(1\\)]\\)\"\>", StripOnInput->False, FontSize->25], {-0.95, 0.25}]}, {RGBColor[1, 0.5, 0], InsetBox[ StyleBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(\\(\[Rule]\\)\\(\\\\ \ \\)\\)]\\)\"\>", StripOnInput->False, FontSize->24], {0.95, -0.45}]}, {GrayLevel[1], InsetBox[ StyleBox["\<\"\[ScriptL]\"\>", StripOnInput->False, FontSize->30], {-0.51, -0.4330127018922193}]}, {GrayLevel[1], InsetBox[ StyleBox["\<\"\\!\\(\\*SubscriptBox[\\(m\\), \\(2\\)]\\)\"\>", StripOnInput->False, FontSize->25], {-0.24999999999999994, -0.7160254037844386}]}, {GrayLevel[1], InsetBox[ StyleBox["\<\"\[ScriptX]\"\>", StripOnInput->False, FontSize->30], {0.2, -1.35}]}, {GrayLevel[1], InsetBox[ StyleBox["\<\"\[ScriptY]\"\>", StripOnInput->False, FontSize->30], {1.35, 0.2}]}, {RGBColor[1, 1, 0], InsetBox[ StyleBox["\<\"y\"\>", StripOnInput->False, FontSize->30], {-1.15, -0.12}]}, {RGBColor[1, 1, 0], InsetBox[ StyleBox["\<\"\[Phi]\"\>", StripOnInput->False, FontSize->25], {-0.6911809548974792, -1.1459258262890681}]}}}, AspectRatio->Automatic, Axes->False, Background->GrayLevel[0], ImageSize->400, PlotRange->{{-1.6500000000000001`, 1.6500000000000001`}, {-1.6500000000000001`, 1.6500000000000001`}}, Ticks->False]],ExpressionUUID->"30789139-8378-4d0f-bb49-940fb6812a1d"], "\n", StyleBox["\nIncluye comandos apenas m\[AAcute]s avanzados, opciones 3D y un \ exportador de gr\[AAcute]ficos. Se da por conocido lo explicado en el \ problema anterior.\n\nExpandir las celdas haciendo doble click en la flechita \ (por dem\[AAcute]s peque\[NTilde]ita) de la derecha.", FontSize->24] }], "Chapter", CellFrame->{{0, 0}, {0, 3}}, CellChangeTimes->{{3.7310969040467997`*^9, 3.731096936454*^9}, { 3.7311560086476*^9, 3.7311560129592*^9}, {3.7311905453122*^9, 3.7311906439182*^9}, {3.7311908569751997`*^9, 3.7311908792202*^9}, { 3.7311909402622004`*^9, 3.7311909705512*^9}, {3.7312377900094*^9, 3.7312378044622*^9}, 3.7755692532621093`*^9},ExpressionUUID->"5f03057c-91c0-4198-bf7b-\ f38279073517"], Cell[CellGroupData[{ Cell["\<\ Lo que sigue: \[FilledSmallCircle] La soluci\[OAcute]n num\[EAcute]rica. \[FilledSmallCircle] La extracci\[OAcute]n del per\[IAcute]odo. \[FilledSmallCircle] El gr\[AAcute]fico en bruto de las funciones \[Phi][t] e \ y[t].\ \>", "Section", CellChangeTimes->{{3.7310980899834003`*^9, 3.7310981529414*^9}, { 3.7311014944354*^9, 3.731101518539*^9}, {3.7311560340376*^9, 3.7311561126162*^9}, {3.7311634121303997`*^9, 3.7311634128993998`*^9}, { 3.7311907820472*^9, 3.7311907832782*^9}, {3.7312378162218*^9, 3.7312378178326*^9}}, FontSize->18,ExpressionUUID->"7d0edde8-10d4-468f-9767-b869cad593f8"], Cell[TextData[{ StyleBox["Antes que nada un ", FontSize->18], StyleBox["Quit", FontSize->18, FontWeight->"Bold"], StyleBox[". Reinicia el kernel del ", FontSize->18], StyleBox["Mathematica", FontSize->18, FontSlant->"Italic"], StyleBox[", libera la memoria y borra las definiciones y resultados \ anteriores.", FontSize->18] }], "Text", CellChangeTimes->{{3.7311561483652*^9, 3.7311563159108*^9}, { 3.7311910224722*^9, 3.7311910565522003`*^9}, {3.7311911610882*^9, 3.7311912712502003`*^9}},ExpressionUUID->"1c2b70ca-8234-4d55-93f0-\ 67674240ded0"], Cell[BoxData[ RowBox[{ RowBox[{"Quit", "[", "]"}], ";"}]], "Input", CellChangeTimes->{{3.7311910993822002`*^9, 3.7311911338022003`*^9}, 3.7311911861772003`*^9, {3.7311912343022003`*^9, 3.7311912350341997`*^9}},ExpressionUUID->"3bbb9371-1196-4484-bb31-\ 7b623990a6cd"], Cell[TextData[{ StyleBox["El comando ", FontSize->18], StyleBox["Module", FontSize->18, FontWeight->"Bold"], StyleBox[" aqu\[IAcute] abajo encierra todo el c\[AAcute]lculo de la soluci\ \[OAcute]n num\[EAcute]rica de la ecuaci\[OAcute]n de movimiento. \n\n", FontSize->18], StyleBox["Module", FontSize->18, FontWeight->"Bold"], StyleBox[" sirve para definir variables locales. As\[IAcute] se evita el \ peligro de definiciones m\[UAcute]ltiples para un mismo s\[IAcute]mbolo. Es \ pr\[AAcute]ctica recomendada. Todo lo que est\[AAcute] definido dentro de las \ primeras llaves tiene significado \[UAcute]nicamente dentro del bloque \ encerrado por ", FontSize->18], StyleBox["Module", FontSize->18, FontWeight->"Bold"], StyleBox[".", FontSize->18] }], "Text", CellChangeTimes->{{3.7311561483652*^9, 3.7311563159108*^9}, { 3.7311910224722*^9, 3.7311910565522003`*^9}, {3.7311912879742002`*^9, 3.7311913163812*^9}},ExpressionUUID->"826773b7-c5af-4c2b-9ae3-daa56a44df05"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"Module", "[", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Phi]", ",", " ", "\[IndentingNewLine]", "y", ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Ccondiciones", " ", "iniciales"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Phi]0", " ", "=", RowBox[{"\[Pi]", "/", "2"}]}], ",", "\[IndentingNewLine]", RowBox[{"\[Phi]p0", " ", "=", " ", RowBox[{"-", "1.42"}]}], ",", "\[IndentingNewLine]", RowBox[{"y0", " ", "=", " ", "0"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{ "Hay", " ", "una", " ", "condici\[OAcute]n", " ", "inicial", " ", "suplementaria", " ", "que", " ", "est\[AAcute]", " ", "impl\[IAcute]cita", " ", "en", " ", "las", " ", "ecuaciones", " ", "de", " ", "movimiento", " ", "dentro", " ", "del", " ", "NDSolve"}], ";", " ", RowBox[{"a", " ", "saber"}]}], ",", " ", RowBox[{ SubscriptBox["P", "y"], " ", "=", " ", "0."}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{"La", " ", "elecci\[OAcute]n", " ", SubscriptBox["P", "y"]}], " ", "=", " ", RowBox[{ "0", " ", "no", " ", "significa", " ", "ninguna", " ", "p\[EAcute]rdida", " ", "de", " ", RowBox[{"generalidad", ".", " ", "Corresponde"}], " ", "a", " ", "tomar", " ", "un", " ", "SR", " ", "que", " ", "se", " ", "mueve", " ", "con", " ", "la", " ", "velocidad", " ", "horizontal", " ", "del", " ", RowBox[{"CM", "."}]}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{"Estoy", " ", "tomando", " ", "m2"}], " ", "=", " ", RowBox[{ RowBox[{"1", " ", "y", " ", RowBox[{"g", "/", "l"}]}], " ", "=", " ", "1"}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"m1", " ", "=", " ", "5"}], ",", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"tmax", " ", "=", " ", "30"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{ "Soluci\[OAcute]n", " ", "num\[EAcute]rica", " ", "y", " ", "cosecha", " ", "de", " ", "los", " ", "tiempos", " ", "de", " ", "paso", " ", "por", " ", "la", " ", "vertical"}], ",", " ", RowBox[{"para", " ", "medir", " ", "el", " ", "per\[IAcute]odo"}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"sol", ",", " ", "cruces"}], "}"}], " ", "=", RowBox[{"Reap", "[", RowBox[{"NDSolve", "[", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Sin", "[", RowBox[{"\[Phi]", "[", "t", "]"}], "]"}], "+", FractionBox[ RowBox[{" ", RowBox[{ RowBox[{"Sin", "[", RowBox[{"2", RowBox[{"\[Phi]", "[", "t", "]"}]}], "]"}], " ", SuperscriptBox[ RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "t", "]"}], "2"]}]}], RowBox[{"2", RowBox[{"(", RowBox[{"1", "+", "m1"}], ")"}]}]], "+", RowBox[{ RowBox[{"(", RowBox[{"1", "-", FractionBox[ SuperscriptBox[ RowBox[{"Cos", "[", RowBox[{"\[Phi]", "[", "t", "]"}], "]"}], "2"], RowBox[{"1", "+", "m1"}]]}], ")"}], " ", RowBox[{ RowBox[{"\[Phi]", "''"}], "[", "t", "]"}]}]}], " ", "\[Equal]", " ", "0"}], ",", RowBox[{ RowBox[{ RowBox[{"y", "'"}], "[", "t", "]"}], " ", "\[Equal]", RowBox[{ RowBox[{"-", FractionBox["1", RowBox[{"1", "+", "m1"}]]}], RowBox[{"Cos", "[", RowBox[{"\[Phi]", "[", "t", "]"}], "]"}], " ", RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "t", "]"}]}]}], ",", " ", RowBox[{ RowBox[{"\[Phi]", "[", "0", "]"}], " ", "\[Equal]", " ", "\[Phi]0"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "0", "]"}], " ", "\[Equal]", " ", "\[Phi]p0"}], ",", " ", RowBox[{ RowBox[{"y", "[", "0", "]"}], " ", "\[Equal]", " ", "y0"}], ",", "\[IndentingNewLine]", RowBox[{"WhenEvent", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", RowBox[{ RowBox[{"\[Phi]", "[", "t", "]"}], "/", "2"}], "]"}], " ", "\[Equal]", " ", "0"}], " ", ",", " ", RowBox[{"Sow", "[", "t", "]"}]}], "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"\[Phi]", ",", " ", "y"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", "tmax"}], "}"}]}], "]"}], "]"}]}], ";"}]}], "\[IndentingNewLine]", "]"}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"\"\\"", ",", RowBox[{"Phi", " ", "=", " ", RowBox[{ RowBox[{ RowBox[{"sol", "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}]}], ",", " ", "\"\<\\n\>\""}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"\"\\"", ",", " ", RowBox[{"Y", " ", "=", " ", RowBox[{ RowBox[{ RowBox[{"sol", "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}]}], ",", " ", "\"\<\\n\>\""}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{ "\"\\"", ",", " ", RowBox[{"cruces", "[", RowBox[{"[", "1", "]"}], "]"}], ",", " ", "\"\<\\n\>\""}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{ "\"\<\[CapitalDelta]t entre cruces consecutivos \[Rule] \>\"", ",", " ", RowBox[{"Differences", "[", RowBox[{"cruces", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], ",", " ", "\"\<\\n\>\""}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{ "\"\\"", ",", " ", RowBox[{"T", " ", "=", RowBox[{"2", " ", RowBox[{ RowBox[{"Differences", "[", RowBox[{"cruces", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}]}]}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Phi", "[", "t", "]"}], ",", " ", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", RowBox[{"2", "T"}]}], "}"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", "Thick"}], ",", " ", RowBox[{"ImageMargins", "\[Rule]", "30"}], ",", " ", RowBox[{"ImageSize", "\[Rule]", "400"}], ",", " ", RowBox[{"PlotLabel", "\[Rule]", " ", RowBox[{"Style", "[", RowBox[{"\"\<\[Phi](t) \\n\>\"", ",", " ", "18"}], "]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Plot", "[", RowBox[{ RowBox[{"Y", "[", "t", "]"}], ",", " ", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", RowBox[{"2", "T"}]}], "}"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", "Thick"}], ",", " ", RowBox[{"ImageMargins", "\[Rule]", "30"}], ",", RowBox[{"ImageSize", "\[Rule]", "400"}], ",", " ", RowBox[{"PlotLabel", "\[Rule]", " ", RowBox[{"Style", "[", RowBox[{"\"\\"", ",", " ", "18"}], "]"}]}]}], "]"}]}], "}"}]}], "Input", CellChangeTimes->{{3.7309299208972*^9, 3.7309299302468*^9}, { 3.7309300836935997`*^9, 3.7309301202862*^9}, {3.7309302411535997`*^9, 3.730930276576*^9}, {3.7309303131898003`*^9, 3.7309303625973997`*^9}, { 3.7309877890039997`*^9, 3.7309879280081997`*^9}, {3.7309879602634*^9, 3.7309884510758*^9}, {3.7309885755596*^9, 3.7309887892925997`*^9}, 3.7309888221022*^9, {3.7309896759948*^9, 3.730989712383*^9}, { 3.7309897723873997`*^9, 3.7309897942402*^9}, {3.7309902840242*^9, 3.7309904315088*^9}, {3.7309904869948*^9, 3.730990530172*^9}, { 3.7309912317482*^9, 3.7309913086118*^9}, {3.730991460476*^9, 3.7309915676963997`*^9}, {3.7309918236628*^9, 3.7309918245364*^9}, { 3.7309919542376003`*^9, 3.7309919669254*^9}, {3.7310048663722*^9, 3.7310048806436*^9}, {3.7310049240706*^9, 3.7310049382806*^9}, { 3.731005038652*^9, 3.7310050478803997`*^9}, 3.7310051689264*^9, { 3.7310052402282*^9, 3.7310052499528*^9}, {3.7310052999700003`*^9, 3.731005323466*^9}, {3.7310053652816*^9, 3.731005402766*^9}, { 3.7310054383266*^9, 3.7310054777248*^9}, {3.7310201669844*^9, 3.7310202546912003`*^9}, {3.7310208508118*^9, 3.7310208562292*^9}, { 3.7310210031142*^9, 3.7310210057124*^9}, {3.7310211439642*^9, 3.7310212229154*^9}, {3.7310212747418003`*^9, 3.7310212831232*^9}, 3.7310213572518*^9, 3.7310213998722*^9, {3.7310214398154*^9, 3.7310214537088003`*^9}, {3.7310214842342*^9, 3.731021529708*^9}, 3.7310215686324*^9, {3.731021608182*^9, 