{ "cells": [ { "cell_type": "markdown", "id": "c1e07947-9b5e-4593-8613-1164417ee953", "metadata": {}, "source": [ "ME 2016 - Nonlinear Dynamical Systems 1\n", "\n", "Homework 3\n", "\n", "**Dane Sabo**" ] }, { "cell_type": "code", "execution_count": 1, "id": "211982e1-a936-47d8-a01e-9a90cfc9de1d", "metadata": {}, "outputs": [], "source": [ "import sympy as sm\n", "import numpy as np\n", "from scipy.integrate import odeint\n", "import matplotlib.pyplot as plt\n", "from math import *" ] }, { "attachments": { "ae0f41aa-f319-4437-bf03-f540055a8e3d.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "a01a46d0-bc05-4b06-a782-431f6f525c9f", "metadata": {}, "source": [ "![image.png](attachment:ae0f41aa-f319-4437-bf03-f540055a8e3d.png)" ] }, { "cell_type": "code", "execution_count": 2, "id": "9db2c23d-bf5d-4c4f-a3ea-78c78aa77569", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x, y = sm.symbols('x,y')\n", "xdot = -y + x*sm.cos(sm.pi*x)\n", "ydot = x - y**3\n", "\n", "#Create Functions\n", "P = lambda x, y: -y + x*np.cos(np.pi*x)\n", "Q = lambda x, y: x - y**3\n", "def dX_dt(X, t, args = (P,Q)):\n", " return [P(X[0], X[1]), Q(X[0], X[1])]\n", "\n", "#Initial Conditions\n", "ts = np.linspace(0, 5, 30)\n", "ic = np.linspace(-1.2, 1.2, 7)\n", "\n", "#Make a vectorfield\n", "X, Y = np.mgrid[ic[0]:ic[-1]:20j, ic[0]:ic[-1]:20j]\n", "u = P(X,Y)\n", "v = Q(X,Y)\n", "plt.quiver(X, Y, u, v, color = 'red')\n", "\n", "#plot trajectories\n", "plt.title(f'Phase Portrait for $\\\\dot x = $ {xdot} and $\\\\dot y = $ {ydot}')\n", "plt.xlabel('x'); plt.ylabel('y'); plt.grid('both')\n", "plt.xlim((ic[0],ic[-1])); plt.ylim((ic[0],ic[-1]))\n", "\n", "for r in ic:\n", " for s in ic:\n", " X0 = [r,s]\n", " Xs = odeint(dX_dt,X0,ts)\n", " plt.plot(Xs[:,0],Xs[:,1], \"royalblue\",linewidth = 0.75)\n", "rect = np.array([[-1, -1], [-1, 1], [1, 1], [1, -1], [-1, -1]])\n", "plt.plot(rect[:,0], rect[:,1], '-g')\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "7d4c7594-806b-4711-9f85-24bfd075763a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dV/dt Expression: \n", "-pi*x*sin(pi*x) - 3*y**2 + cos(pi*x)\n", "\n", "dV/dt Simplified:\n", "-pi*x*sin(pi*x) - 3*y**2 + cos(pi*x)\n", "\n", "Sign Changes: \n", "[(x, -sqrt(-3*pi*x*sin(pi*x) + 3*cos(pi*x))/3), (x, sqrt(-3*pi*x*sin(pi*x) + 3*cos(pi*x))/3)]\n" ] } ], "source": [ "#Guess a psi for Poincare - Bendixson Theorem\n", "psi = 1\n", "def sign_change_test(xdot, ydot, psi):\n", " div_psiX = sm.diff(psi*xdot,x) + sm.diff(psi*ydot, y)\n", " print(f'dV/dt Expression: \\n{div_psiX}')\n", " print(f'\\ndV/dt Simplified:\\n{sm.simplify(div_psiX)}\\n')\n", " \n", " sign_changes = sm.solve(sm.Eq(0,div_psiX),x,y)\n", " print(f'Sign Changes: \\n{sign_changes}')\n", " return div_psiX\n", "\n", "expr = sign_change_test(xdot, ydot, psi)" ] }, { "cell_type": "code", "execution_count": 4, "id": "5f3e5930-f283-47f2-b6f7-e88131fec12b", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - 3 y^{2} - 1$" ], "text/plain": [ "-3*y**2 - 1" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr.subs(x,-1)\n", "#This is clearly always < 0. No sign change" ] }, { "cell_type": "code", "execution_count": 5, "id": "22f92f82-2559-4cf0-9323-46be12b52a4f", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - \\pi x \\sin{\\left(\\pi x \\right)} + \\cos{\\left(\\pi x \\right)} - 3$" ], "text/plain": [ "-pi*x*sin(pi*x) + cos(pi*x) - 3" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr.subs(y,-1)" ] }, { "cell_type": "code", "execution_count": 6, "id": "159811ac-97c6-4676-a6e1-dcdf084d32a6", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - 3 y^{2} - 1$" ], "text/plain": [ "-3*y**2 - 1" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr.subs(x,1)" ] }, { "cell_type": "code", "execution_count": 7, "id": "b2493449-3b2b-43d4-8635-2513c65ca16c", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - \\pi x \\sin{\\left(\\pi x \\right)} + \\cos{\\left(\\pi x \\right)} - 3$" ], "text/plain": [ "-pi*x*sin(pi*x) + cos(pi*x) - 3" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr.subs(y,1)" ] }, { "cell_type": "code", "execution_count": 8, "id": "21246928-c9c0-4c06-833e-8e8dde8b9b33", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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PG0f0g87HC0U1TdhxvFLucojciqxjhBYtWoR58+Z1eExiYqLz/0tLSzF16lRMnDgRb7/9dpd/37hx4wDYW5SSkpK6fD4Rte94RT2yTlZDJQF3jmO3WE/y1ajx8yvi8K9vT+HdnadxTUqk3CURuQ1Zg1B4eDjCw8M7dWxJSQmmTp2K0aNHY/ny5VCput6YdeDAAQBAdDSb7Il6mmNW04yhUYgJ8pW3GDd01/j++Pd3p7Dj+FmcqmrEgDB/uUsicguKGCNUUlKCKVOmID4+HsuWLcPZs2dRXl6O8vLyNsekpKRgz549AICCggI899xzyM7ORmFhIdasWYN77rkHkyZNQnp6ulyXQuSW6lrMWPWDfQHFeyayNag39A/1x9TkCADA+1mnZa6GyH0oYvr8119/jfz8fOTn5yM2NrbN94SwDxw0m83Iy8tzzgrTaDTYvHkzXn31VTQ2NiIuLg4ZGRn4wx/+0Of1E7m7z7LPoMlkxaCIAExIDJW7HLd1z4T+2JpbiZXZxVg0YzD8tYp4CSdyaZJwJAm6qLq6Ouj1ehgMBg6cJroIm01g+ss7cLKqEc/dlIq7x7NFqLfYbALX/HU7Cqub8Jf/S+VYLKIOdPb9WxFdY0Tkur7Lr8LJqkYEar0wd2Q/uctxayqVhLsnJAAA3tt5GvwcS3T5GISI6LI4BklnjI5lV00fuHl0LHy91cirqMfuUzVyl0OkeAxCRNRtxTVN2JJrX9fmbq4k3Sf0vt74v1H2ljcOmia6fAxCRNRtH+w+DSGAqweFISk8QO5yPMY9raFzQ045yg0tMldDpGwMQkTULS1mKz7ea9+C5t7WcSvUN1KidBg3IARWm8BHu9kqRHQ5GISIqFvWHCxFbZMZscG+mJoSIXc5HufeiQkAgI/2FMFoscpbDJGCMQgRUZcJIfDuzkIAwN3j+0OtkuQtyANdOzQSUTofVDWYsOFI+aVPIKKLYhAioi77oagWOaV10HqpcOuYOLnL8UjeahXuHBcPAM5QSkRdxyBERF3mmDJ/44gYBPtr5C3Gg902Nh7eagk/FNXi8BmD3OUQKRKDEBF1SWV9C9YdLgMA3MNB0rIKD9Ti+jT7JtKOcEpEXcMgRERdsmJPMcxWgVHxQUjtp5e7HI/nCKOrD5biXKNJ3mKIFIhBiIg6zWoT+N+eIgA/zloiedkDqQ4miw2fZp+RuxwixWEQIqJO21lQhTJDC/S+3piVGiV3OQRAkiTcPtY+aPqzH85w/zGiLmIQIqJO+6y1xWHO8BhovdQyV0MOs9NioPFSIbe8HjmldXKXQ6QoDEJE1Cn1LWZsyLGvVzN3FHeZdyV6P29cOyQSgL1ViIg6j0GIiDpl/eFytJhtSAz3x4i4ILnLoZ/IGG0Pp2sOlMJstclcDZFyMAgRUad82trSkDEqFpLElaRdzaRB4QgL0KK60YTteWflLodIMRiEiOiSimuasOdUDSSJ3WKuykutwk0jYgD8OJaLiC6NQYiILskx7uTKpDBE631lrobakzE6FgCwJbeCawoRdRKDEBF1SAiBVT+UAPhxHAq5piHROgyN1sFsFVh7qFTucogUgUGIiDq0t/Acimqa4K9RY+Ywrh3k6hytQuweI+ocBiEi6pDjDfX6tGj4abxkroYu5cYRMfBSSTh4xoD8ynq5yyFyeQxCRNSuZpMVX7VusOpoaSDXFhagxZTkcADAp9klMldD5PoYhIioXZuOlqPBaEFssC/GJoTIXQ51UsYoe2j9fP8ZWG3ccoOoIwxCRNQuxyaec0fFQqXi2kFKcc2QCOh9vVFRZ8T3+VVyl0Pk0hiEiOiiyg0tzjfRDK4dpChaLzXmDLevKbSKW24QdYhBiIgu6osDJbAJ4IqEYPQP9Ze7HOoix5iuDTnlqG8xy1wNketiECKiCwghnLPFHONNSFmGx+qRFO6PFrMN6w+Xy10OkctiECKiCxwuMeBEZQO0Xipcnx4tdznUDZIkYW5riP2U3WNE7WIQIqILOFqDZgyLgs7HW+ZqqLvmjuoHSQL2nKpBcU2T3OUQuSQGISJqw2SxYc1B+/YMHCStbNF6X1yZFAbgx/3iiKgtBiEiamNrbiXONZkREajF1YPC5S6HLpNjf7hVP5RACK4pRPRTDEJE1Iaj5eD/RvaDmmsHKd7MYVHw16hRVNOEvYXn5C6HyOUwCBGRU3WDEdtyKwFwSw134afxwvVp9gHv3IiV6EIMQkTktOZgKSw2gbR+egyODJS7HOohjlD71eEyNJusMldD5FoYhIjIydEtxkHS7mVsQghig33RYLRg01GuKUR0PgYhIgIA5FfW40hJHbxUEuaMYBByJyrVj2sKfb6fO9ITnY9BiIgAAF8eKgMAXD0oDCH+GpmroZ7m2HvsuxNVONdokrkaItehmCA0Z84cxMfHw8fHB9HR0bj77rtRWlra4TktLS14+OGHERoaioCAAGRkZKCioqKPKiZSDiGEMwjNTo+RuRrqDQMjApASFQiLTWBjDrvHiBwUE4SmTp2KTz75BHl5efjss89QUFCAm2++ucNzFi5ciLVr12LlypXYsWMHSktLMXfu3D6qmEg58irqkV/ZAI1ahWuHRcpdDvWSn7W2Cn11uEzmSohchyQUusLWmjVrcNNNN8FoNMLb+8ItAAwGA8LDw/HRRx85A1Nubi6GDBmCrKwsjB8/vlO/p66uDnq9HgaDATqdrkevgchVLNuYh39sy8e1QyPxr3vGyF0O9ZLT1Y2Y/NJ2qFUS9vxuGkIDtHKXRNRrOvv+rZgWofPV1NTgww8/xMSJEy8aggAgOzsbZrMZ06dPd96XkpKC+Ph4ZGVltfuzjUYj6urq2tyI3Jm9W8zezTybG6y6tf6h/kjrp4fVJrD+CLvHiACFBaEnn3wS/v7+CA0NRVFREVavXt3useXl5dBoNAgKCmpzf2RkJMrL238BWLJkCfR6vfMWFxfXU+UTuaSc0joUVjfBx1uF6UPYLebuHGHXEX6JPJ2sQWjx4sWQJKnDW25urvP4xx9/HPv378emTZugVqtxzz339PjeOZmZmTAYDM5bcXFxj/58IleztvUN8ZqUCPhrvWSuhnrbDa1BaPepGlTWtchcDZH8ZH3VW7RoEebNm9fhMYmJic7/DwsLQ1hYGAYPHowhQ4YgLi4Ou3btwoQJEy44LyoqCiaTCbW1tW1ahSoqKhAVFdXu79NqtdBq2W9OnkEIga84W8yjxAb7YWR8EPYX1WLd4TLMu3KA3CURyUrWIBQeHo7w8O7tbm2z2QDYx/RczOjRo+Ht7Y0tW7YgIyMDAJCXl4eioqKLBiciT3SguBZnzjXDT6PG1OQIucuhPjI7PQb7i2rx5SEGISJFjBHavXs3/vGPf+DAgQM4ffo0tm7dittvvx1JSUnOUFNSUoKUlBTs2bMHAKDX6zF//nw89thj2LZtG7Kzs3HfffdhwoQJnZ4xRuTuHGsHTR8SCV+NWuZqqK/c0LoJ677T51Ba2yxzNUTyUkQQ8vPzw6pVqzBt2jQkJydj/vz5SE9Px44dO5zdWGazGXl5eWhqanKe98orr2D27NnIyMjApEmTEBUVhVWrVsl1GUQuxWb7sVvsBs4W8yhReh9ckRAMAFjHNYXIwyl2HaG+wnWEyF3tK6zBzW9mIVDrhb1/mA4fb7YIeZJ3dxbi6TU5GB4XhNUPXyl3OUQ9zq3XESKiy+foFrt2aCRDkAe6Li0KKgk4WFyL4pqmS59A5KYYhIg8kNUmnNsszB7ObjFPFBHog3EDQgH8GIqJPBGDEJEH2nOqBmfrjdD7euOqgd2buUnK5wjBXFyRPBmDEJEHcrzxzRwWCY0XXwY81XWp0VCrJOSU1uFUVaPc5RDJgq+ARB7GYrVhQ+s+U1xE0bOF+GswMam1e+wgW4XIMzEIEXmYrJPVqG40tXkTJM/1s9YwzHFC5KkYhIg8zJcH7W94s1Kj4KXmS4CnmzksCt5qCXkV9ThRUS93OUR9jq+CRB7EZLFhQ46jW4yzxQjQ+3nj6kH2AfNsFSJPxCBE5EG+z6+CodmM8ECtc+o0kSMUf3moFFxjlzwNgxCRB1nbOlvs+tQoqFWSzNWQq7h2qH32YMHZRuSWs3uMPAuDEJGHMFqs+DqnAgAwezhni9GPAn28MWWwo3uMs8fIszAIEXmIb45Xod5oQZTOB6Pjg+Uuh1yMIxx/eaiM3WPkURiEiDyE45P+DenRULFbjH5iWkoEfLxVOF3dhCMldXKXQ9RnGISIPECL2YrNR+3dYjdwthhdhL/WC9ekRABg9xh5FgYhIg+wPa8SjSYr+gX5YmRckNzlkItyrDT+1WF2j5HnYBAi8gCOLTWuT4uCJLFbjC5uarK9e+zMuWbklLJ7jDwDgxCRmzNZbNhyrBKAfTVpovb4atSYMtjePeYIz0TujkGIyM19X2CfLRYRqMXIOM4Wo445wrJjBXIid8cgROTmNrZ+sp85LIqzxeiSrhkSAW+1hPzKBuRXcnFFcn8MQkRuzGoT2NQ6W4zdYtQZOh9vXDkwDAC7x8gzMAgRubE9p2pQ02hCkJ83xg4IkbscUohZw9g9Rp6DQYjIjW1sfSO7dkgkvNV8ulPnXDs0EioJOFJSh+KaJrnLIepVfGUkclM2m3B2bbBbjLoiNEDrbEHcyFYhcnMMQkRu6uCZWpTXtcBfo3aO+SDqLGf3GMcJkZtjECJyU47xHdcMiYSPt1rmakhpZra2ImYXnUNlXYvM1RD1HgYhIjckhHBOm3d8sifqimi9L0bEBUEIYGPrzEMid8QgROSGcsvrUVjdBK2XClOSw+UuhxTKMbZsI7vHyI0xCBG5Ice4jkmDw+Gv9ZK5GlIqR2ti1slq1DaZZK6GqHcwCBG5IcdMH3aL0eVICPNHSlQgrDaBr9k9Rm6KQYjIzZyqakRueT28VBKmD4mUuxxSOGf3GKfRk5tiECJyM45usQlJodD7ectcDSnddanRAIBvTlShwWiRuRqinscgRORmHNPmuYgi9YTBkQEYEOYPk8WGbbmVcpdD1OMYhIjcSGltMw4W10KS7NskEF0uSZIwk3uPkRtjECJyI45xHFf0D0FEoI/M1ZC7uK61dXFbbiVazFaZqyHqWQxCRG7EMT5oJrvFqAelx+oRrfdBk8mKb09UyV0OUY9iECJyE1UNRuwtrAEAzBzGbjHqOW26x7i4IrkZBiEiN/H10QrYhP3Te2ywn9zlkJtxdI9tPlYBs9UmczVEPYdBiMhNOLvFuIgi9YIxCSEI9dfA0GzGrpPVcpdD1GMYhIjcgKHZjJ0F9rEbnDZPvUGtkjCjtcuV3WPkThQThObMmYP4+Hj4+PggOjoad999N0pLSzs8Z8qUKZAkqc3twQcf7KOKifrO1twKmK0CgyMDkBQeIHc55KZmtS6uuDGnAlabkLkaop6hmCA0depUfPLJJ8jLy8Nnn