3.7310217440572*^9}, 3.7310217752282*^9, {3.7310218076730003`*^9, 3.7310218239502*^9}, { 3.731096973901*^9, 3.7310971095478*^9}, {3.7310972051238003`*^9, 3.7310972367676*^9}, {3.7310972732720003`*^9, 3.7310973049374*^9}, { 3.731097416513*^9, 3.7310974461102*^9}, {3.7310981634421997`*^9, 3.7310982263613997`*^9}, {3.7311015262752*^9, 3.7311016212054*^9}, { 3.7311016685987997`*^9, 3.7311016985492*^9}, {3.7311032200559998`*^9, 3.7311032228016*^9}, {3.7311561201308002`*^9, 3.7311561467398*^9}, { 3.7311563391012*^9, 3.7311563505208*^9}, {3.7311564179608*^9, 3.7311564405846*^9}, {3.7311564934756002`*^9, 3.7311565448803997`*^9}, { 3.731156578178*^9, 3.7311566194435997`*^9}, {3.7311568048188*^9, 3.7311568072720003`*^9}, {3.7311605676482*^9, 3.731160690524*^9}, { 3.7311913476362*^9, 3.7311914291912003`*^9}, {3.7311915106652*^9, 3.7311915372892*^9}, {3.731237870126*^9, 3.7312378723784*^9}, { 3.731237947115*^9, 3.7312379870534*^9}, {3.7312380312028*^9, 3.7312380528204*^9}, {3.7312380950298*^9, 3.7312381105362*^9}, { 3.731238142583*^9, 3.7312382682718*^9}},ExpressionUUID->"3b2f5472-cd8f-4725-bb81-\ ade09996329a"] }, Open ]], Cell[CellGroupData[{ Cell["Abajo, la animaci\[OAcute]n:", "Subchapter", CellChangeTimes->{{3.7311017159926*^9, 3.7311017198450003`*^9}}, FontSize->24,ExpressionUUID->"46689e17-7c96-4745-9d63-fd2cbcb1b982"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ "El", " ", "bloque", " ", "DynamicModule", " ", "es", " ", "igual", " ", "que", " ", "el", " ", "Module", " ", "pero", " ", "para", " ", "celdas", " ", "que", " ", "se", " ", "eval\[UAcute]an", " ", RowBox[{"din\[AAcute]micamente", ".", " ", "Puede"}], " ", "omitirse", " ", "sin", " ", "peligro", " ", "si", " ", "no", " ", "repiten", " ", "definiciones", " ", "de", " ", "los", " ", RowBox[{"s\[IAcute]mbolos", "."}]}], " ", "*)"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ "DynamicModule", "[", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"y", ",", " ", "\[Phi]", ",", " ", "t", ",", " ", RowBox[{"ran", " ", "=", " ", "2"}], ",", " ", RowBox[{"\[CapitalDelta]", " ", "=", " ", RowBox[{"T", "/", "100"}]}], ",", " ", "ejes", ",", " ", "orb"}], "}"}], ",", " ", RowBox[{"(*", " ", RowBox[{"Todas", " ", "estas", " ", "variables", " ", "son", " ", RowBox[{"locales", ".", " ", "Fijo"}], " ", "en", " ", RowBox[{"T", "/", "100"}], " ", "el", " ", "intervalo", " ", "entre", " ", "dos", " ", "cuadros", " ", RowBox[{"sucesivos", "."}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ejes", " ", "=", " ", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"AbsoluteThickness", "[", "2", "]"}], ",", " ", "White", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "ran"}], ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"ran", ",", " ", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", "ran"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "ran"}], "}"}]}], "}"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"orb", " ", "=", " ", RowBox[{"ParametricPlot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Y", "[", "\[Tau]", "]"}], "+", RowBox[{"Sin", "[", RowBox[{"Phi", "[", "\[Tau]", "]"}], "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", RowBox[{"Phi", "[", "\[Tau]", "]"}], "]"}]}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"\[Tau]", ",", " ", "0", ",", " ", "T"}], "}"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Dotted", ",", "Orange"}], "}"}]}]}], "]"}]}], ";", " ", RowBox[{"(*", " ", RowBox[{ "La", " ", "\[OAcute]rbita", " ", "de", " ", "la", " ", "segunda", " ", "masa"}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Manipulate", "[", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"y", " ", "=", " ", RowBox[{"Y", "[", "t", "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"\[Phi]", " ", "=", " ", RowBox[{"Phi", "[", "t", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Show", "[", "\[IndentingNewLine]", RowBox[{ "ejes", ",", "\[IndentingNewLine]", "orb", ",", "\[IndentingNewLine]", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"AbsoluteThickness", "[", "2", "]"}], ",", " ", "Blue", ",", " ", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"y", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"y", " ", "+", " ", RowBox[{"Sin", "[", "\[Phi]", "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], "}"}]}], "}"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{"Green", ",", " ", RowBox[{"Disk", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"y", " ", "+", " ", RowBox[{"Sin", "[", "\[Phi]", "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], "}"}], ",", " ", "0.1"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{"Red", ",", " ", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"y", ",", " ", "0"}], "}"}], ",", " ", "0.1"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"AspectRatio", "\[Rule]", " ", "Automatic"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", " ", RowBox[{"ran", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}]}], "}"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Ticks", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Background", "\[Rule]", " ", "Black"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", " ", "600"}]}], "\[IndentingNewLine]", "]"}]}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"Abajo", ":", " ", RowBox[{ RowBox[{ "el", " ", "tiempo", " ", "m\[AAcute]ximo", " ", "llega", " ", "hasta", " ", "T"}], " ", "-", " ", "\[CapitalDelta]"}]}], ",", " ", RowBox[{ "porque", " ", "si", " ", "llegase", " ", "hasta", " ", "T", " ", "la", " ", "animaci\[OAcute]n", " ", "repetir\[IAcute]a", " ", "el", " ", "primer", " ", "cuadro"}], ",", " ", RowBox[{ RowBox[{"ya", " ", "que", " ", "en", " ", "t"}], " ", "=", " ", RowBox[{ RowBox[{"0", " ", "y", " ", "t"}], " ", "=", " ", RowBox[{ "T", " ", "la", " ", "configuraci\[OAcute]n", " ", "es", " ", "la", " ", RowBox[{"misma", "."}]}]}]}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", RowBox[{"T", "-", "\[CapitalDelta]"}], ",", " ", "\[CapitalDelta]", ",", " ", RowBox[{"Appearance", "\[Rule]", " ", "\"\\""}]}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"TrackedSymbols", "\[RuleDelayed]", " ", RowBox[{"{", "t", "}"}]}]}], " ", RowBox[{"(*", RowBox[{ "S\[OAcute]lo", " ", "recalcula", " ", "las", " ", "cosas", " ", "cuando", " ", "cambia", " ", RowBox[{"t", "."}]}], "*)"}], "\[IndentingNewLine]", "]"}]}]}], "\[IndentingNewLine]", "]"}]}]], "Input", CellChangeTimes->{{3.7309893676366*^9, 3.7309896446464*^9}, { 3.730989872724*^9, 3.7309898902634*^9}, {3.7309905906118*^9, 3.7309905946521997`*^9}, {3.7310199483114*^9, 3.7310201463822002`*^9}, { 3.7310202717964*^9, 3.7310203332836*^9}, {3.7310215566038*^9, 3.7310215570425997`*^9}, {3.731021598109*^9, 3.731021598299*^9}, { 3.7310973353156*^9, 3.7310974361085997`*^9}, {3.731097487684*^9, 3.731097510391*^9}, {3.7311017222096*^9, 3.7311018121378*^9}, { 3.7311019121818*^9, 3.7311019409941998`*^9}, {3.7311045633208*^9, 3.7311045904376*^9}, {3.7311046494316*^9, 3.7311046748344*^9}, { 3.7311566346464*^9, 3.7311566640984*^9}, {3.7311567267236*^9, 3.731156781646*^9}, {3.7311571660044003`*^9, 3.7311571892084*^9}, 3.7311634184634*^9, {3.7311691040856*^9, 3.7311691160256*^9}, { 3.7311915657972*^9, 3.7311915661452*^9}, {3.7312383944700003`*^9, 3.7312383952686*^9}},ExpressionUUID->"3f911791-88cf-49bc-8150-\ 481c145b2d29"], Cell["\<\ Ya est\[AAcute] ajustado para que el loop sea cerrado. Lo podemos subir a \ Tumblr sin que nos averg\[UDoubleDot]ence (al menos no por esa raz\[OAcute]n).\ \>", "Text", CellChangeTimes->{{3.731238299458*^9, 3.7312383786608*^9}},ExpressionUUID->"1127106b-01fa-4a35-b32a-21a502d1918d"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "En ", Cell[BoxData[ FormBox[ SuperscriptBox["glorioso", "*"], TraditionalForm]],ExpressionUUID-> "7dff6d32-4eea-4c24-b733-2290704db8f5"], " 3D, pero nada \[OAcute]ptimo." }], "Subchapter", CellChangeTimes->{{3.7310980596842003`*^9, 3.7310980627604*^9}, { 3.7310982700844*^9, 3.7310982720811996`*^9}, {3.7311019742448*^9, 3.7311019820164003`*^9}, {3.7311568515366*^9, 3.731156868163*^9}, { 3.7311691441586*^9, 3.7311691459370003`*^9}, {3.7311915796102*^9, 3.7311915800692*^9}}, FontSize->24,ExpressionUUID->"ec422f92-e3f0-4abe-9f13-042d8335a8ea"], Cell[BoxData[ RowBox[{"DynamicModule", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"y", ",", " ", "\[Phi]", ",", " ", "t", ",", " ", RowBox[{"ran", " ", "=", " ", "2"}], ",", " ", RowBox[{"\[CapitalDelta]", " ", "=", " ", RowBox[{"T", "/", "200"}]}], ",", " ", "ejes", ",", " ", "orb"}], "}"}], ",", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"ejes", " ", "=", " ", RowBox[{"Graphics3D", "[", RowBox[{"{", " ", RowBox[{"White", ",", RowBox[{"Specularity", "[", RowBox[{"White", ",", "100"}], "]"}], ",", RowBox[{"Tube", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "ran"}], ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "ran", ",", " ", "0"}], "}"}]}], "}"}], ",", " ", "0.012"}], "]"}], ",", RowBox[{"Tube", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", " ", RowBox[{"-", "ran"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "0", ",", "ran"}], "}"}]}], "}"}], ",", " ", "0.012"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"orb", " ", "=", " ", RowBox[{"ParametricPlot3D", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{ RowBox[{"Y", "[", "\[Tau]", "]"}], "+", RowBox[{"Sin", "[", RowBox[{"Phi", "[", "\[Tau]", "]"}], "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", RowBox[{"Phi", "[", "\[Tau]", "]"}], "]"}]}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"\[Tau]", ",", " ", "0", ",", " ", "T"}], "}"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", " ", RowBox[{ RowBox[{"AbsoluteDashing", "[", RowBox[{"{", RowBox[{"5", ",", " ", "8"}], "}"}], "]"}], ",", "Orange"}], "}"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Manipulate", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"y", " ", "=", " ", RowBox[{"Y", "[", "t", "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"\[Phi]", " ", "=", " ", RowBox[{"Phi", "[", "t", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Show", "[", "\[IndentingNewLine]", RowBox[{ "ejes", ",", "\[IndentingNewLine]", "orb", ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{ RowBox[{"AbsoluteThickness", "[", "1", "]"}], ",", " ", "Blue", ",", " ", RowBox[{"Specularity", "[", RowBox[{"White", ",", "20"}], "]"}], ",", " ", RowBox[{"Tube", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "y", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", RowBox[{"y", " ", "+", " ", RowBox[{"Sin", "[", "\[Phi]", "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], "}"}]}], "}"}], ",", " ", "0.03"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{"Green", ",", RowBox[{"Specularity", "[", RowBox[{"White", ",", "100"}], "]"}], ",", RowBox[{"Sphere", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"y", " ", "+", " ", RowBox[{"Sin", "[", "\[Phi]", "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], "}"}], ",", " ", "0.08"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{"Red", ",", " ", RowBox[{"Specularity", "[", RowBox[{"White", ",", "100"}], "]"}], ",", RowBox[{"Sphere", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "y", ",", " ", "0"}], "}"}], ",", " ", "0.08"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"AspectRatio", "\[Rule]", " ", "Automatic"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", " ", RowBox[{"ran", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "0.5"}], ",", " ", "0.5"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Ticks", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Background", "\[Rule]", " ", "Black"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", " ", "600"}], ",", "\[IndentingNewLine]", RowBox[{"ViewVector", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"8", RowBox[{"{", RowBox[{"2", ",", " ", RowBox[{"-", "0.9"}], ",", " ", "0.5"}], "}"}]}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ViewAngle", "\[Rule]", " ", RowBox[{"20", "\[Degree]"}]}]}], "\[IndentingNewLine]", "]"}]}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", RowBox[{"T", "-", "\[CapitalDelta]"}], ",", " ", "\[CapitalDelta]", ",", " ", RowBox[{"Appearance", "\[Rule]", " ", "\"\\""}], ",", " ", RowBox[{"AnimationRate", "\[Rule]", " ", "2"}]}], "}"}], ",", " ", "\[IndentingNewLine]", RowBox[{"TrackedSymbols", "\[RuleDelayed]", " ", RowBox[{"{", "t", "}"}]}]}], "\[IndentingNewLine]", "]"}]}]}], "\[IndentingNewLine]", "]"}]], "Input", CellChangeTimes->{{3.7310223701512003`*^9, 