32GgoIC3HzzzZc8b8GCBSgrK3PeXnzxxT6olqhvOT6hc28x6k0TEkMR6OOFqgYj9hedk7scoh6hmG2pFy5c6Pz//v37Y/HixbjppptgNpvh7d3+NgJ+fn6IiuKbA7mvJpMFO46fBcBp89S7NF4qTB8Sic/3l2D9kXKMSQiRuySiy6aYFqHz1dTU4MMPP8TEiRM7DEEA8OGHHyIsLAypqanIzMxEU1NTh8cbjUbU1dW1uRG5sh15Z9FitiE+xA9Do3Vyl0NuzjEGbcORcgjB7jFSPkUFoSeffBL+/v4IDQ1FUVERVq9e3eHxd9xxBz744ANs27YNmZmZeP/993HXXXd1eM6SJUug1+udt7i4uJ68BKIe51hNeuawSEiSJHM15O4mDQqHr7caJbXNyCnlB0VSPlmD0OLFiy8YzPzTW25urvP4xx9/HPv378emTZugVqtxzz33dPiJ5P7778fMmTORlpaGO++8E++99x4+//xzFBQUtHtOZmYmDAaD81ZcXNyj10zUk0wWG7a0boTJafPUF3w1akwaHAYA2MS9x8gNyDpGaNGiRZg3b16HxyQmJjr/PywsDGFhYRg8eDCGDBmCuLg47Nq1CxMmTOjU7xs3bhwAID8/H0lJSRc9RqvVQqvVdu4CiGS2+1Q16lssCAvQYmR8sNzlkIeYOSwKG3MqsOloBR6bkSx3OUSXRdYgFB4ejvDw8G6da7PZVzY1Go2dPufAgQMAgOjo6G79TiJXsymnAgBw7dAIqFXsFqO+cU2K/e8tt7wep6sb0T/UX+6SiLpNEWOEdu/ejX/84x84cOAATp8+ja1bt+L2229HUlKSszWopKQEKSkp2LNnDwCgoKAAzz33HLKzs1FYWIg1a9bgnnvuwaRJk5Ceni7n5RD1CJtNYNNRe9fEjKHsFqO+E+SnwfhE+4wxRxgnUipFBCE/Pz+sWrUK06ZNQ3JyMubPn4/09HTs2LHD2Y1lNpuRl5fnnBWm0WiwefNmzJgxAykpKVi0aBEyMjKwdu1aOS+FqMccKjGgos4If40aEweGyl0OeRhH+HaEcSKlUsQ6Qmlpadi6dWuHxyQkJLQZOB0XF4cdO3b0dmlEsnHMFpuSEgGtl1rmasjTXDs0Ek+vycG+0+dwtt6I8ECOrSRlUkSLEBFdaFMON1kl+cQE+SI9Vg8hgC3H2D1GysUgRKRA+ZUNKDjbCG+1hCnJ3ZtwQHS5Zgy1b8K66SiDECkXgxCRAjnGZUxICoPOp+PV1Yl6i6M18rsTVWgwWmSuhqh7GISIFMgxU2fmsEiZKyFPNjAiAAPC/GGy2rAj76zc5RB1C4MQkcKUG1pwoLgWAHDtEAYhko8kSc7usY1cZZoUikGISGG+bh2YOjI+CBE6H5mrIU83o7V7bFtuJUwWm8zVEHUdgxCRwnC2GLmSkXFBCA/Uot5owa6T1XKXQ9RlDEJECmJoNiOrwP5m4+iSIJKTSiXhWnaPkYIxCBEpyPa8SlhsAoMiApAYHiB3OUQAfgzlXx+tgM0mLnE0kWthECJSEMdssRmcLUYuZGJSGAK1XqisN+LgmVq5yyHqki4HoXvvvRfffPNNb9RCRB1oMVuxPa8SADdZJdei8VJhSkoEAGAjN2ElhelyEDIYDJg+fToGDRqE559/HiUlJb1RFxH9xM6CKjSarIjS+SA9Vi93OURt/LjKNMcJkbJ0OQh98cUXKCkpwUMPPYSPP/4YCQkJuO666/Dpp5/CbDb3Ro1EBGDjkR+7xSRJkrkaoramJIdDo1bh5NlG5FfWy10OUad1a4xQeHg4HnvsMRw8eBC7d+/GwIEDcffddyMmJgYLFy7EiRMnerpOIo9mtQlsPuZYTZrdYuR6An28MXFgKAB2j5GyXNZg6bKyMnz99df4+uuvoVarcf311+Pw4cMYOnQoXnnllZ6qkcjj/VB0DtWNJuh8vDB2QIjc5RBdlCOkcxNWUpIuByGz2YzPPvsMs2fPRv/+/bFy5Uo8+uijKC0txbvvvovNmzfjk08+wbPPPtsb9RJ5pI1H7OMupg2JhLeakz3JNU0bEgFJAg4W16Lc0CJ3OUSd4tXVE6Kjo2Gz2XD77bdjz549GDFixAXHTJ06FUFBQT1QHhEJIZyfsLnJKrmyiEAfjIoPRvbpc/j6aDnunpAgd0lEl9Tlj5avvPIKSktL8frrr180BAFAUFAQTp06dbm1ERGA3PJ6FNU0QeulwqTB4XKXQ9QhR1jnOCFSii4Hobvvvhs+PtzokaivOBZRvHpQGPw0XW7EJepTjjWudp2shqGJM4nJ9XGwAZGLc6zLMoOzxUgBEsL8kRwZCItNYFvrAqBEroxBiMiFFdc0Iae0DioJmNa6ci+Rq5sxjJuwknIwCBG5sK9bB0lfkRCC0ACtzNUQdY5jGv2O42fRYrbKXA1RxxiEiFyY4xM1u8VISYbF6NAvyBdNJiu+O1EldzlEHWIQInJR1Q1G7C2sAfDjPk5ESiBJEq4dyu4xUgYGISIXteVYJWwCGBqtQ1yIn9zlEHWJY5zQ5mMVsFhtMldD1D4GISIX5fgkzb3FSInGJoQg2M8b55rM2Ft4Tu5yiNrFIETkghqMFnybbx9bMTOV3WKkPF5qFaYNYfcYuT4GISIX9M3xszBZbOgf6ofkyEC5yyHqFkdr5tdHKyCEkLkaootjECJyQed3i0mSJHM1RN1jXw1djZLaZuSU1sldDtFFMQgRuRiTxYatufYVebnJKimZj7cak1v3x2P3GLkqBiEiF5N1shr1LRaEB2oxMi5Y7nKILouje4xBiFwVgxCRi3G8YVw7NBIqFbvFSNmmJkfASyXheEUDTlU1yl0O0QUYhIhciM0mnNtqcNo8uQO9nzcmJIUCYKsQuSYGISIXsr/4HM7WGxGo9cKExFC5yyHqETPYPUYujEGIyIVsyrG3Bk1NiYDGi09Pcg+OLWL2F9Wioq5F5mqI2uIrLZGLEEJwNWlyS5E6H4yMDwIAbGrt+iVyFQxCRC7ieEUDCquboPFSYUpyuNzlEPUoR7jfxO4xcjEMQkQuwtEadPXAMPhrvWSuhqhnOYJQVkE1DE1mmash+hGDEJGLYLcYubMBYf4YHBkAi01gax67x8h1KC4IGY1GjBgxApIk4cCBAx0e29LSgocffhihoaEICAhARkYGKir4BCTXU1zThJzSOqgkYNqQCLnLIeoVM4Y6usf4OkyuQ3FB6IknnkBMTEynjl24cCHWrl2LlStXYseOHSgtLcXcuXN7uUKirnMMIL0iIQShAVqZqyHqHY7Wzu15Z9FitspcDZGdooLQ+vXrsWnTJixbtuySxxoMBrzzzjt4+eWXcc0112D06NFYvnw5du7ciV27dvVBtR3LKqjGy5vyUGZolrsUcgHsFiNPkNpPh35Bvmg2W/HtiSq5yyEXsOqHM/hodxHKDfItq6CYIFRRUYEFCxbg/fffh5+f3yWPz87OhtlsxvTp0533paSkID4+HllZWe2eZzQaUVdX1+bWG17YkIu/b83HzvzqXvn5pBzVDUbsK6wBAMzgJqvkxiRJwrWtawpxcUUCgLe/OYnffX4Y2afPyVaDIoKQEALz5s3Dgw8+iDFjxnTqnPLycmg0GgQFBbW5PzIyEuXl7T8BlyxZAr1e77zFxcVdTuntGpcYAgDYfYpByNNtOVYJm7B/Wo4NvnTIJ1IyR6vnlmMVsFhtMldDcqptMiGvoh4AMHZAiGx1yBqEFi9eDEmSOrzl5ubitddeQ319PTIzM3u9pszMTBgMBuetuLi4V37PuNYHfc+pml75+aQczm6xoewWI/d3RUIwgv28ca7JjD2FfP3zZHsLz0EIIDHcH+GB8o2NlHWxkkWLFmHevHkdHpOYmIitW7ciKysLWm3bf6gxY8bgzjvvxLvvvnvBeVFRUTCZTKitrW3TKlRRUYGoqPbfcLRa7QW/pzeMSQiBSgIKq5tQUdeCSJ1Pr/9Ocj0NRgu+zbePlZjB8UHkAbzUKkwfEomV2WewKacCE5PC5C6JZLL7pL1HZNwAefdVlDUIhYeHIzz80ivo/v3vf8ef//xn59elpaWYOXMmPv74Y4wbN+6i54wePRre3t7YsmULMjIyAAB5eXkoKirChAkTeuYCLoPOxxtDY3Q4UlKHXSerceOIfnKXRDLYkXcWJosNCaF+GBwZIHc5RH1i5rCo1iBUjqd/NhSSJMldEslgd2uPyPhE+brFAIWMEYqPj0dqaqrzNnjwYABAUlISYmNjAQAlJSVISUnBnj17AAB6vR7z58/HY489hm3btiE7Oxv33XcfJkyYgPHjx8t2LedzpGB2j3mu82eL8c2APMVVg8Lgp1Gj1NCCwyUGucshGdS3mJFTan/s5RwfBCgkCHWG2WxGXl4empqanPe98sormD17NjIyMjBp0iRERUVh1apVMlbZluPB380g5JFMFhu25VYCYLcYeRYfbzUmD7b3BnD2mGfad/ocbAKID/FDtN5X1loUuaFRQkIChBCXvM/Hxwevv/46Xn/99b4sr9PGJtiDUH5lA6oajAjjQnoeZWdBFeqNFkQEajEyLkjucoj61MxhUVh/pBybcirw+MwUucuhPrb7pL0BYJzMrUGAG7UIKVGwvwYpUYEAgL1sFfI4jtWkrx0aCZWK3WLkWaamRMBLJeFEZQNOnm2QuxzqY3tal44ZlyjvQGmAQUh27B7zTFabcO63xNWkyRPpfb0xIcn+JriB3WMepclkwaEz9vFBbBEi54DpXSe5sKInyT59DlUNxjZvBkSe5rrUaADAhiMMQp7kh9O1sNgEYvQ+iA2Wd3wQwCAkO0eLUF5FPWqbTDJXQ31l3eEyAPZuMW81n4bkmWYMi4RKAg6dMaC4punSJ5BbOL9bzBVmy/IVWGbhgVokhvtDCPsqm+T+bDbh/AR8fRq7xchzhQVona3ibBXyHLtah4LIPW3egUHIBTheCHaze8wj7C+uRXldCwK1XrhyIFfVJc/m+DCw7kiZzJVQX2gxW3GguBaAa4wPAhiEXIJjVU3uu+MZ1rd2i00fGgmtl1rmaojkZV9MFNhfVIvS2ma5y6FedrC4FiaLDeGBWgwI85e7HAAMQi7B0Tx4pMSA+hazzNVQbxJCYH1rF8B1qewWI4rQ+eCK/vbXQHaPuT/HDOlxA0JcYnwQwCDkEqL1vogP8YNN2FfbJPd16IwBJbXN8NOoMWnwpffZI/IEs1o/FKxn95jb2+0YKO0i3WIAg5DLcPxRcN8x9+YYB3FNSgR8vNktRgT8GIT2nT6HiroWmauh3mKy2JDd+mHfFRZSdGAQchGOPwoOmHZfQgisP+yYLRYtczVEriMmyBcj44MgBPcec2eHSwxoMdsQ4q/BoIgAuctxYhByEY4WoUNnDGgyWWSuhnpDTmkdimqa4OOtwpRkdosRne/61sUVHWtskftxdItdkRDsMuODAAYhlxEb7IsYvQ8sNoEfTtfKXQ71Asf4h6nJEfDTKHK/Y6Je4+ge23OqBmfrjTJXQ73hx41WXadbDGAQchmSJDm7xxyrbpL7EEJgXWu32HXsFiO6QFyIH9Jj9bAJYNNRdo+5G4v1/PFBrjNQGmAQcimOafS7OGDa7eRV1ONUVSM0XipckxIhdzlELsmx95hjLB25j6NldWgwWhDo44WUKJ3c5bTBIORCHOOEDhTXosVslbka6kmO1qDJg8MRoGW3GNHFONbWyjpZjXON3HvRnTi6xcYmhECtcp3xQQCDkEsZEOaP8EAtTBYbDrYuQU7uwbGaNPcWI2pfQpg/hkbrYLUJfH20Qu5yqAc5F1J0sW4xgEHIpUiS5GwV2s3uMbdxoqIeJyob4K2WMG1IpNzlELk07j3mfmw2gb2FrjlQGmAQcjk/BiEOmHYXji01rh4UDp2Pt8zVELk2x2SC7/OrYGjilkPuILe8HoZmM/w1agyLca3xQQCDkMtxzBzLPn0OJotN5mqoJzjWReHeYkSXlhQegOTIQJitApuPsXvMHThmQo9OCIGX2vVih+tV5OEGRQQgxF+DFrMNh0sMcpdDl+nk2QbkltfDSyXh2qHsFiPqjOvSuPeYOzl/o1VXxCDkYiRJwhUJwQDYPeYOHN1iE5JCEeSnkbkaImVwTKP/5ngV6lvYPaZkQgjnHpoMQtRpjsFk3IBV+RyfaLm3GFHnDY4MQGK4P0xWG7bmVspdDl2GgrMNqG40wcdbhfTYILnLuSgGIRfkmF64r/AcLFaOE1KqouomHCmpg0oCZrBbjKjTJEni3mNuYlfr+kGj4oOh8XLNyOGaVXm4lCgdAn280GC04GhZndzlUDc5WoPGJ4YiNEArczVEyuIYJ7Q97ywajdyIWqkc44PGumi3GMAg5JLUKgljE+x/NOweUy7H+CDuLUbUdUOjdegf6gejxYZteeweUyL7+CD7WFdXXD/IgUHIRTm6xxzNiqQsJbXNOFBcC0kCZg5jtxhRV0mSxL3HFO50dRMq6ozQqFUYGR8kdzntYhByUY70vLewBjabkLka6qoNra1BVySEICLQR+ZqiJTJscr0trxKNJu4/6LSOGY+j4gLgo+3WuZq2scg5KKGxejgr1HD0GxGXkW93OVQFzn3FuMiikTdltZPj35BvmgyWbHj+Fm5y6EuUsL4IIBByGV5qVUY3TpOaPdJriekJGWGZuw7fQ4AMCuV44OIukuSJGer0FecPaY4jh3nXXGj1fMxCLmw8a1/PN/lV8lcCXXF2oOlAICxCSGI0rNbjOhyzE6PAQBsPlrB2WMKcqqqESW1zfBWSxgVHyx3OR1iEHJhkweHAwC+z6+G0cL+caVYfcAehOaMiJG5EiLlS4/VIyHUD81mK74+yr3HlGJ760y/KxJC4K/1krmajjEIubCh0TpEBGrRbLZyGr1C5FfWI6e0Dl4qiatJE/UASZIwZ0Q/AMDqAyUyV0OdtS3PPqZranKEzJVcGoOQC5MkCVOS7a1C2/M4UFAJ1rS2Bk0aHI4Qf+4tRtQT5gy3t65+c6IK1Q1GmauhS2k2WbGrdWyr4z3MlTEIuThHmuaCYq5PCIHVreODbmS3GFGPGRgRgNR+OlhtAuuOcE0hV5d1sgomiw39gnwxMCJA7nIuiUHIxV05KAxeKgknzzaiuKZJ7nKoAwfPGHC6ugm+3mpMH8JFFIl60o3D7d1ja9g95vIcPRhTksMhSZLM1Vwag5CL0/l4Y3R/+4j77WwVcmmO8QszhkW6/OBAIqX52fAYSBKwt/Aczpzjh0JXJYRwBiEljA8CGIQUYYqze4zjhFyV1Saw9qB9nRN2ixH1vCi9D8a3rrjveK6R6zlZ1YiimiZo1CpMHOi6+4udj0FIARyDzXYWVKHFzGn0riiroBpVDUYE+3nj6kGuPziQSIkcHzI4e8x1OVqDxg4IgZ9GGS3jigtCRqMRI0aMgCRJOHDgQIfHTpkyBZIktbk9+OCDfVNoD0qJCkSUzgctZptzyXJyLV+0vjBfnxYNb7XinlZEinBdajS81RJyy+uRV86th1yRYwiHEmaLOSjuFfuJJ55ATEznux4WLFiAsrIy5+3FF1/sxep6R9tp9Bwn5GpazFbnJqs3tq53QkQ9T+/n7RwqwFYh19Nksji31ZiikPFBgMKC0Pr167Fp0yYsW7as0+f4+fkhKirKedPpdB0ebzQaUVdX1+bmChx/VFxPyPVsy61Eg9GCGL0PxvR37aXkiZTux+6xUgghZK6Gzrczvxomqw1xIb5ICveXu5xOU0wQqqiowIIFC/D+++/Dz8+v0+d9+OGHCAsLQ2pqKjIzM9HU1PFsgyVLlkCv1ztvcXFxl1t6j7hyYCi8VBJOVTXidHWj3OXQeRxbavxsRAxUKtefKkqkZNNSIuGvUaOkthk/FJ2Tuxw6z/bjrd1igyMUMW3eQRFBSAiBefPm4cEHH8SYMWM6fd4dd9yBDz74ANu2bUNmZibef/993HXXXR2ek5mZCYPB4LwVFxdfbvk9ItDHG2MSHNPo2SrkKgzNZmxt7a50rHNCRL3HV6PGzGH2HekdH0JIfudPm1fS+CBA5iC0ePHiCwYz//SWm5uL1157DfX19cjMzOzSz7///vsxc+ZMpKWl4c4778R7772Hzz//HAUFBe2eo9VqodPp2txcBVeZdj0bc8phstgwODIAQ6ID5S6HyCPcONL+oeOrQ2UwW20yV0MAUHC2AWfONUPjpcKEJGVMm3eQdW7bokWLMG/evA6PSUxMxNatW5GVlQWtVtvme2PGjMGdd96Jd999t1O/b9y4cQCA/Px8JCUldatmOU1JjsCS9bnIKqhGi9kKH2+13CV5PMfeYjeO6KeopmAiJbsyKRSh/hpUN5rwfX6VogbmuitHa9A4BU2bd5C12vDwcISHX7oJ7e9//zv+/Oc/O78uLS3FzJkz8fHHHzvDTWc4pttHRytzV/DBkQGI0fug1NCCrJPVilm1011V1rVgZ0EVgB83hSSi3uelVmF2ejTezTqNNQdKGYRcgKOnQonvS4oYIxQfH4/U1FTnbfDgwQCApKQkxMbGAgBKSkqQkpKCPXv2AAAKCgrw3HPPITs7G4WFhVizZg3uueceTJo0Cenp6bJdy+WQJAmTW//IdnCckOzWHiqDTQCj4oMQF9L5AfxEdPnmtC5VsTGnHM0mLjQrp0ajBXtP2QeuK218EKCQINQZZrMZeXl5zllhGo0GmzdvxowZM5CSkoJFixYhIyMDa9eulbnSy8P1hFyHY/NHrh1E1PdGxQchNtgXjSYrNh+rkLscj7azwD5tPj7EDwPClDNt3kFZHXmtEhISLlg/4qf3xcXFYceOHX1dWq+7cmAYvNUSCqubcKqqUZF/dO7gVFUjDp4xQK2ScH2aMrtaiZRMkiTcOCIGr28rwOoDpfgZu6dl82O3mDJ2m/8pt2kR8hQBWi9ckRACgK1CcnIMkr5yYBjCA7WXOJqIeoOjNXbH8UrUNplkrsYzCSGcQzWUOlaLQUiBpnI3elkJIbD6YGu3GD+FEslmcGQgUqICYbYKrG/d5ob61onKBpTUNkPrpcL4RGVNm3dgEFIgxzihXSerOUhQBjmldTh5thFaLxVmpkbJXQ6RR7updU0h7j0mD0fPxPjEUPhqlLmkC4OQAg2MCEC/IF+YLDZknaySuxyP43jBnT40EgFaRQ6zI3IbjrFBu0/VoMzQLHM1nmdbrjJXkz4fg5ACtd2Nnt1jfclqE1hzsHURRXaLEcmuX5AvxiaEQAjgy4NlcpfjURqMFuw7bd9tXonrBzkwCCnU+bvRcwfmvrP7ZDUq6ozQ+XhhsoI/ARG5kzmtO9Kv2l/C18M+9H1+FcxWgYRQPyQoeAYzg5BCTUwKhUatQlFNE05WcTf6vrJir30T3tnDY6D1UmZ/OJG7mZ0eDY2XCsfK6nCkpE7ucjyGY3yQUmeLOTAIKZS/1gtjBzim0bN7rC+cazRhQ+vMlNuviJe5GiJyCPLTYFbrjvT/21skczWeQcm7zf8Ug5CCcZXpvrVqfwlMVhuGxeiQFquXuxwiOs9tY+MA2Nf4ajRaZK7G/eVV1KPM0KLoafMODEIK5miO3H2yBk0mPvF7kxACK/bYP2neNpatQUSuZkJiKBJC/dBgtOCrQxw03dscrUETk0Lh463sYQIMQgqWFO6P2GBfmKw27Myvlrsct/ZD0TmcqGyAr7caN47gbDEiVyNJEn7e2mXN7rHety