3.7310223841015997`*^9}, { 3.731022427184*^9, 3.7310225225062*^9}, {3.7310974700290003`*^9, 3.7310974827212*^9}, {3.731097516943*^9, 3.7310975174578*^9}, { 3.7310975600528*^9, 3.7310976150987997`*^9}, {3.7310976647756*^9, 3.7310978284254*^9}, {3.7310978781702003`*^9, 3.7310980400408*^9}, { 3.731101868626*^9, 3.7311018966563997`*^9}, {3.7311019466940002`*^9, 3.7311019606664*^9}, {3.7311043348476*^9, 3.7311044298828*^9}, 3.731104557736*^9, 3.7311046376516*^9, {3.7311571460668*^9, 3.731157153755*^9}, 3.731157719769*^9, 3.7311634319723997`*^9, { 3.7311637128814*^9, 3.7311637347264*^9}, {3.7311638867344*^9, 3.731163891903*^9}, {3.7311691664952*^9, 3.7311693500922003`*^9}, 3.7311693855643997`*^9, {3.7312384105243998`*^9, 3.7312384136689997`*^9}},ExpressionUUID->"6253d822-7c78-4425-a464-\ 021fdc1bf9d9"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ Cell[BoxData[ FormBox[ SuperscriptBox["\[InvisiblePrefixScriptBase]", "*"], TraditionalForm]], CellDingbat->"\[NeutralSmiley]", FontSize->18,ExpressionUUID->"87658435-c71c-46cb-91c4-38cfdbbdb4d8"], StyleBox["Al menos hasta la versi\[OAcute]n 10.0, que es la que estoy \ usando, los gr\[AAcute]ficos 3D del ", FontSize->18], StyleBox["Mathematica", FontSize->18, FontSlant->"Italic"], StyleBox[" no se caracterizan por un ", FontSize->18], StyleBox["rendering", FontSize->18, FontSlant->"Italic"], StyleBox[" muy delicado ni muy veloz. \n\nSi todo lo que interesa es la \ velocidad, \[EAcute]sta puede mejorarse si calculan antes todos los cuadros y \ los guardan como im\[AAcute]genes 2D. Eso es lo que hace la tabla de abajo. \ Las im\[AAcute]genes se guardan en la tabla llamada tgraf. Para un \ gr\[AAcute]fico con tan pocos elementos, la ganancia no es muy notable.", FontSize->18] }], "Subchapter", CellDingbat->"\[NeutralSmiley]", CellChangeTimes->{{3.7310982793352003`*^9, 3.7310984112855997`*^9}, { 3.7311019906099997`*^9, 3.7311020169184*^9}, {3.7311020687696*^9, 3.7311020977396*^9}, {3.731156888818*^9, 3.7311568910986*^9}, { 3.731156923365*^9, 3.731157003677*^9}, {3.7311570790514*^9, 3.7311571056456003`*^9}, {3.7311573157844*^9, 3.731157331505*^9}, { 3.7311575965822*^9, 3.7311576010956*^9}, {3.7311694766032*^9, 3.7311694886942*^9}, {3.731238506949*^9, 3.7312385297244*^9}, { 3.7312385645282*^9, 3.7312385703943996`*^9}, {3.7312386095290003`*^9, 3.7312386196436*^9}}, FontSize->36,ExpressionUUID->"d20350d3-2182-4c47-af76-e8a1f180de4e"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Puede", " ", "tardar", " ", "varios", " ", "segundos"}], "*)"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Module", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"y", ",", " ", "\[Phi]", ",", " ", "t", ",", "\[Tau]", ",", " ", RowBox[{"ran", " ", "=", " ", "2"}], ",", " ", RowBox[{"\[CapitalDelta]", " ", "=", " ", RowBox[{"T", "/", "100"}]}], ",", " ", "ejes", ",", " ", "orb", ",", " ", "imagentemp"}], "}"}], ",", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ejes", " ", "=", " ", RowBox[{"Graphics3D", "[", RowBox[{"{", " ", RowBox[{"White", ",", RowBox[{"Specularity", "[", RowBox[{"White", ",", "100"}], "]"}], ",", RowBox[{"Tube", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "ran"}], ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "ran", ",", " ", "0"}], "}"}]}], "}"}], ",", " ", "0.012"}], "]"}], ",", RowBox[{"Tube", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", " ", RowBox[{"-", "ran"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "0", ",", "ran"}], "}"}]}], "}"}], ",", " ", "0.012"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"orb", " ", "=", " ", RowBox[{"ParametricPlot3D", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{ RowBox[{"Y", "[", "\[Tau]", "]"}], "+", RowBox[{"Sin", "[", RowBox[{"Phi", "[", "\[Tau]", "]"}], "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", RowBox[{"Phi", "[", "\[Tau]", "]"}], "]"}]}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"\[Tau]", ",", " ", "0", ",", " ", "T"}], "}"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", " ", RowBox[{ RowBox[{"AbsoluteDashing", "[", RowBox[{"{", RowBox[{"5", ",", " ", "8"}], "}"}], "]"}], ",", "Orange"}], "}"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"tgraf", " ", "=", " ", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"y", " ", "=", " ", RowBox[{"Y", "[", "t", "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"\[Phi]", " ", "=", " ", RowBox[{"Phi", "[", "t", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Image", "[", RowBox[{"Show", "[", "\[IndentingNewLine]", RowBox[{ "ejes", ",", "\[IndentingNewLine]", "orb", ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{ RowBox[{"AbsoluteThickness", "[", "1", "]"}], ",", " ", "Blue", ",", RowBox[{"Specularity", "[", RowBox[{"White", ",", "20"}], "]"}], ",", " ", RowBox[{"Tube", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "y", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", RowBox[{"y", " ", "+", " ", RowBox[{"Sin", "[", "\[Phi]", "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], "}"}]}], "}"}], ",", " ", "0.03"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{"Green", ",", RowBox[{"Specularity", "[", RowBox[{"White", ",", "100"}], "]"}], ",", RowBox[{"Sphere", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"y", " ", "+", " ", RowBox[{"Sin", "[", "\[Phi]", "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], "}"}], ",", " ", "0.08"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{"Red", ",", " ", RowBox[{"Specularity", "[", RowBox[{"White", ",", "100"}], "]"}], ",", RowBox[{"Sphere", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "y", ",", " ", "0"}], "}"}], ",", " ", "0.08"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"AspectRatio", "\[Rule]", " ", "Automatic"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", " ", RowBox[{"ran", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "0.5"}], ",", " ", "0.5"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Ticks", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Background", "\[Rule]", " ", "Black"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", " ", "600"}], ",", "\[IndentingNewLine]", RowBox[{"ViewVector", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"8", RowBox[{"{", RowBox[{"2", ",", " ", RowBox[{"-", "0.9"}], ",", " ", "0.5"}], "}"}]}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ViewAngle", "\[Rule]", " ", RowBox[{"20", "\[Degree]"}]}]}], "\[IndentingNewLine]", "]"}], "]"}]}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", RowBox[{"T", "-", "\[CapitalDelta]"}], ",", " ", "\[CapitalDelta]"}], "}"}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}], "\[IndentingNewLine]", "]"}]}]], "Input", CellChangeTimes->{{3.731157008755*^9, 3.7311570761448*^9}, { 3.731157110474*^9, 3.7311571377254*^9}, {3.7311573446924*^9, 3.7311573882866*^9}, {3.7311574443176003`*^9, 3.7311574862068*^9}, { 3.7311575227386*^9, 3.7311575277854*^9}, {3.7311576284406*^9, 3.7311576403*^9}, 3.7311577130726*^9, {3.7311635888262*^9, 3.731163609237*^9}, {3.7311636676014*^9, 3.731163695252*^9}, { 3.7311638759049997`*^9, 3.7311638797748003`*^9}, {3.7311694181802*^9, 3.731169422517*^9}, {3.7311695093982*^9, 3.731169518572*^9}, { 3.7312385533458*^9, 3.7312385541902*^9}},ExpressionUUID->"c53e11df-e0f3-4aff-a0a9-\ 5dd513888b85"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Ahora puede hacerse la animaci\[OAcute]n con todo ya calculado y guardado \ previamente:\ \>", "Subchapter", CellChangeTimes->{{3.73115765366*^9, 3.7311576771438*^9}, { 3.7311695284206*^9, 3.731169529733*^9}}, FontSize->18,ExpressionUUID->"f6d43fc1-6b82-4570-bc8c-b41181870639"], Cell[BoxData[ RowBox[{"Manipulate", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"tgraf", "[", RowBox[{"[", "i", "]"}], "]"}], ",", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", " ", "1", ",", " ", RowBox[{"Length", "[", "tgraf", "]"}], ",", " ", "1", ",", " ", RowBox[{"Appearance", "\[Rule]", " ", "\"\\""}]}], "}"}]}], "\[IndentingNewLine]", "]"}]], "Input", CellChangeTimes->{{3.731157679676*^9, 3.7311576986756*^9}},ExpressionUUID->"d2712577-152b-4bf5-9391-3a7fa65a875d"], Cell["\<\ El movimiento es m\[AAcute]s fluido pero los gr\[AAcute]ficos siguen siendo \ espantosos.\ \>", "Text", CellChangeTimes->{{3.731157751565*^9, 3.7311577792218*^9}, { 3.7311607378266*^9, 3.731160739293*^9}, {3.7312386459021997`*^9, 3.7312386488294*^9}},ExpressionUUID->"c7c72302-6bdf-48b8-8bdd-b07865a93d60"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Para obtener buenos gr\[AAcute]ficos 3D hay que hacer primero los gr\ \[AAcute]ficos en un tama\[NTilde]o exagerado y luego reducirlos. As\[IAcute] \ obtienen una resoluci\[OAcute]n aceptable.\n\nEso es lo que hace la funci\ \[OAcute]n ", StyleBox["antialias", FontWeight->"Bold"], " definida aqu\[IAcute] abajo. Hace un imagen 2D ", Cell[BoxData[ FormBox["n", TraditionalForm]],ExpressionUUID-> "556e5ae3-21ae-4c6e-a78a-478fa3b3eda6"], " veces m\[AAcute]s grande de lo que queremos, v\[IAcute]a el comando ", StyleBox["Rasterize", FontWeight->"Bold"], ", y luego la reduce. " }], "Subchapter", CellFrame->{{0, 0}, {0, 0.5}}, CellChangeTimes->{{3.7310982793352003`*^9, 3.7310984112855997`*^9}, { 3.7311019906099997`*^9, 3.7311020169184*^9}, {3.7311020687696*^9, 3.7311020977396*^9}, {3.731156888818*^9, 3.7311568910986*^9}, { 3.731156923365*^9, 3.731157003677*^9}, {3.7311570511935997`*^9, 3.7311570521140003`*^9}, {3.7311577638008003`*^9, 3.731157885175*^9}, { 3.7311579268004*^9, 3.7311579494086*^9}, 3.7311579798297997`*^9}, FontSize->24,ExpressionUUID->"3f4f1de7-4f95-42cb-b321-fb75b43abf8c"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"antialias", "[", RowBox[{"g_", ",", RowBox[{"n_:", " ", "1"}]}], "]"}], ":=", RowBox[{"ImageResize", "[", RowBox[{ RowBox[{"Rasterize", "[", RowBox[{"g", ",", "\"\\"", ",", RowBox[{"ImageResolution", "\[Rule]", RowBox[{"n", " ", "72"}]}], ",", " ", RowBox[{"Background", "\[Rule]", "None"}]}], "]"}], ",", RowBox[{"Scaled", "[", RowBox[{"1", "/", "n"}], "]"}]}], "]"}]}], ";"}], " ", RowBox[{"(*", RowBox[{"ejecutar", " ", "esta", " ", "celda"}], "*)"}]}]], "Input", CellChangeTimes->{{3.7311032746092*^9, 3.7311032799132*^9}},ExpressionUUID->"4e06899b-33f4-450c-b40e-291c055e71fd"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Ejemplo: primero va el gr\[AAcute]fico en bruto y luego el antialiasiado. \ Comparen.\ \>", "Subchapter", CellChangeTimes->{{3.7310984416949997`*^9, 3.7310984455794*^9}, { 3.7310986974198*^9, 3.7310987098016*^9}, {3.7310987502146*^9, 3.7310987521022*^9}, {3.731102121543*^9, 3.7311021232352*^9}, { 3.7311579941288*^9, 3.7311580044398003`*^9}, {3.7312387764049997`*^9, 3.7312387797398*^9}}, FontSize->24,ExpressionUUID->"72eef60c-e16b-4e2e-8e98-663aec31c765"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"antialias", "[", RowBox[{"g_", ",", RowBox[{"n_:", " ", "1"}]}], "]"}], ":=", RowBox[{"ImageResize", "[", RowBox[{ RowBox[{"Rasterize", "[", RowBox[{"g", ",", "\"\\"", ",", RowBox[{"ImageResolution", "\[Rule]", RowBox[{"n", " ", "72"}]}], ",", " ", RowBox[{"Background", "\[Rule]", "None"}]}], "]"}], ",", RowBox[{"Scaled", "[", RowBox[{"1", "/", "n"}], "]"}]}], "]"}]}], ";"}], " ", RowBox[{"(*", RowBox[{ "repito", " ", "la", " ", "definici\[OAcute]n", " ", "por", " ", "las", " ", "dudas"}], "*)"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Module", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"y", ",", " ", "\[Phi]", ",", " ", RowBox[{"t", " ", "=", "2"}], ",", " ", RowBox[{"ran", " ", "=", " ", "2"}], ",", " ", "orb", ",", " ", "ejes"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"y", " ", "=", " ", RowBox[{"Y", "[", "t", "]"}]}], ",", " ", RowBox[{"\[Phi]", " ", "=", " ", RowBox[{"Phi", "[", "t", "]"}]}]}], "}"}], ";", "\[IndentingNewLine]", RowBox[{"orb", " ", "=", " ", RowBox[{"ParametricPlot3D", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{ RowBox[{"Y", "[", "\[Tau]", "]"}], "+", RowBox[{"Sin", "[", RowBox[{"Phi", "[", "\[Tau]", "]"}], "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", RowBox[{"Phi", "[", "\[Tau]", "]"}], "]"}]}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"\[Tau]", ",", " ", "0", ",", " ", "T"}], "}"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", " ", RowBox[{ RowBox[{"AbsoluteDashing", "[", RowBox[{"{", RowBox[{"5", ",", "8"}], "}"}], "]"}], ",", "Orange"}], "}"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ejes", " ", "=", " ", RowBox[{"Graphics3D", "[", RowBox[{"{", " ", RowBox[{"White", ",", RowBox[{"Specularity", "[", RowBox[{"White", ",", "100"}], "]"}], ",", RowBox[{"Tube", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "ran"}], ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "ran", ",", " ", "0"}], "}"}]}], "}"}], ",", " ", "0.012"}], "]"}], ",", RowBox[{"Tube", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", " ", RowBox[{"-", "ran"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "0", ",", "ran"}], "}"}]}], "}"}], ",", " ", "0.012"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"bruto", " ", "=", " ", RowBox[{"Show", "[", "\[IndentingNewLine]", RowBox[{ "orb", ",", "\[IndentingNewLine]", "ejes", ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{ RowBox[{"AbsoluteThickness", "[", "1", "]"}], ",", " ", "Blue", ",", RowBox[{"Specularity", "[", RowBox[{"White", ",", "20"}], "]"}], ",", " ", RowBox[{"Tube", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "y", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", RowBox[{"y", " ", "+", " ", RowBox[{"Sin", "[", "\[Phi]", "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], "}"}]}], "}"}], ",", " ", "0.03"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{"Green", ",", RowBox[{"Specularity", "[", RowBox[{"White", ",", "100"}], "]"}], ",", RowBox[{"Sphere", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"y", " ", "+", " ", RowBox[{"Sin", "[", "\[Phi]", "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], "}"}], ",", " ", "0.08"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{"Red", ",", " ", RowBox[{"Specularity", "[", RowBox[{"White", ",", "100"}], "]"}], ",", RowBox[{"Sphere", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "y", ",", " ", "0"}], "}"}], ",", " ", "0.08"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"AspectRatio", "\[Rule]", " ", "Automatic"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", " ", RowBox[{"ran", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "0.5"}], ",", " ", "0.5"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Ticks", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Background", "\[Rule]", " ", "Black"}], ",", "\[IndentingNewLine]", RowBox[{"BoxStyle", "\[Rule]", " ", RowBox[{"{", RowBox[{"White", ",", " ", RowBox[{"AbsoluteThickness", "[", "3", "]"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", " ", "600"}], ",", "\[IndentingNewLine]", RowBox[{"ViewVector", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"8", RowBox[{"{", RowBox[{"2", ",", " ", RowBox[{"-", "0.9"}], ",", " ", "0.5"}], "}"}]}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ViewAngle", "\[Rule]", " ", RowBox[{"17", "\[Degree]"}]}], ",", " ", "\[IndentingNewLine]", RowBox[{"PlotRangePadding", "\[Rule]", " ", "None"}]}], "\[IndentingNewLine]", "]"}]}]}]}], "\[IndentingNewLine]", "]"}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"antibruto", " ", "=", " ", RowBox[{"antialias", "[", RowBox[{"bruto", ",", " ", "3"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"ImageAssemble", "[", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"Image", "[", "bruto", "]"}], ",", " ", "antibruto"}], "}"}], "}"}], "]"}]}], "Input", CellChangeTimes->{{3.7310984527251997`*^9, 3.7310985845042*^9}, { 3.731098615995*^9, 3.731098740682*^9}, {3.7311021323929996`*^9, 3.731102156118*^9}, {3.7311032445011997`*^9, 3.7311032723627996`*^9}, { 3.7311582778*^9, 3.7311582882368*^9}, {3.7311595401774*^9, 3.731159558703*^9}, {3.7311607458606*^9, 3.7311607611566*^9}, { 3.7311635430802*^9, 3.7311635707178*^9}, {3.731163625175*^9, 3.7311636504393997`*^9}, {3.7311637062464*^9, 3.7311637078552*^9}, { 3.7311638132662*^9, 3.7311638656382*^9}, {3.731169580472*^9, 3.7311696187637997`*^9}, {3.7311696857167997`*^9, 3.7311697133554*^9}, { 3.7311697871034*^9, 3.7311697908473997`*^9}, {3.7311698501826*^9, 3.7311698785146*^9}},ExpressionUUID->"1ccef054-63f1-4a14-a3fd-9296ffae9f70"], Cell[TextData[{ "Noten sobre todo c\[OAcute]mo cambian las l\[IAcute]neas rectas entre una \ figura y la otra. Noten tambi\[EAcute]n que rescalear y antialiazar el gr\ \[AAcute]fico no es un proceso r\[AAcute]pido.\n\nNo exageren con la ampliaci\ \[OAcute]n auxiliar. Aqu\[IAcute] un valor de n = 3 significa que en los \ pasos intermedios el ", StyleBox["Mathematica", FontSlant->"Italic"], " maneja im\[AAcute]genes de 1800 px, ya que el original tiene 600 px" }], "Text", CellChangeTimes->{{3.7311021734102*^9, 3.731102250598*^9}, { 3.7311581805966*^9, 3.731158183079*^9}, {3.7311607795666*^9, 3.7311608053624*^9}, {3.7311699095404*^9, 3.7311699170188*^9}, { 3.7311917340002003`*^9, 3.7311917548752003`*^9}, {3.7314179150998*^9, 3.731417917824*^9}},ExpressionUUID->"4e224949-7649-47ce-bb70-7c76a4f67508"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "L\[IAcute]nea de producci\[OAcute]n para hacer un gif como la gente.\n\n\ Cada gr\[AAcute]fico es sometido al proceso de antialias.\n\nPresten atenci\ \[OAcute]n al uso del comando ", StyleBox["Monitor", FontWeight->"Bold"], ", que les permite ir viendo los resultados, y, en caso de que est\[EAcute] \ dando cualquier cosa, pueden interrumpir la evaluaci\[OAcute]n (\"Alt + .\") \ sin necesidad de esperar a que llegue a su t\[EAcute]rmino natural. \n\nPuede \ tardar varios minutos." }], "Subchapter", CellFrame->{{0, 0}, {0, 0.5}}, CellChangeTimes->{{3.7310987987164*^9, 3.7310988097953997`*^9}, { 3.7310988573386*^9, 3.7310989645994*^9}, {3.7310994739962*^9, 3.7310994981470003`*^9}, {3.7311023940467997`*^9, 3.7311024126085997`*^9}, { 3.7311570665982*^9, 3.7311570678638*^9}, {3.7311576225982*^9, 3.7311576235341997`*^9}, {3.7311582020488*^9, 3.7311582025656*^9}, { 3.7311608231982*^9, 3.7311608348096*^9}, {3.7311917877132*^9, 3.7311918053012*^9}}, FontSize->24,ExpressionUUID->"4857f20c-f536-49f6-9065-2cfe6430cbd6"], Cell[TextData[StyleBox["ATENCI\[CapitalOAcute]N: A esta altura ya sabr\ \[AAcute]n si el movimiento que van a animar es de rotaci\[OAcute]n o de \ oscilaci\[OAcute]n. Para no calcular cosas de m\[AAcute]s, en el primer caso \ habr\[AAcute] que redefinir Tverdadero = T/2.", FontSize->18]], "Text", CellDingbat->"\[WatchIcon]", CellChangeTimes->{{3.7311639382852*^9, 3.7311640106806*^9}, { 3.731164075072*^9, 3.7311640765861998`*^9}}, FontColor->RGBColor[ 1, 0, 0],ExpressionUUID->"e82fa16c-d4e6-4a44-b54e-375e573b712b"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"antialias", "[", RowBox[{"g_", ",", RowBox[{"n_:", " ", "1"}]}], "]"}], ":=", RowBox[{"ImageResize", "[", RowBox[{ RowBox[{"Rasterize", "[", RowBox[{"g", ",", "\"\\"", ",", RowBox[{"ImageResolution", "\[Rule]", RowBox[{"n", " ", "72"}]}], ",", " ", RowBox[{"Background", "\[Rule]", "None"}]}], "]"}], ",", RowBox[{"Scaled", "[", RowBox[{"1", "/", "n"}], "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"$HistoryLength", " ", "=", " ", "0"}], ";"}], " ", RowBox[{"(*", " ", RowBox[{ "Prevenci\[OAcute]n", " ", "v\[AAcute]lida", " ", "para", " ", "que", " ", "no", " ", "queden", " ", "resultados", " ", "innecesarios", " ", "almacenados", " ", "en", " ", "el", " ", "Historial"}], " ", "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Clear", "[", "AnimaTabla", "]"}], ";"}], " ", RowBox[{"(*", " ", RowBox[{ "En", " ", "prevenci\[OAcute]n", " ", "de", " ", "que", " ", "se", " ", "haya", " ", "calculado", " ", "antes", " ", "y", " ", "ocupe", " ", "mucha", " ", RowBox[{"memoria", "."}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Module", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Tverdadero", " ", "=", " ", RowBox[{"T", "/", "2"}]}], ",", " ", RowBox[{"(*", RowBox[{ "dejar", " ", "\"\\"", " ", "si", " ", "el", " ", "movimiento", " ", "es", " ", "de", " ", "oscilaci\[OAcute]n"}], "*)"}], "\[IndentingNewLine]", " ", RowBox[{"Ncuadros", " ", "=", " ", "100"}], ",", " ", RowBox[{"(*", " ", RowBox[{ "Disminuyan", " ", "el", " ", "n\[UAcute]mero", " ", "de", " ", "cuadros", " ", "si", " ", "tienen", " ", "poca", " ", RowBox[{"paciencia", "."}]}], " ", "*)"}], "\[IndentingNewLine]", " ", "y", ",", " ", "\[Phi]", ",", " ", RowBox[{"ran", " ", "=", " ", "2"}], ",", " ", "\[CapitalDelta]", ",", " ", RowBox[{"pasos", " ", "=", " ", "0"}], ",", " ", "orb", ",", "ejes", ",", " ", RowBox[{"bruto", "=", RowBox[{"Graphics", "[", "]"}]}], ",", " ", RowBox[{"rescaleado", "=", RowBox[{"Graphics", "[", "]"}]}]}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[CapitalDelta]", " ", "=", " ", RowBox[{"Tverdadero", "/", "Ncuadros"}]}], ";", " ", RowBox[{"(*", RowBox[{ "el", " ", "paso", " ", "temporal", " ", "entre", " ", "cuadros", " ", "sucesivos"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"orb", " ", "=", " ", RowBox[{"ParametricPlot3D", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{ RowBox[{"Y", "[", "\[Tau]", "]"}], "+", RowBox[{"Sin", "[", RowBox[{"Phi", "[", "\[Tau]", "]"}], "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", RowBox[{"Phi", "[", "\[Tau]", "]"}], "]"}]}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"\[Tau]", ",", " ", "0", ",", " ", "Tverdadero"}], "}"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", " ", RowBox[{ RowBox[{"AbsoluteDashing", "[", RowBox[{"{", RowBox[{"5", ",", " ", "8"}], "}"}], "]"}], ",", "Orange"}], "}"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ejes", " ", "=", " ", RowBox[{"Graphics3D", "[", RowBox[{"{", " ", RowBox[{"White", ",", RowBox[{"Specularity", "[", RowBox[{"White", ",", "100"}], "]"}], ",", RowBox[{"Tube", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "ran"}], ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "ran", ",", " ", "0"}], "}"}]}], "}"}], ",", " ", "0.012"}], "]"}], ",", RowBox[{"Tube", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", " ", RowBox[{"-", "ran"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "0", ",", "ran"}], "}"}]}], "}"}], ",", " ", "0.012"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Monitor", " ", "[", " ", RowBox[{"(*", RowBox[{ "este", " ", "comando", " ", "permite", " ", "ir", " ", "viendo", " ", "las", " ", "variables", " ", "que", " ", "uno", " ", RowBox[{"elija", " ", "[", RowBox[{ "que", " ", "se", " ", "indican", " ", "al", " ", "final", " ", "de", " ", "todo"}], "]"}], " ", "a", " ", "medida", " ", "que", " ", "se", " ", "ejecuta", " ", "la", " ", "celda"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"AnimaTabla", " ", "=", " ", RowBox[{"(*", RowBox[{ "en", " ", "esta", " ", "tabla", " ", "voy", " ", "almacenando", " ", "los", " ", "cuadros", " ", "para", " ", "hacer", " ", "luego", " ", "la", " ", "animaci\[OAcute]n"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", " ", RowBox[{"Table", "[", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"y", " ", "=", " ", RowBox[{"Y", "[", "t", "]"}]}], ",", " ", RowBox[{"\[Phi]", " ", "=", " ", RowBox[{"Phi", "[", "t", "]"}]}]}], "}"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"bruto", " ", "=", " ", RowBox[{"Show", "[", "\[IndentingNewLine]", RowBox[{ "orb", ",", "\[IndentingNewLine]", "ejes", ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{ RowBox[{"AbsoluteThickness", "[", "1", "]"}], ",", " ", "Blue", ",", RowBox[{"Specularity", "[", RowBox[{"White", ",", "20"}], "]"}], ",", " ", RowBox[{"Tube", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "y", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", RowBox[{"y", " ", "+", " ", RowBox[{"Sin", "[", "\[Phi]", "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], "}"}]}], "}"}], ",", " ", "0.02"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{"Green", ",", RowBox[{"Specularity", "[", RowBox[{"White", ",", "100"}], "]"}], ",", RowBox[{"Sphere", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"y", " ", "+", " ", RowBox[{"Sin", "[", "\[Phi]", "]"}]}], ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], "}"}], ",", " ", "0.08"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{"Red", ",", " ", RowBox[{"Specularity", "[", RowBox[{"White", ",", "100"}], "]"}], ",", RowBox[{"Sphere", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "y", ",", " ", "0"}], "}"}], ",", " ", "0.08"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"AspectRatio", "\[Rule]", " ", "Automatic"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", " ", RowBox[{"ran", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "0.5"}], ",", " ", "0.5"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Ticks", "\[Rule]", " ", "False"}], ",", "\[IndentingNewLine]", RowBox[{"Background", "\[Rule]", " ", "Black"}], ",", "\[IndentingNewLine]", RowBox[{"BoxStyle", "\[Rule]", " ", RowBox[{"{", RowBox[{"White", ",", " ", RowBox[{"AbsoluteThickness", "[", "3", "]"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", " ", "600"}], ",", "\[IndentingNewLine]", RowBox[{"ViewVector", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"8", RowBox[{"{", RowBox[{"2", ",", " ", RowBox[{"-", "0.9"}], ",", " ", "0.5"}], "}"}]}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ViewAngle", "\[Rule]", " ", RowBox[{"17", "\[Degree]"}]}], ",", " ", "\[IndentingNewLine]", RowBox[{"PlotRangePadding", "\[Rule]", " ", "None"}]}], "\[IndentingNewLine]", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"++", "pasos"}], ";", " ", RowBox[{"(*", RowBox[{ "voy", " ", "llevando", " ", "la", " ", "cuenta", " ", "de", " ", "los", " ", "cuadros", " ", "para", " ", "que", " ", "los", " ", "muestre", " ", "Monitor"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"rescaleado", " ", "=", " ", RowBox[{"antialias", "[", RowBox[{"bruto", ",", " ", "3"}], "]"}]}]}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", RowBox[{"Tverdadero", "-", "\[CapitalDelta]"}], ",", "\[CapitalDelta]"}], "}"}]}], "\[IndentingNewLine]", "]"}]}], ";"}], " ", ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{"Abajo", ":", " ", RowBox[{ "las", " ", "variables", " ", "que", " ", "muestra", " ", "el", " ", "comando", " ", RowBox[{"Monitor", ".", " ", "Incluyo"}], " ", "la", " ", "Memoria", " ", "en", " ", "Uso", " ", "para", " ", "tener", " ", "una", " ", "idea", " ", "de", " ", "si", " ", "va", " ", "a", " ", "alcanzar", " ", "la", " ", "memoria", " ", RowBox[{"RAM", ".", " ", "Caso"}], " ", "contrario"}]}], ",", " ", RowBox[{ "habr\[AAcute]", " ", "que", " ", "ir", " ", "guardando", " ", "las", " ", "figuras", " ", "en", " ", RowBox[{"archivos", "."}]}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"pasos", ",", " ", RowBox[{"Show", "[", RowBox[{"bruto", ",", " ", RowBox[{"ImageSize", "\[Rule]", " ", "400"}]}], "]"}], ",", " ", RowBox[{"Show", "[", RowBox[{"rescaleado", ",", " ", RowBox[{"ImageSize", "\[Rule]", " ", "400"}]}], "]"}], ",", " ", RowBox[{"MemoryInUse", "[", "]"}]}], "}"}]}], " ", "\[IndentingNewLine]", "]"}]}]}], "\[IndentingNewLine]", "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"$HistoryLength", " ", "=", " ", "\[Infinity]"}], ";"}]}], "Input", CellChangeTimes->{{3.731098827521*^9, 3.7310988553417997`*^9}, { 3.7310989786902*^9, 3.7310992668464003`*^9}, {3.7310993137958*^9, 3.731099317572*^9}, {3.73109935475*^9, 3.7310994540866003`*^9}, { 3.7311022933532*^9, 3.731102345531*^9}, {3.7311033047952003`*^9, 3.7311033049824*^9}, {3.73110334626*^9, 3.73110337044*^9}, 3.7311034553196*^9, {3.7311044481036*^9, 3.7311044614728003`*^9}, { 3.7311582251738*^9, 3.7311582635518*^9}, {3.7311583023318*^9, 3.7311583919166*^9}, {3.7311584930629997`*^9, 3.7311584934091997`*^9}, { 3.7311585308602*^9, 3.731158613002*^9}, {3.7311586923774*^9, 3.7311587092530003`*^9}, {3.7311595785868*^9, 3.7311596076196003`*^9}, 3.7311596467223997`*^9, {3.731160865377*^9, 3.7311608756468*^9}, { 3.7311613852539997`*^9, 3.7311613881108*^9}, {3.731161612039*^9, 3.731161670799*^9}, {3.7311617059236*^9, 3.7311617360358*^9}, { 3.7311638468066*^9, 3.7311638703202*^9}, {3.7311640290193996`*^9, 3.7311642360722*^9}, {3.7311918597911997`*^9, 3.7311918779512*^9}, { 3.7312388489868*^9, 3.7312388491428003`*^9}, {3.7312388792886*^9, 3.731238921374*^9}},ExpressionUUID->"e19fcc93-ec46-47e9-a17c-f2c78e9b258c"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Abajo: la animaci\[OAcute]n con los gr\[AAcute]ficos ", StyleBox["remasterizados.", FontSlant->"Italic"] }], "Subchapter", CellChangeTimes->{{3.731158465172*^9, 3.7311584869231997`*^9}}, FontSize->24,ExpressionUUID->"921f8316-6218-431a-a75e-5894956aa950"], Cell[BoxData[ RowBox[{"Manipulate", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"AnimaTabla", "[", RowBox[{"[", "i", "]"}], "]"}], ",", " ", RowBox[{"{", RowBox[{"i", ",", " ", "1", ",", " ", RowBox[{"Length", "[", "AnimaTabla", "]"}], ",", " ", "1", ",", " ", RowBox[{"Appearance", "\[Rule]", " ", "\"\\""}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.7311033781776*^9, 3.7311034032*^9}},ExpressionUUID->"884a4a7f-48da-452c-b8c7-4312e9c97196"], Cell["\[DownExclamation]Qu\[EAcute] diferencia, se\[NTilde]ores!", "Text", CellDingbat->"\[HappySmiley]", CellChangeTimes->{{3.7311920400662003`*^9, 3.7311920492412*^9}},ExpressionUUID->"29598463-e782-4406-a8aa-8d65b9dca49b"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Exporto un gif con los cuadros de la animaci\[OAcute]n guardados en \ AnimaTabla. Puede tomar de 1 a 3 minutos.\ \>", "Subchapter", CellDingbat->"\[WatchIcon]", CellChangeTimes->{{3.7311024321198*^9, 3.7311024595692*^9}, { 3.7311619874676*^9, 3.731161991587*^9}, {3.7311919264312*^9, 3.7311919501672*^9}}, FontSize->24,ExpressionUUID->"58848a57-3702-445e-aa38-feb2d6f9ddcc"], Cell[BoxData[{ RowBox[{ RowBox[{"SetDirectory", "[", RowBox[{"NotebookDirectory", "[", "]"}], "]"}], ";"}], "\n", RowBox[{"AbsoluteTiming", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Export", "[", RowBox[{ "\"\\"", ",", " ", "AnimaTabla", ",", " ", "\"\\"", ",", " ", RowBox[{"\"\\"", "\[Rule]", " ", RowBox[{"1", "/", "25"}]}]}], "]"}], ";"}], "\[IndentingNewLine]", "]"}]}], "Input", CellChangeTimes->{{3.7311024687022*^9, 3.7311025099578*^9}, { 3.7311038846784*^9, 3.73110389967*^9}, {3.7311618458964*^9, 3.7311618654611998`*^9}, {3.7311619989*^9, 3.7311620021926003`*^9}, { 3.73116284906*^9, 3.7311628523282003`*^9}, {3.7311628911736*^9, 3.7311629239546003`*^9}},ExpressionUUID->"4996f75c-3de1-4b0b-9158-\ f432c120874a"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Alternativamente, para poder editar los cuadros por fuera del ", StyleBox["Mathematica", FontSlant->"Italic"], ", los guardo en un directorio aparte. Luego puedo manipularlos en otro \ programa." }], "Subchapter", CellChangeTimes->{{3.7311047137332*^9, 3.7311047416008*^9}}, FontSize->24,ExpressionUUID->"2efd6b1c-1f5d-4e11-aea7-d5239a219396"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{ "Presten", " ", "atenci\[OAcute]n", " ", "al", " ", "uso", " ", "de", " ", "las", " ", "dobles", " ", "barras", " ", "para", " ", "indicar", " ", "la", " ", RowBox[{"ruta", ".", " ", "Si"}], " ", "est\[AAcute]n", " ", "usando", " ", "Linux", " ", "deber\[AAcute]n", " ", "cambiarlas", " ", RowBox[{"por", " ", "/", " ", "o"}], " ", "quiz\[AAcute]"}], " ", "//"}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ "SetDirectory", "[", "\"\\"", "]"}], ";"}], " ", "\n", "\[IndentingNewLine]", RowBox[{"Monitor", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"i", " ", "=", " ", "1"}], ",", " ", RowBox[{"i", " ", "\[LessEqual]", " ", RowBox[{"Length", "[", "AnimaTabla", "]"}]}], ",", " ", RowBox[{"++", "i"}], ",", " ", RowBox[{"(*", " ", RowBox[{ "El", " ", "comando", " ", "For", " ", "tiene", " ", "una", " ", "sint\[AAcute]xis", " ", "transparente"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"Export", "[", RowBox[{ RowBox[{"StringJoin", "[", RowBox[{"\"\\"", ",", " ", RowBox[{"If", "[", RowBox[{ RowBox[{"i", " ", "<", " ", "10"}], ",", " ", "\"\<000\>\"", ",", " ", RowBox[{"If", "[", RowBox[{ RowBox[{"i", " ", "<", " ", "100"}], ",", " ", "\"\<00\>\"", ",", " ", "\"\<0\>\""}], "]"}]}], "]"}], ",", " ", RowBox[{"ToString", "[", "i", "]"}], ",", " ", "\"\<.png\>\""}], "]"}], ",", " ", RowBox[{"AnimaTabla", "[", RowBox[{"[", "i", "]"}], "]"}], ",", " ", "\"\\""}], "]"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";"}], ",", " ", "\[IndentingNewLine]", "i"}], " ", RowBox[{"(*", " ", RowBox[{ RowBox[{ "\"\\"", " ", "es", " ", "la", " ", "variable", " ", "que", " ", "muestra", " ", "el", " ", "comando", " ", "Monitor"}], ";", " ", RowBox[{ "la", " ", "cosa", " ", "no", " ", "se", " ", "acaba", " ", "hasta", " ", "que", " ", "\"\\"", " ", "no", " ", "llega", " ", "al", " ", "n\[UAcute]mero", " ", "de", " ", "cuadros", " ", "guardados", " ", "en", " ", "AnimaTabla"}]}], "*)"}], "\[IndentingNewLine]", "]"}]}]}]], "Input", CellChangeTimes->{{3.7311039599639997`*^9, 3.7311040046268*^9}, 3.7311047128908*^9, {3.7311047498375998`*^9, 3.7311047555492*^9}, { 3.7311618673176003`*^9, 3.7311618840332003`*^9}, {3.7311620362106*^9, 3.7311620414230003`*^9}, {3.7311621160366*^9, 3.7311621205304003`*^9}},ExpressionUUID->"bd971b87-7c6e-495e-b4db-\ 81ce536a9705"], Cell[TextData[{ "Dentro del ", StyleBox["Export", FontWeight->"Bold"], ", la funci\[OAcute]n del StringJoin es construir el nombre de cada archivo. \ El par de If agrega ceros antes del n\[UAcute]mero de cuadro para que luego \ se ordenen correctamente. El comando Monitor nos permite planificar en qu\ \[EAcute] usaremos los pr\[OAcute]ximos segundos, minutos u horas, en el peor \ de los casos. " }], "Text", CellChangeTimes->{{3.7311041039208*^9, 3.7311042686256*^9}, 3.7311619295620003`*^9}, FontSize->18,ExpressionUUID->"065ed977-8563-4faf-acfe-b812179b474c"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Detr\[AAcute]s de la escena: el Lagrangiano y las ecuaciones de \ movimiento a trav\[EAcute]s del ", FontSize->24], StyleBox["Mathematica.", FontSize->24, FontSlant->"Italic"], " ", StyleBox["(expandir