3XPcYHAQxCiiZJknPK4vbj7B7rTf/bYx8kfUN6NHQ+3jJXQ0QXkzG6H7xUEvYX1SKvvF7uctxWfYsZ2aftu80redq8A4OQwl2TYv8j3JRTAauN00Z7Q12LGV8esq8ddNsVcTJXQ0TtiQj0wbQh9tfE/+1hq1Bv2XKsEhabQGK4P+JD/eQu57IxCCnclQPDoPf1RmW9EbtPsnusN6w5UIoWsw0DIwIwun+w3OUQUQccY/g+31+CFjO3IOoNjtX1f5buHsMEGIQUTuOlwvVp0QCA1a07olPPWtE63uC2K+IgSZLM1RBRRyYNCke/IF8Yms3YmMONWHtadYMR35ywb+00x03GSzIIuQHH4N11R8pgtPATUE86UmLAkZI6aNQqzB0VK3c5RHQJapWEW8bYn6vsHut5646Uw2oTSOunR1J4gNzl9AgGITcwNiEEUTof1LdYnBvgUc9wvJDOTI1CiL9G5mqIqDNuHRMHlQTsOlmDU1x5v0et3m/vFnOn2bMMQm5ApZKcTZRrDpbIXI37aDJZnN2Nt3OQNJFixAT5YvJg+4KzKziVvscU1zRh3+lzkCRgtpuMDwIYhNzGnNad0Dcfq0R9i1nmatzDl4fK0GC0oH+on+JXTiXyNI5B059ln4HJYpO5GvewtnX27PgBoYjS+8hcTc9hEHITw2J0GBgRAJPFho05FXKX4xY+bt1g9dYxcVCpOEiaSEmuSYlAWIAWVQ0mbM3la2JPWNPaQu5O3WIAg5DbkCQJN7a2CjmmNlL3Ha+oR/bpc/aBl6M5SJpIabzVqvMGTRfLXI3y5ZbXIbe8Hhq1CtelRstdTo9iEHIjjnFC3+dX4Wy9UeZqlG1F6wvntJQIROjcpwmYyJM4FkD95sRZnDnXJHM1yuZoDZqSHA69n3utrs8g5Eb6h/pjRFwQbAL46hDXFOquFrMVq/afAQDczg1WiRSrf6g/JiaFQgjgk31n5C5HsYQQzokjN47oJ3M1PY9ByM04+m5XH2QQ6q6NOeWobTIjRu+DSa0zT4hImRyDplfuK+Y2RN30Q9E5lNQ2w1+jdm5h4k4YhNzMDenRUEnA/qJaFFWzKbg7HN1it4yJg5qDpIkUbeawSAT7eaPM0IId3Jy6WxytQTNTo+DjrZa5mp7HIORmIgJ9cOXAMABcU6g7CqsakXWyGpIE3Mq1g4gUT+uldq4Kz0HTXWe22vDVoTIA7tktBjAIuSXHH+sXB0ohBJuCu+LjffYXSsd+RUSkfI5B01tzK1FZ1yJzNcryXX4VqhtNCPXX4Mok91xPjUHIDc0cFgmNlwr5lQ04WlYndzmKYbbasHKfY5A0W4OI3MWgyECM7h8Mq01gZTYHTXeFY7bY7PRoeKndMzK451V5uEAfb0xvHdC2hjvSd9qWY5WoajAiLECLaUMi5S6HiHqQo1Xo473FsHHQdKc0m6zYmFMOAJjjpt1iAIOQ25oz3P5Hu+ZgKZ/0nfTvb08CAG4ZEwtvN/3kQ+SpZqfHQOfjhaKaJmw6ypWmO2PzsQo0mayIDfbFqPggucvpNXy1d1NTksMR6OOFMkML9hbWyF2Oy9tXWIN9p89Bo1bhvokJcpdDRD3MV6PG3RP6AwDe3FHA8ZOdsPq8LTUkyX1n0DIIuSkfbzWuS40CwDWFOuPNHQUAgLmj+nElaSI3NW/iAGi8VDhQXIvdp/gBsSO1TSbncgPuOlvMgUHIjTn+eNcdLuPuyx04XlGPzccqIUnA/ZMS5S6HiHpJeKDWuXeg48MPXdz6I+UwWwWGROswODJQ7nJ6FYOQGxufGIqIQC1qm8z49sRZuctxWW/tsI8Nmjk0ConhATJXQ0S96f5JiVBJwPa8szjGWbXtcmze7W47zV8Mg5AbU6sk/My5Iz27xy6mtLbZ+YR/cEqSzNUQUW/rH+qP69Lsu6e/xVahiyozNDu7Dh3vIe6MQcjNOdL810cr0Gi0yFyN63nnu1Ow2ATGJ4ZgRFyQ3OUQUR94aLL9Q8/aQ2UoruFWRD/15cEyCAGMTQjxiIVlGYTcXFo/PQaE+aPZbMXXnDLaRm2TCf/bUwQAeHAyW4OIPEVqPz2uGhgGq004l82gH33R2ko+xwO6xQAGIbcnSRLmOLvHuPfY+d7LOo0mkxVDonWYzF3miTyK48PPx/uKUd1glLka15FfWY+c0jp4qSRc39qF6O4YhDyAo3tsx/GzbAZu1Wyy4r87CwEAD05OdOs1MojoQlcODEVqPx1azDa8m3Va7nJcxke7W/dbHByOEH+NzNX0DcUEoYSEBEiS1Oa2dOnSDs9paWnBww8/jNDQUAQEBCAjIwMVFZ7XPZQYHoCrB4XBJsBm4FYrs4tR02hCbLAvbvCQTz1E9CNJkvDQ5IEAgPeyCtFk4hjK2iYTVuy1DxeY50ELyyomCAHAs88+i7KyMuftN7/5TYfHL1y4EGvXrsXKlSuxY8cOlJaWYu7cuX1UrWs5vxm4ptEkczXyslhtePsbeyC8f1Ki224kSEQdm5UahYRQP9Q2mbFiT7Hc5cju/fOGC1w9KEzucvqMot4BAgMDERUV5bz5+/u3e6zBYMA777yDl19+Gddccw1Gjx6N5cuXY+fOndi1a1e75xmNRtTV1bW5uYOJST82A7+XVSh3ObL66nAZzpxrRoi/BreM5i7zRJ5KrZKwoHUR1Xe+OwWz1XMXnm0xe+5wAUUFoaVLlyI0NBQjR47ESy+9BIul/abM7OxsmM1mTJ8+3XlfSkoK4uPjkZWV1e55S5YsgV6vd97i4tzjjVKSJGer0Ls7PbcZWAiBN1sXUJw3MQG+GrXMFRGRnDJGxSIsQIuS2mas9eDtiD7NPoPqRhP6BXnecAHFBKFHHnkEK1aswLZt2/DAAw/g+eefxxNPPNHu8eXl5dBoNAgKCmpzf2RkJMrLy9s9LzMzEwaDwXkrLnaf5tJZw6IQH+KHc01mrNx3Ru5yZPHNiSocK6uDn0aNe1o3YCQiz+XjrcZ9VyYAsG+7YbN53masVpvAv1rHjy64eoDHDReQ9WoXL158wQDon95yc3MBAI899himTJmC9PR0PPjgg/jrX/+K1157DUZjz0571Gq10Ol0bW7uwkutwoKrBwAA/vXtSVg8sBn4je35AIDbrohHkJ9nzIggoo7dNb4/ArReOF7RgG15lXKX0+c2HCnH6eomBPt549Yr3KMXpCtkDUKLFi3CsWPHOrwlJl58E8xx48bBYrGgsLDwot+