la celda)", FontSize->18] }], "Chapter", CellFrame->{{0, 0}, {0, 2}}, CellDingbat->"\[GrayCircle]", CellChangeTimes->{{3.7312389855204*^9, 3.731239015547*^9}, { 3.7312422120722*^9, 3.7312422167858*^9}},ExpressionUUID->"f52ab122-7cd0-4141-9792-96a27b025e70"], Cell[CellGroupData[{ Cell["Problema 5:", "Subchapter", CellChangeTimes->{{3.7312390232774*^9, 3.7312390264114*^9}},ExpressionUUID->"9d8340b2-be1d-467a-b269-9142899d064d"], Cell[BoxData[ RowBox[{ RowBox[{"Quit", "[", "]"}], ";"}]], "Input", CellChangeTimes->{{3.7312391720797997`*^9, 3.731239187289*^9}, { 3.73123924446*^9, 3.7312392447408*^9}, {3.7312399033532*^9, 3.7312399086284*^9}, {3.7312409373746*^9, 3.7312409384695997`*^9}},ExpressionUUID->"ae4c363c-43c0-4627-8016-\ 1335ca2fd204"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ "Posiciones", " ", "en", " ", "t\[EAcute]rminos", " ", "de", " ", "la", " ", "coordenada", " ", "generalizada", " ", "\[Phi]"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"r1", "[", "\[Phi]_", "]"}], ":=", RowBox[{"l", " ", RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"Sin", "[", "\[Phi]", "]"}]}], ",", " ", "0"}], "}"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"r2", "[", "\[Phi]_", "]"}], ":=", " ", RowBox[{"l", RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], "}"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "Energ\[IAcute]a", " ", "cin\[EAcute]tica", " ", "y", " ", "energ\[IAcute]a", " ", "potencial"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"T", "[", RowBox[{"\[Phi]_", ",", " ", "\[Phi]p_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", "Phi", "}"}], ",", " ", RowBox[{"(*", " ", RowBox[{ "variable", " ", "auxiliar", " ", "para", " ", "hacer", " ", "reemplazos"}], " ", "*)"}], "\[IndentingNewLine]", " ", RowBox[{ RowBox[{ RowBox[{ FractionBox["1", "2"], "m1", " ", RowBox[{"(", RowBox[{ RowBox[{"D", "[", RowBox[{ RowBox[{"r1", "[", RowBox[{"Phi", "[", "t", "]"}], "]"}], ",", " ", "t"}], "]"}], " ", ".", " ", RowBox[{"D", "[", RowBox[{ RowBox[{"r1", "[", RowBox[{"Phi", "[", "t", "]"}], "]"}], ",", " ", "t"}], "]"}]}], ")"}]}], " ", "+", " ", RowBox[{ FractionBox["1", "2"], "m2", " ", RowBox[{"(", RowBox[{ RowBox[{"D", "[", RowBox[{ RowBox[{"r2", "[", RowBox[{"Phi", "[", "t", "]"}], "]"}], ",", " ", "t"}], "]"}], " ", ".", " ", RowBox[{"D", "[", RowBox[{ RowBox[{"r2", "[", RowBox[{"Phi", "[", "t", "]"}], "]"}], ",", " ", "t"}], "]"}]}], ")"}]}]}], " ", "/.", " ", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Phi", "[", "t", "]"}], "\[Rule]", " ", "\[Phi]"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"Phi", "'"}], "[", "t", "]"}], "\[Rule]", " ", "\[Phi]p"}]}], "}"}]}]}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"V", "[", "\[Phi]_", "]"}], ":=", " ", RowBox[{"m2", " ", "g", " ", "l", " ", RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", "Lagrangiano", " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"L", "[", RowBox[{"\[Phi]_", ",", " ", "\[Phi]p_"}], "]"}], ":=", " ", RowBox[{ RowBox[{"T", "[", RowBox[{"\[Phi]", ",", " ", "\[Phi]p"}], "]"}], " ", "-", " ", RowBox[{"V", "[", "\[Phi]", "]"}]}]}], ";"}]}]}]], "Input", CellChangeTimes->{{3.731239029712*^9, 3.731239134333*^9}, { 3.7312392064318*^9, 3.7312392505192003`*^9}, {3.7312392863157997`*^9, 3.731239354568*^9}, {3.7312397538742*^9, 3.7312397946893997`*^9}, { 3.7312420611486*^9, 3.7312420674086*^9}},ExpressionUUID->"589c7058-654c-41c2-877e-1d78a9f60038"], Cell[BoxData[ RowBox[{"Collect", "[", RowBox[{ RowBox[{"L", "[", RowBox[{"\[Phi]", ",", " ", "\[Phi]p"}], "]"}], ",", " ", RowBox[{"{", RowBox[{"\[Phi]p", ",", " ", "m1", ",", " ", "m2"}], "}"}], ",", " ", "Simplify"}], "]"}]], "Input", CellChangeTimes->{{3.7312420941142*^9, 3.7312421307827997`*^9}},ExpressionUUID->"bd0b03f8-7d54-48f1-85f2-\ d2cce1c731f4"], Cell[CellGroupData[{ Cell["\<\ Ecuaci\[OAcute]n de movimiento en forma directa. Simplificada paso a paso \ como hicimos en clase.\ \>", "Subsection", CellChangeTimes->{{3.7312405028696003`*^9, 3.731240534801*^9}},ExpressionUUID->"455f6745-5178-4414-9a49-c9022d566972"], Cell[BoxData[ RowBox[{"ec", " ", "=", " ", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{"D", "[", RowBox[{ RowBox[{"D", "[", RowBox[{ RowBox[{"L", "[", RowBox[{ RowBox[{"\[Phi]", "[", "t", "]"}], ",", " ", RowBox[{"\[Phi]p", "[", "t", "]"}]}], "]"}], ",", " ", RowBox[{"\[Phi]p", "[", "t", "]"}]}], "]"}], ",", " ", "t"}], "]"}], " ", "-", " ", RowBox[{"D", "[", RowBox[{ RowBox[{"L", "[", RowBox[{ RowBox[{"\[Phi]", "[", "t", "]"}], ",", " ", RowBox[{"\[Phi]p", "[", "t", "]"}]}], "]"}], ",", " ", RowBox[{"\[Phi]", "[", "t", "]"}]}], "]"}]}], " ", "/.", " ", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"\[Phi]p", "[", "t", "]"}], "\[Rule]", " ", RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "t", "]"}]}], ",", " ", RowBox[{ RowBox[{ RowBox[{"\[Phi]p", "'"}], "[", "t", "]"}], "\[Rule]", " ", RowBox[{ RowBox[{"\[Phi]", "''"}], "[", "t", "]"}]}]}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.731239299729*^9, 3.7312393065858*^9}, { 3.7312393604556*^9, 3.731239393809*^9}, {3.7312394518938*^9, 3.7312395375708*^9}, {3.7312398405634003`*^9, 3.7312398976870003`*^9}, 3.7312400498526*^9, {3.7312404996918*^9, 3.731240511617*^9}},ExpressionUUID->"ab44661f-71f2-4770-8759-782626281fb2"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{ "Para", " ", "hacerla", " ", "m\[AAcute]s", " ", "legible", " ", "abrevio", " ", RowBox[{"\[Phi]", "[", "t", "]"}], " ", "como", " ", "\[Phi]"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "t", "]"}], " ", "como", " ", RowBox[{"\[Phi]", "'"}], " ", "y", " ", RowBox[{ RowBox[{"\[Phi]", "''"}], "[", "t", "]"}], " ", "como", " ", RowBox[{"\[Phi]", "''"}]}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"ecsimple", " ", "=", " ", RowBox[{"ec", " ", "/.", " ", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"\[Phi]", "[", "t", "]"}], "\[Rule]", " ", "\[Phi]"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "t", "]"}], "\[Rule]", " ", RowBox[{"\[Phi]", "'"}]}], ",", " ", RowBox[{ RowBox[{ RowBox[{"\[Phi]", "''"}], "[", "t", "]"}], "\[Rule]", " ", RowBox[{"\[Phi]", "''"}]}]}], "}"}]}]}]}]], "Input", CellChangeTimes->{{3.7312400592436*^9, 3.7312401311400003`*^9}, { 3.7312402160274*^9, 3.7312402621434*^9}},ExpressionUUID->"dba70983-95c3-4c89-9f81-7a3f362d30ce"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{"Defino", " ", "la", " ", "frecuencia", " ", "g"}], " ", "=", " ", RowBox[{ SuperscriptBox["\[Omega]", RowBox[{"2", " "}]], "l"}]}], ",", " ", RowBox[{ "y", " ", "divido", " ", "la", " ", "ecuaci\[OAcute]n", " ", "por", " ", RowBox[{ SuperscriptBox["l", "2"], ".", " ", "Se"}], " ", "va", " ", RowBox[{"l", "."}]}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"ecsimple2", " ", "=", " ", RowBox[{"Simplify", "[", RowBox[{ FractionBox["1", SuperscriptBox["l", "2"]], RowBox[{"(", RowBox[{"ecsimple", "/.", " ", RowBox[{"g", "\[Rule]", " ", RowBox[{"l", " ", SuperscriptBox["\[Omega]", "2"]}]}]}], ")"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.7312399234546003`*^9, 3.7312400458938*^9}, { 3.7312401400484*^9, 3.7312402092194*^9}, {3.7312402806858*^9, 3.7312402898096*^9}, {3.731240325351*^9, 3.731240332007*^9}, { 3.73124045345*^9, 3.7312404568598003`*^9}, {3.7312405580629997`*^9, 3.7312406036152*^9}},ExpressionUUID->"22128bfb-1c94-494b-b3b3-638c546548cf"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{"Luego", " ", "defino", " ", "m1"}], " ", "=", " ", RowBox[{ "\[Mu]", " ", "m2", " ", "y", " ", "divido", " ", "la", " ", "ecuaci\[OAcute]n", " ", "por", " ", RowBox[{"m2", ".", " ", "Se"}], " ", "va", " ", "m2"}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"ecsimple3", " ", "=", " ", RowBox[{"Simplify", "[", RowBox[{ FractionBox["1", "m2"], RowBox[{"(", RowBox[{"ecsimple2", "/.", " ", RowBox[{"{", RowBox[{"m1", "\[Rule]", " ", RowBox[{"\[Mu]", " ", "m2"}]}], "}"}]}], ")"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.7312399234546003`*^9, 3.7312400458938*^9}, { 3.7312401400484*^9, 3.7312402092194*^9}, {3.7312402806858*^9, 3.7312403393304*^9}, {3.7312404586688004`*^9, 3.7312404598262*^9}, { 3.7312405824558*^9, 3.7312406021896*^9}},ExpressionUUID->"1ad5acf1-161f-41c4-b6d2-ed44340a64d0"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{"Por", " ", "\[UAcute]ltimo"}], ",", " ", RowBox[{ RowBox[{"usar", " ", "\[Tau]"}], " ", "=", " ", RowBox[{ RowBox[{ "\[Omega]", " ", "t", " ", "en", " ", "lugar", " ", "de", " ", "t", " ", "equivale", " ", "a", " ", "definir", " ", "\[Omega]"}], " ", "=", " ", RowBox[{"1.", " ", "Se", " ", "va", " ", RowBox[{"\[Omega]", "."}]}]}]}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"ecfinal", "=", RowBox[{"ecsimple3", " ", "/.", " ", RowBox[{"\[Omega]", "\[Rule]", " ", "1"}]}]}]}]], "Input", CellChangeTimes->{{3.7312403619175997`*^9, 3.7312404682812*^9}, { 3.7312405872142*^9, 3.7312406049598*^9}},ExpressionUUID->"e5c696cb-ca3d-4457-90da-5ecadd7c799b"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Ecuaci\[OAcute]n de movimiento obtenida usando el comando EulerEquations:\ \>", "Subsection", CellChangeTimes->{{3.7312406915875998`*^9, 3.7312407197966003`*^9}},ExpressionUUID->"3146b37b-69ed-4337-80de-\ b1db5baaaa2b"], Cell[BoxData[ RowBox[{"Needs", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{{3.731240619472*^9, 3.7312406498062*^9}},ExpressionUUID->"277ebd5b-224f-4f5c-bc09-0e20daf95b96"], Cell[BoxData[ RowBox[{"ecEE", " ", "=", " ", RowBox[{ RowBox[{"EulerEquations", "[", RowBox[{ RowBox[{"L", "[", RowBox[{ RowBox[{"\[Phi]", "[", "t", "]"}], ",", " ", RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "t", "]"}]}], "]"}], ",", " ", RowBox[{"\[Phi]", "[", "t", "]"}], ",", " ", "t"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.7312406527314*^9, 3.7312406847162*^9}, { 3.7312407357278*^9, 3.731240745227*^9}, {3.7312408298198*^9, 3.7312408305861998`*^9}},ExpressionUUID->"75f6c674-3a7c-41f5-ae0e-\ 6c152f00a7a8"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"La", " ", "simplificamos", " ", "como", " ", "antes"}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"ecEEfinal", " ", "=", " ", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ FractionBox["1", RowBox[{ SuperscriptBox["l", "2"], "m2"}]], RowBox[{"(", RowBox[{"ecEE", " ", "/.", " ", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"\[Phi]", "[", "t", "]"}], "\[Rule]", " ", "\[Phi]"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "t", "]"}], "\[Rule]", " ", RowBox[{"\[Phi]", "'"}]}], ",", " ", RowBox[{ RowBox[{ RowBox[{"\[Phi]", "''"}], "[", "t", "]"}], "\[Rule]", " ", RowBox[{"\[Phi]", "''"}]}], ",", " ", RowBox[{"g", "\[Rule]", " ", RowBox[{"l", " ", SuperscriptBox["\[Omega]", "2"]}]}], ",", " ", RowBox[{"m1", "\[Rule]", " ", RowBox[{"\[Mu]", " ", "m2"}]}]}], "}"}]}], ")"}]}], "/.", " ", RowBox[{"\[Omega]", "\[Rule]", " ", "1"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.7312407499084*^9, 3.7312408160584*^9}, { 3.7312408554736*^9, 3.731240880358*^9}},ExpressionUUID->"132cb96b-90e3-4651-8c03-9350a4d37715"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"Salvo", " ", "el", " ", "signo"}], ",", " ", RowBox[{ "es", " ", "el", " ", "mismo", " ", "resultado", " ", "de", " ", "antes"}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Simplify", "[", RowBox[{"ecEEfinal", " ", "+", " ", "ecfinal"}], "]"}]}]], "Input", CellChangeTimes->{{3.731240881531*^9, 3.731240912611*^9}},ExpressionUUID->"6bc62cd3-c061-40a5-adfc-8ce3760a5073"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Problema 17:", "Subchapter", CellChangeTimes->{{3.7312390232774*^9, 3.7312390264114*^9}, { 3.7312409307528*^9, 3.7312409309712*^9}},ExpressionUUID->"2577ec34-0ae1-47fc-8156-c5804fca3157"], Cell[BoxData[ RowBox[{ RowBox[{"Quit", "[", "]"}], ";"}]], "Input", CellChangeTimes->{{3.7312391720797997`*^9, 3.731239187289*^9}, { 3.73123924446*^9, 3.7312392447408*^9}, {3.7312399033532*^9, 3.7312399086284*^9}, {3.7312409435794*^9, 3.7312409462872*^9}},ExpressionUUID->"b9a40ebb-121b-41d5-a9da-d252be07e217"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ "Posiciones", " ", "en", " ", "t\[EAcute]rminos", " ", "de", " ", "las", " ", "coordenadas", " ", "generalizadas", " ", RowBox[{"{", RowBox[{"y", ",", " ", "\[Phi]"}], "}"}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"r1", "[", RowBox[{"y_", ",", " ", "\[Phi]_"}], "]"}], ":=", " ", RowBox[{"{", RowBox[{"y", ",", " ", "0"}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"r2", "[", RowBox[{"y_", ",", " ", "\[Phi]_"}], "]"}], ":=", " ", RowBox[{ RowBox[{"r1", "[", RowBox[{"y", ",", " ", "\[Phi]"}], "]"}], " ", "+", " ", RowBox[{"l", RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"Cos", "[", "\[Phi]", "]"}]}], ",", " ", RowBox[{"Sin", "[", "\[Phi]", "]"}]}], "}"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "Energ\[IAcute]a", " ", "cin\[EAcute]tica", " ", "y", " ", "energ\[IAcute]a", " ", "potencial"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"T", "[", RowBox[{ "y_", ",", " ", "\[Phi]_", ",", " ", "yp_", ",", " ", "\[Phi]p_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"Phi", ",", " ", "Y"}], "}"}], ",", " ", RowBox[{"(*", " ", RowBox[{ "variables", " ", "auxiliares", " ", "para", " ", "hacer", " ", "reemplazos"}], " ", "*)"}], "\[IndentingNewLine]", " ", RowBox[{ RowBox[{ RowBox[{ FractionBox["1", "2"], "m1", " ", RowBox[{"(", RowBox[{ RowBox[{"D", "[", RowBox[{ RowBox[{"r1", "[", RowBox[{ RowBox[{"Y", "[", "t", "]"}], ",", " ", RowBox[{"Phi", "[", "t", "]"}]}], "]"}], ",", " ", "t"}], "]"}], " ", ".", " ", RowBox[{"D", "[", RowBox[{ RowBox[{"r1", "[", RowBox[{ RowBox[{"Y", "[", "t", "]"}], ",", " ", RowBox[{"Phi", "[", "t", "]"}]}], "]"}], ",", " ", "t"}], "]"}]}], ")"}]}], " ", "+", " ", RowBox[{ FractionBox["1", "2"], "m2", " ", RowBox[{"(", RowBox[{ RowBox[{"D", "[", RowBox[{ RowBox[{"r2", "[", RowBox[{ RowBox[{"Y", "[", "t", "]"}], ",", " ", RowBox[{"Phi", "[", "t", "]"}]}], "]"}], ",", " ", "t"}], "]"}], " ", ".", " ", RowBox[{"D", "[", RowBox[{ RowBox[{"r2", "[", RowBox[{ RowBox[{"Y", "[", "t", "]"}], ",", " ", RowBox[{"Phi", "[", "t", "]"}]}], "]"}], ",", " ", "t"}], "]"}]}], ")"}]}]}], " ", "/.", " ", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Y", "[", "t", "]"}], "\[Rule]", " ", "y"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"Y", "'"}], "[", "t", "]"}], "\[Rule]", " ", "yp"}], ",", " ", RowBox[{ RowBox[{"Phi", "[", "t", "]"}], "\[Rule]", " ", "\[Phi]"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"Phi", "'"}], "[", "t", "]"}], "\[Rule]", " ", "\[Phi]p"}]}], "}"}]}]}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"V", "[", RowBox[{"y_", ",", " ", "\[Phi]_"}], "]"}], ":=", " ", RowBox[{"m2", " ", "g", " ", "l", " ", RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", "Lagrangiano", " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"L", "[", RowBox[{ "y_", ",", " ", "\[Phi]_", ",", " ", "yp_", ",", " ", "\[Phi]p_"}], "]"}], ":=", " ", RowBox[{ RowBox[{"T", "[", RowBox[{"y", ",", " ", "\[Phi]", ",", " ", "yp", ",", " ", "\[Phi]p"}], "]"}], " ", "-", " ", RowBox[{"V", "[", RowBox[{"y", ",", " ", "\[Phi]"}], "]"}]}]}], ";"}]}]}]], "Input", CellChangeTimes->{{3.731239029712*^9, 3.731239134333*^9}, { 3.7312392064318*^9, 3.7312392505192003`*^9}, {3.7312392863157997`*^9, 3.731239354568*^9}, {3.7312397538742*^9, 3.7312397946893997`*^9}, { 3.7312409582602*^9, 3.731241166757*^9}, 3.7312412150698*^9, { 3.731242018222*^9, 3.7312420519955997`*^9}},ExpressionUUID->"351a6a90-cd43-4b44-a066-\ 12e6b6130951"], Cell[BoxData[ RowBox[{"Collect", "[", RowBox[{ RowBox[{"L", "[", RowBox[{"y", ",", " ", "\[Phi]", ",", " ", "yp", ",", " ", "\[Phi]p"}], "]"}], ",", " ", RowBox[{"{", RowBox[{"m1", ",", " ", "m2"}], "}"}], ",", " ", "Simplify"}], "]"}]], "Input", CellChangeTimes->{{3.7312411495797997`*^9, 3.7312412036865997`*^9}, { 3.7312412452792*^9, 3.731241247126*^9}},ExpressionUUID->"ff37a524-dc96-4eef-af36-65aaa61ee49e"], Cell[CellGroupData[{ Cell["\<\ Ecuaci\[OAcute]n de movimiento obtenida usando directamente EulerEquations:\ \>", "Subsection", CellChangeTimes->{{3.7312406915875998`*^9, 3.7312407197966003`*^9}, { 3.7312419257332*^9, 3.7312419307265997`*^9}},ExpressionUUID->"5b779bef-4e8b-467f-8265-\ 0f87807d5fd1"], Cell[BoxData[ RowBox[{"Needs", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{{3.731240619472*^9, 3.7312406498062*^9}},ExpressionUUID->"9d74b26b-2773-449d-b12d-778cec93ab3d"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Ahora", " ", "son", " ", "dos", " ", "ecuaciones"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"ecEE", " ", "=", " ", RowBox[{ RowBox[{"EulerEquations", "[", RowBox[{ RowBox[{"L", "[", RowBox[{ RowBox[{"y", "[", "t", "]"}], ",", " ", RowBox[{"\[Phi]", "[", "t", "]"}], ",", RowBox[{ RowBox[{"y", "'"}], "[", "t", "]"}], ",", " ", RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "t", "]"}]}], "]"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"y", "[", "t", "]"}], ",", " ", RowBox[{"\[Phi]", "[", "t", "]"}]}], "}"}], ",", " ", "t"}], "]"}], "[", RowBox[{"[", RowBox[{"All", ",", " ", "1"}], "]"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.7312406527314*^9, 3.7312406847162*^9}, { 3.7312407357278*^9, 3.731240745227*^9}, {3.7312408298198*^9, 3.7312408305861998`*^9}, {3.7312412992644*^9, 3.7312413373602*^9}, { 3.7312414983227997`*^9, 3.7312415115186*^9}},ExpressionUUID->"00ba6cb2-ca5f-42e7-b6e9-296aa8842c47"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{"Las", " ", "simplificamos", " ", "como", " ", "antes"}], ",", " ", RowBox[{ RowBox[{"definiendo", " ", "adicionalmente", " ", "l"}], " ", "=", " ", "1."}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"ecEEfinal", " ", "=", " ", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ FractionBox["1", "m2"], RowBox[{"(", RowBox[{"ecEE", " ", "/.", " ", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"y", "[", "t", "]"}], "\[Rule]", " ", "y"}], ",", " ", RowBox[{ RowBox[{"\[Phi]", "[", "t", "]"}], "\[Rule]", " ", "\[Phi]"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"y", "'"}], "[", "t", "]"}], "\[Rule]", " ", RowBox[{"y", "'"}]}], ",", " ", RowBox[{ RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "t", "]"}], "\[Rule]", " ", RowBox[{"\[Phi]", "'"}]}], ",", " ", RowBox[{ RowBox[{ RowBox[{"y", "''"}], "[", "t", "]"}], "\[Rule]", " ", RowBox[{"y", "''"}]}], ",", " ", RowBox[{ RowBox[{ RowBox[{"\[Phi]", "''"}], "[", "t", "]"}], "\[Rule]", " ", RowBox[{"\[Phi]", "''"}]}], ",", " ", RowBox[{"g", "\[Rule]", " ", RowBox[{"l", " ", SuperscriptBox["\[Omega]", "2"]}]}], ",", " ", RowBox[{"m1", "\[Rule]", " ", RowBox[{"\[Mu]", " ", "m2"}]}]}], "}"}]}], ")"}]}], "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"\[Omega]", "\[Rule]", " ", "1"}], ",", " ", RowBox[{"l", "\[Rule]", " ", "1"}]}], "}"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.7312407499084*^9, 3.7312408160584*^9}, { 3.7312408554736*^9, 3.731240880358*^9}, {3.7312413590648003`*^9, 3.7312413949886*^9}, {3.7312414374849997`*^9, 3.7312415454038*^9}, { 3.7312421836029997`*^9, 3.7312421846376*^9}},ExpressionUUID->"b19fa712-417b-4c85-9908-48d2b8eb40a5"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{"Despejando", " ", RowBox[{"y", "''"}], " ", "de", " ", "la", " ", "primera", " ", "ecuaci\[OAcute]n", " ", "y", " ", "reemplazando", " ", "en", " ", "la", " ", "segunda"}], ",", " ", RowBox[{ "se", " ", "obtiene", " ", "una", " ", "ecuaci\[OAcute]n", " ", "s\[OAcute]lo", " ", "para", " ", RowBox[{"\[Phi]", "."}]}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ypp", " ", "=", " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"ecEEfinal", "[", RowBox[{"[", "1", "]"}], "]"}], " ", "\[Equal]", " ", "0"}], ",", " ", RowBox[{"y", "''"}]}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"ec\[Phi]", " ", "=", RowBox[{"Collect", "[", RowBox[{ RowBox[{ RowBox[{"ecEEfinal", "[", RowBox[{"[", "2", "]"}], "]"}], " ", "/.", " ", RowBox[{ RowBox[{"y", "''"}], " ", "\[Rule]", " ", "ypp"}]}], ",", " ", RowBox[{"\[Phi]", "''"}], ",", " ", "FullSimplify"}], "]"}]}]}]}]], "Input", CellChangeTimes->{{3.7312415540576*^9, 3.731241671528*^9}, { 3.7312417969382*^9, 3.7312418077372*^9}, {3.7312419506144*^9, 3.7312419515222*^9}},ExpressionUUID->"df51f8a8-456a-46ad-9c89-96961133d39b"], Cell["\<\ Identidades trigonom\[EAcute]tricas mediante, con \[Mu] = m1, es la misma \ ecuaci\[OAcute]n que usamos al resolver num\[EAcute]ricamente el problema.\ \>", "Text", CellChangeTimes->{{3.7312418524358*^9, 3.7312419091944*^9}},ExpressionUUID->"a955cd3e-f690-4be8-94ed-a287da344c46"] }, Open ]] }, Open ]] }, Closed]] }, Open ]] }, WindowSize->{1440, 830}, WindowMargins->{{-8, Automatic}, {Automatic, -8}}, PrintingCopies->1, PrintingPageRange->{32000, 32000}, PrintingOptions->{"Magnification"->1., "PaperOrientation"->"Portrait", "PaperSize"->{595.2, 841.8000000000001}}, FrontEndVersion->"11.2 for Microsoft Windows (64-bit) (September 10, 2017)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[558, 20, 196, 5, 28, "Input",ExpressionUUID->"ad8591ff-5b42-4c26-962c-848863189d68"], Cell[757, 27, 278, 4, 67, "Chapter",ExpressionUUID->"9c4e5505-f8f1-481d-984d-2299da6278e6"], Cell[CellGroupData[{ Cell[1060, 35, 1179, 34, 186, "Title",ExpressionUUID->"8bdad1dd-09dc-4155-b357-b1d930cbc3f4"], Cell[2242, 71, 26401, 446, 844, "Text",ExpressionUUID->"8c96ebac-ca89-443f-967a-3e9ca7f35cf2"], Cell[CellGroupData[{ Cell[28668, 521, 347, 6, 53, "Subsection",ExpressionUUID->"546f0bb7-0235-4b53-b156-7f64a522c9de"], Cell[CellGroupData[{ Cell[29040, 531, 400, 7, 69, "Subsubsection",ExpressionUUID->"5ed0f335-5563-42a9-97c3-29ef72b4edd4"], Cell[29443, 540, 652, 12, 48, "Input",ExpressionUUID->"3fa9c547-8fea-451c-bd1b-1ae2cb3296a4"], Cell[30098, 554, 988, 20, 48, "Input",ExpressionUUID->"4fb22377-08c2-4ae8-9697-0e2f74f3468a"], Cell[31089, 576, 690, 13, 53, "Input",ExpressionUUID->"cf52d435-9dd1-44b8-a540-9195521b0511"], Cell[31782, 591, 1219, 26, 48, "Input",ExpressionUUID->"0dc369fc-41d3-49d4-80f0-49e55ae0af5e"], Cell[33004, 619, 878, 16, 48, "Input",ExpressionUUID->"d150aeb9-db72-4bb9-8eb9-81ebb5667dd6"], Cell[33885, 637, 966, 18, 67, "Input",ExpressionUUID->"69053c99-1681-4d93-ab6c-a145e058cdd0"], Cell[34854, 657, 1293, 27, 67, "Input",ExpressionUUID->"18c605f7-584b-4ae2-b261-1d1c7a22fc8f"], Cell[36150, 686, 483, 12, 136, "Input",ExpressionUUID->"3a2c607a-bab2-420e-a3e8-0095090e046e"], Cell[36636, 700, 2013, 41, 241, "Input",ExpressionUUID->"8eb7aded-d7db-46e8-8922-f0bbc7fc4cdc"], Cell[38652, 743, 629, 12, 72, "Input",ExpressionUUID->"b6005fc9-420b-4a37-9f8b-4a9a1da773b0"], Cell[39284, 757, 905, 20, 74, "Input",ExpressionUUID->"be1296cf-2dc0-41ba-ae18-326cf85b0000"], Cell[40192, 779, 1465, 35, 87, "Input",ExpressionUUID->"22d704fa-fcc6-44fe-850a-663a45401845"], Cell[41660, 816, 1867, 44, 162, "Input",ExpressionUUID->"fb1e753b-3815-4d78-9fbb-32b2d8689dec"], Cell[43530, 862, 436, 8, 38, "Text",ExpressionUUID->"b70631b8-0243-40f2-b06e-c1f2020787b3"], Cell[43969, 872, 619, 14, 48, "Input",ExpressionUUID->"f143dfec-1e17-47c7-9de1-2a05cb68b02b"], Cell[44591, 888, 801, 18, 52, "Input",ExpressionUUID->"c67a7358-722f-4338-80b0-d9962c6788e0"], Cell[45395, 908, 664, 16, 67, "Input",ExpressionUUID->"663fe9f3-35d1-4fb8-b70a-dd694dd0f376"], Cell[46062, 926, 1728, 40, 163, "Input",ExpressionUUID->"3b63bc71-8961-4104-9354-1383bceff509"], Cell[47793, 968, 826, 19, 52, "Input",ExpressionUUID->"baec48e4-bf84-41fc-9f0b-e090e69dad74"], Cell[48622, 989, 743, 18, 28, "Input",ExpressionUUID->"4924e4ae-298c-4991-a1a5-6e6f42b1778a"], Cell[49368, 1009, 1158, 31, 86, "Input",ExpressionUUID->"82f049e6-ffa9-47f4-a981-6be700b741bd"], Cell[50529, 1042, 1121, 25, 105, "Input",ExpressionUUID->"48660189-dacc-48e8-b790-1f2fc18ca073"], Cell[51653, 1069, 919, 22, 111, "Input",ExpressionUUID->"ea39819d-712c-4d3d-ad28-6c61145d7d95"], Cell[52575, 1093, 1159, 33, 256, "Text",ExpressionUUID->"941c29a9-91b6-429a-b371-2960aa3ae000"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[53783, 1132, 33206, 568, 900, "Chapter",ExpressionUUID->"5cf578f3-9a65-466f-a3b6-f0e47de816ba"], Cell[CellGroupData[{ Cell[87014, 1704, 1066, 29, 91, "Subchapter",ExpressionUUID->"41c0ffb3-534c-415e-9813-c3aabebbd088"], Cell[88083, 1735, 2650, 59, 417, "Output",ExpressionUUID->"e2c3dd99-f597-4540-8e8e-9d653486a56d"] }, Open ]], Cell[90748, 1797, 6036, 172, 632, "Subchapter",ExpressionUUID->"2f180f7e-a0f9-4ab7-b7ea-22e9ea48c02d"], Cell[CellGroupData[{ Cell[96809, 1973, 866, 16, 212, "Subchapter",ExpressionUUID->"43a29b54-1a66-469a-8eb8-b5b643bf2ded"], Cell[97678, 1991, 560, 11, 90, "Text",ExpressionUUID->"f061db74-98fa-43fb-89ea-e6f2c820b8fe"], Cell[98241, 2004, 6474, 147, 533, "Input",ExpressionUUID->"61e50612-bb55-4ecd-a422-69f81336b06b"] }, Open ]], Cell[CellGroupData[{ Cell[104752, 2156, 12578, 243, 436, "Subchapter",ExpressionUUID->"0b9c32f4-c8e3-4512-880f-59486011539e"], Cell[117333, 2401, 703, 19, 67, "Input",ExpressionUUID->"89aaeb0d-4710-4dec-aff4-49dc94f6c01b"] }, Open ]], Cell[CellGroupData[{ Cell[118073, 2425, 476, 8, 91, "Subchapter",ExpressionUUID->"14a72643-a6b1-4dfb-95e2-64acd5555a33"], Cell[118552, 2435, 347, 10, 28, "Input",ExpressionUUID->"ca63bb95-0d54-4b75-ba48-ee45a3cc9ff1"] }, Open ]], Cell[CellGroupData[{ Cell[118936, 2450, 303, 4, 59, "Subchapter",ExpressionUUID->"735c7a1f-dea0-4ec4-abf5-9a2f1b749d1b"], Cell[119242, 2456, 1942, 42, 276, "Input",ExpressionUUID->"cdbff3ed-7a58-4b57-a760-3445301282a3"], Cell[121187, 2500, 441, 8, 34, "Text",ExpressionUUID->"354c4176-7501-49ee-940d-67da4b1fd514"], Cell[121631, 2510, 310, 7, 28, "Input",ExpressionUUID->"9f3f5b30-dfe0-4973-b551-27b17a0c089d"] }, Open ]], Cell[CellGroupData[{ Cell[121978, 2522, 795, 17, 155, "Subchapter",ExpressionUUID->"d4438861-2645-45aa-b5bb-bae4755c6426"], Cell[122776, 2541, 7227, 173, 637, "Input",ExpressionUUID->"0692414a-1332-4a67-8c5b-f1c84ec3bd43"], Cell[130006, 2716, 568, 13, 34, "Text",ExpressionUUID->"7d12eb58-1388-4691-a8c9-e12a085e18d1"] }, Open ]], Cell[CellGroupData[{ Cell[130611, 2734, 668, 15, 91, "Subchapter",ExpressionUUID->"17d936da-2009-4a9a-9182-3bbb69cf60af"], Cell[131282, 2751, 4640, 100, 492, "Input",ExpressionUUID->"41ef6b99-e2ff-4547-9c5b-cb19e2a258a9"], Cell[135925, 2853, 557, 14, 34, "Text",ExpressionUUID->"64485fe9-68e4-48b4-beb3-4f3602fc4d90"], Cell[136485, 2869, 1127, 19, 116, "Text",ExpressionUUID->"914fb612-fc74-4269-aa87-1ca2c470fb28"] }, Open ]], Cell[137627, 2891, 2438, 46, 364, "Subchapter",ExpressionUUID->"7134e300-dc09-4987-87d2-58f165ba0d2a"], Cell[CellGroupData[{ Cell[140090, 2941, 877, 17, 140, "Subchapter",ExpressionUUID->"585316a5-eeaf-4156-b69c-860fb8ab91de"], Cell[140970, 2960, 3739, 89, 370, "Input",ExpressionUUID->"258f9772-57ba-4e16-a669-b6db5d3f6b83"] }, Open ]], Cell[CellGroupData[{ Cell[144746, 3054, 12630, 248, 276, "Subchapter",ExpressionUUID->"e673cd50-a7ac-4eb6-802d-052a21e711a1"], Cell[157379, 3304, 648, 17, 48, "Input",ExpressionUUID->"c976fb29-0cbe-46e1-9a26-6594a8a614fb"] }, Open ]], Cell[CellGroupData[{ Cell[158064, 3326, 235, 4, 59, "Subchapter",ExpressionUUID->"8739149d-a517-40bd-9f6b-4c23166179e8"], Cell[158302, 3332, 225, 4, 28, "Input",ExpressionUUID->"7169b827-182b-4e7a-8e70-5bebf396dd64"], Cell[158530, 3338, 979, 23, 52, "Input",ExpressionUUID->"d7bc6ecf-bb95-48da-a5f0-db54cc3397dc"], Cell[159512, 3363, 292, 4, 34, "Text",ExpressionUUID->"55043a09-7572-4f44-929f-93cbe70f009b"] }, Open ]], Cell[CellGroupData[{ Cell[159841, 3372, 626, 10, 91, "Subchapter",ExpressionUUID->"3c66edac-fcdd-434d-bce4-8f315bb39c77"], Cell[160470, 3384, 6622, 164, 703, "Input",ExpressionUUID->"1ec9e3c0-d840-4b73-bca5-6c04630e90e6"], Cell[167095, 3550, 345, 7, 34, "Text",ExpressionUUID->"f97d9f85-b0c9-4c87-8143-aae5d0983e7a"] }, Open ]], Cell[CellGroupData[{ Cell[167477, 3562, 551, 17, 123, "Subchapter",ExpressionUUID->"53374855-4acb-454b-8ca8-118025f22804"], Cell[168031, 3581, 4485, 105, 454, "Input",ExpressionUUID->"dd9ad189-8011-4d6a-8046-0ae6c1b36c33"], Cell[CellGroupData[{ Cell[172541, 3690, 390, 9, 53, "Subsection",ExpressionUUID->"1b404d34-b3f1-44a4-9193-913cbb0e7fdb"], Cell[172934, 3701, 718, 15, 28, "Input",ExpressionUUID->"8d2f5c42-1770-4c85-bfcd-edbfa0b39db6"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[173701, 3722, 410, 8, 59, "Subchapter",ExpressionUUID->"4c6b15bd-baae-4753-a208-f56b1771dcd6"], Cell[174114, 3732, 572, 14, 48, "Input",ExpressionUUID->"bb89b7de-afa9-4f3e-8710-04ba9d1262b0"], Cell[174689, 3748, 338, 6, 34, "Text",ExpressionUUID->"fa3678cb-2c39-48cd-bcc3-b3fb9dce8094"], Cell[175030, 3756, 194, 2, 38, "Text",ExpressionUUID->"45b40045-3466-482f-92d8-93a7080c7dac"], Cell[175227, 3760, 275, 6, 28, "Input",ExpressionUUID->"f84b80ed-8824-4286-a8fa-322023c12692"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[175551, 3772, 3783, 82, 688, "Chapter",ExpressionUUID->"5f03057c-91c0-4198-bf7b-f38279073517"], Cell[CellGroupData[{ Cell[179359, 3858, 617, 13, 144, "Section",ExpressionUUID->"7d0edde8-10d4-468f-9767-b869cad593f8"], Cell[179979, 3873, 572, 18, 36, "Text",ExpressionUUID->"1c2b70ca-8234-4d55-93f0-67674240ded0"], Cell[180554, 3893, 279, 6, 31, "Input",ExpressionUUID->"3bbb9371-1196-4484-bb31-7b623990a6cd"], Cell[180836, 3901, 1001, 26, 107, "Text",ExpressionUUID->"826773b7-c5af-4c2b-9ae3-daa56a44df05"], Cell[181840, 3929, 11159, 252, 689, "Input",ExpressionUUID->"3b2f5472-cd8f-4725-bb81-ade09996329a"] }, Open ]], Cell[CellGroupData[{ Cell[193036, 4186, 186, 2, 56, "Subchapter",ExpressionUUID->"46689e17-7c96-4745-9d63-fd2cbcb1b982"], Cell[193225, 4190, 8638, 192, 752, "Input",ExpressionUUID->"3f911791-88cf-49bc-8150-481c145b2d29"], Cell[201866, 4384, 297, 5, 30, "Text",ExpressionUUID->"1127106b-01fa-4a35-b32a-21a502d1918d"] }, Open ]], Cell[CellGroupData[{ Cell[202200, 4394, 584, 13, 56, "Subchapter",ExpressionUUID->"ec422f92-e3f0-4abe-9f13-042d8335a8ea"], Cell[202787, 4409, 7668, 176, 632, "Input",ExpressionUUID->"6253d822-7c78-4425-a464-021fdc1bf9d9"] }, Open ]], Cell[CellGroupData[{ Cell[210492, 4590, 1619, 34, 118, "Subchapter",ExpressionUUID->"d20350d3-2182-4c47-af76-e8a1f180de4e"], Cell[212114, 4626, 7805, 175, 692, "Input",ExpressionUUID->"c53e11df-e0f3-4aff-a0a9-5dd513888b85"] }, Open ]], Cell[CellGroupData[{ Cell[219956, 4806, 292, 6, 50, "Subchapter",ExpressionUUID->"f6d43fc1-6b82-4570-bc8c-b41181870639"], Cell[220251, 4814, 536, 11, 92, "Input",ExpressionUUID->"d2712577-152b-4bf5-9391-3a7fa65a875d"], Cell[220790, 4827, 322, 6, 30, "Text",ExpressionUUID->"c7c72302-6bdf-48b8-8bdd-b07865a93d60"] }, Open ]], Cell[CellGroupData[{ Cell[221149, 4838, 1148, 23, 179, "Subchapter",ExpressionUUID->"3f4f1de7-4f95-42cb-b321-fb75b43abf8c"], Cell[222300, 4863, 742, 19, 31, "Input",ExpressionUUID->"4e06899b-33f4-450c-b40e-291c055e71fd"] }, Open ]], Cell[CellGroupData[{ Cell[223079, 4887, 480, 9, 56, "Subchapter",ExpressionUUID->"72eef60c-e16b-4e2e-8e98-663aec31c765"], Cell[223562, 4898, 8425, 200, 632, "Input",ExpressionUUID->"1ccef054-63f1-4a14-a3fd-9296ffae9f70"], Cell[231990, 5100, 823, 14, 68, "Text",ExpressionUUID->"4e224949-7649-47ce-bb70-7c76a4f67508"] }, Open ]], Cell[CellGroupData[{ Cell[232850, 5119, 1063, 19, 261, "Subchapter",ExpressionUUID->"4857f20c-f536-49f6-9065-2cfe6430cbd6"], Cell[233916, 5140, 528, 9, 59, "Text",ExpressionUUID->"e82fa16c-d4e6-4a44-b54e-375e573b712b"], Cell[234447, 5151, 13858, 305, 1092, "Input",ExpressionUUID->"e19fcc93-ec46-47e9-a17c-f2c78e9b258c"] }, Open ]], Cell[CellGroupData[{ Cell[248342, 5461, 278, 6, 57, "Subchapter",ExpressionUUID->"921f8316-6218-431a-a75e-5894956aa950"], Cell[248623, 5469, 498, 11, 52, "Input",ExpressionUUID->"884a4a7f-48da-452c-b8c7-4312e9c97196"], Cell[249124, 5482, 230, 3, 30, "Text",ExpressionUUID->"29598463-e782-4406-a8aa-8d65b9dca49b"] }, Open ]], Cell[CellGroupData[{ Cell[249391, 5490, 392, 8, 55, "Subchapter",ExpressionUUID->"58848a57-3702-445e-aa38-feb2d6f9ddcc"], Cell[249786, 5500, 829, 18, 92, "Input",ExpressionUUID->"4996f75c-3de1-4b0b-9158-f432c120874a"] }, Open ]], Cell[CellGroupData[{ Cell[250652, 5523, 367, 8, 84, "Subchapter",ExpressionUUID->"2efd6b1c-1f5d-4e11-aea7-d5239a219396"], Cell[251022, 5533, 3034, 67, 232, "Input",ExpressionUUID->"bd971b87-7c6e-495e-b4db-81ce536a9705"], Cell[254059, 5602, 575, 12, 59, "Text",ExpressionUUID->"065ed977-8563-4faf-acfe-b812179b474c"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[254683, 5620, 505, 15, 66, "Chapter",ExpressionUUID->"f52ab122-7cd0-4141-9792-96a27b025e70"], Cell[CellGroupData[{ Cell[255213, 5639, 153, 2, 62, "Subchapter",ExpressionUUID->"9d8340b2-be1d-467a-b269-9142899d064d"], Cell[255369, 5643, 329, 7, 31, "Input",ExpressionUUID->"ae4c363c-43c0-4627-8016-1335ca2fd204"], Cell[255701, 5652, 3643, 100, 256, "Input",ExpressionUUID->"589c7058-654c-41c2-877e-1d78a9f60038"], Cell[259347, 5754, 387, 10, 31, "Input",ExpressionUUID->"bd0b03f8-7d54-48f1-85f2-d2cce1c731f4"], Cell[CellGroupData[{ Cell[259759, 5768, 251, 5, 43, "Subsection",ExpressionUUID->"455f6745-5178-4414-9a49-c9022d566972"], Cell[260013, 5775, 1436, 38, 31, "Input",ExpressionUUID->"ab44661f-71f2-4770-8759-782626281fb2"], Cell[261452, 5815, 1246, 34, 72, "Input",ExpressionUUID->"dba70983-95c3-4c89-9f81-7a3f362d30ce"], Cell[262701, 5851, 1176, 29, 67, "Input",ExpressionUUID->"22128bfb-1c94-494b-b3b3-638c546548cf"], Cell[263880, 5882, 961, 23, 67, "Input",ExpressionUUID->"1ad5acf1-161f-41c4-b6d2-ed44340a64d0"], Cell[264844, 5907, 802, 19, 52, "Input",ExpressionUUID->"e5c696cb-ca3d-4457-90da-5ecadd7c799b"] }, Open ]], Cell[CellGroupData[{ Cell[265683, 5931, 233, 5, 43, "Subsection",ExpressionUUID->"3146b37b-69ed-4337-80de-b1db5baaaa2b"], Cell[265919, 5938, 203, 3, 31, "Input",ExpressionUUID->"277ebd5b-224f-4f5c-bc09-0e20daf95b96"], Cell[266125, 5943, 612, 15, 31, "Input",ExpressionUUID->"75f6c674-3a7c-41f5-ae0e-6c152f00a7a8"], Cell[266740, 5960, 1373, 35, 88, "Input",ExpressionUUID->"132cb96b-90e3-4651-8c03-9350a4d37715"], Cell[268116, 5997, 489, 11, 72, "Input",ExpressionUUID->"6bc62cd3-c061-40a5-adfc-8ce3760a5073"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[268654, 6014, 199, 3, 62, "Subchapter",ExpressionUUID->"2577ec34-0ae1-47fc-8156-c5804fca3157"], Cell[268856, 6019, 323, 6, 31, "Input",ExpressionUUID->"b9a40ebb-121b-41d5-a9da-d252be07e217"], Cell[269182, 6027, 4705, 128, 284, "Input",ExpressionUUID->"351a6a90-cd43-4b44-a066-12e6b6130951"], Cell[273890, 6157, 447, 11, 31, "Input",ExpressionUUID->"ff37a524-dc96-4eef-af36-65aaa61ee49e"], Cell[CellGroupData[{ Cell[274362, 6172, 284, 6, 43, "Subsection",ExpressionUUID->"5b779bef-4e8b-467f-8265-0f87807d5fd1"], Cell[274649, 6180, 203, 3, 31, "Input",ExpressionUUID->"9d74b26b-2773-449d-b12d-778cec93ab3d"], Cell[274855, 6185, 1107, 28, 52, "Input",ExpressionUUID->"00ba6cb2-ca5f-42e7-b6e9-296aa8842c47"], Cell[275965, 6215, 2067, 52, 67, "Input",ExpressionUUID->"b19fa712-417b-4c85-9908-48d2b8eb40a5"], Cell[278035, 6269, 1569, 41, 92, "Input",ExpressionUUID->"df51f8a8-456a-46ad-9c89-96961133d39b"], Cell[279607, 6312, 294, 5, 30, "Text",ExpressionUUID->"a955cd3e-f690-4be8-94ed-a287da344c46"] }, Open ]] }, Open ]] }, Closed]] }, Open ]] } ] *)