PioqCyWRCbW1tm/srKioQFRXVw1eiHLeMiUOovwZnzjXjq8NlcpfTpw4U12LXyRp4qST8sjUQEhHpfb1xx7h4AJ63Gat9uID9mu+ZkAA/jZfMFfU9Wa84PDwc4eHdW8juwIEDUKlUiIiIuOj3R48eDW9vb2zZsgUZGRkAgLy8PBQVFWHChAndrlnpfLzVuHdiAl7++jje2nESc4bHeMyguDe325/sc0bEIMYDlo0nos77xZUDsPz7U9hbeA7Zp2swun+I3CX1iayCahwuMcDHW4V7PWjK/PkU0RGYlZWFV199FQcPHsTJkyfx4YcfYuHChbjrrrsQHBwMACgpKUFKSgr27NkDANDr9Zg/fz4ee+wxbNu2DdnZ2bjvvvswYcIEjB8/Xs7Lkd09E/rD11uNo2V1+PZEldzl9ImCsw3YeNQ+NozbaRDRT0XpffB/I/sBAN7Y7jnrrb3ZupTIz8fEecwCij+liCCk1WqxYsUKTJ48GcOGDcNf/vIXLFy4EG+//bbzGLPZjLy8PDQ1/bhy8iuvvILZs2cjIyMDkyZNQlRUFFatWiXHJbiUID8Nbhtr7wd+6xvPaAb+57YCCAFMS4nA4MhAucshIhd0/6QkSBKw+VgFjpa6x9IpHTlaWodvjp+FSgJ+efXFh6F4AkkI4XlD5Lugrq4Oer0eBoPBrQZOnznXhMkvbYfVJrD211chLVYvd0m9Zn/ROfzfP3cCAFb9aiJGxQfLXBERuapff/QDvjxUhrEJIfj4gfFuPXTgtyv2Y/WBUvxseAxeu32k3OX0uM6+fyuiRYh6Xmywn3Mz1jfduFXIahN4anUOAGDuqH4MQUTUoczrh8DXW409hTVY48brChXXNOHLQ/YJMw9M8tzWIIBByKPd3/rHv/5wGU5XN8pcTe/4ZF8xDpcYEKj1wuLrUuQuh4hcXL8gX/z6GvseZH/56hgajO65+Ow7352C1SZw9aAwpPZz3x6BzmAQ8mBDonWYPDi8dTPWU3KX0+Nqm0x4cYN9HapHrx2MiEAfmSsiIiX45dUDkBDqh8p6I17bckLucnrcuUYTPt5rXyz4gUmcPMIg5OEcM6g+2VeMqoaeXZxSbss25eFckxmDIwO4ijQRdZrWS42nfzYMgL3lJL+yXuaKetZ7WafRbLYitZ8OVw4Mlbsc2TEIebjxiSEYHquH0WLDe60b7rmDIyUGfLi7CADwzJxUeHvYkvFEdHmmpkRg+pAIWGwCf1pzFO4yr6jZZMW7rRtvPzApya0Hg3cW3x08nCRJeMCxGWvWaTS6QX+4zSbw1OojEAL42fAYTEjiJx4i6rqnZg+DxkuF7/KrsOFI+3tUKsnK7GLUNJoQF+KL61I9d5eF8zEIEWYOi0JCqB8MzWZnv7GSfb6/BD8U1cJPo8bvrucAaSLqnvhQP+fwgee+PIpmk1Xmii6PxWpzbq56/9WJHre5anv4r0BQqyQsaJ1B9s53p2CyKHcz1roWM5astw+QfmTaIETruZUGEXXfQ5OT0C/IF6WGFry+LV/uci7LuiPlKK5pRoi/BjeP9rzNVdvDIEQAgIxRsQgL0KKkthn/2KrcWRKvfn0CVQ1GJIb54xdXcmNVIro8vho1/jh7KADg7W9OorBKmUuNGJrMeP6rYwCAeyckwFejlrki18EgRADsm7H+aY79yf769gIcLK6Vt6BuyCuvdw4C/NMce98+EdHlmjksEpMGh8NkteHZL4/KXU63PLM2B+V1LRgQ5u9cQ47s+E5BTrPTYzA7PRpWm8CilQfRYlZOf7gQAk+vOQKrTThftIiIeoIkSXj6Z0PhrZawNbcSW45VyF1Sl2w4Uo5V+0ugkoBltwxna9BPMAhRG8/dmIqwAC3yKxvw1015cpfTaWsPlWHXyRpovVTOZmwiop6SFB6A+VfZW1KeWXtUMR8UqxuM+P3nhwEAD0xOwuj+3GbopxiEqI1gfw1eyEgDAPz7u1PYc6pG5oourdFowV++sjdXPzx1IGKD/WSuiIjc0W+uGYgonQ+Kaprw9jcn5S7nkoQQ+P3nR1DdaEJKVCAenT5I7pJcEoMQXWDakEjcOiYWQgD/b+VBl19b6O9bTqCizoj4ED/2fRNRr/HXeuH3NwwBALy+LR/FNU0yV9Sx1QdKsSGnHF4qCX+9dTi0XuwSuxgGIbqoP84ein5BviiqacKS9cfkLqddXx0qw1utn8yemj0UPt58ohNR75mdHo3xiSEwWmxY8N4+1LWY5S7posoNLXhq9REAwG+nDcKwGM/eWLUjDEJ0UYE+3njx5nQAwAe7ivDN8bMyV3ShvYU1WPjJAQDAvIkJmD40Ut6CiMjtSZKEv946AhGBWuSW1+NXH/zgcmuvCSHw5GeHUNdiwfBYPR6awo1VO8IgRO26cmAY7m3drPSJTw/B0Ow6n3wKzjZgwXv7YLLYMGNoJAdIE1Gf6Rfki//MuwJ+GjW+y6/C4lWHXGovshV7i7Hj+FlovFT4663DuYL0JfBfhzq0+LohGBDmj/K6FjyzNkfucgAAZ+uNmLd8D2qbzBgRF4S/3TYSahU3DiSivpPaT4/X7xwFtUrCqh9K8Mpm11iItrimCX9uXevoiZnJGBgRKHNFro9BiDrkq1Fj2S3pUEnAqh9KsDFH3o0Hm0wW/PLdvSiuaUb/UD+8c+8YrolBRLKYmhyBP9+UCsA+aeMTmfdqtLWuAddosmLsgBCurt9JDEJ0SaP7h+D+SfY+5t9/fhjVDUZZ6rDaBB75334cPGNAsJ83ls+7AqEBWllqISICgNvHxuPXUwcCADI/P4wdMo6nXL6zEHtO1cBPo8aym4dDxZbyTmEQok5ZeO0gDI4MQFWDCX/44kif94cLIfCnNTnYfKwSGi8V/n3vGCSGB/RpDUREF7NoxmDMHdkPVpvArz7IRk6poc9ryK9swIsb7BtO//6GIYgP5XpqncUgRJ2i9VLj5VtHwEslYf2Rcjz75VGYrX03U+Jf357E+7tOQ5KAv/18BEb3D+mz301E1BFJkrA0Ix0TEkPRaLLivuV7UVLb3Ge/P6+8Hr98dy+MFhsmDQ7HHWPj++x3uwMGIeq01H56/O56+2Jiy78vxO1v70JFXUuv/94vD5Xi+XWtn3SuH4Lr0qJ7/XcSEXWFxkuFN+8ejcGRAaisN+K+5Xv6ZKbtF/tLcNPr36Owugn9gnzxYkY6JIldYl3BIERd8ourBuDtu0cjUOuFfafP4Ya/f4ddJ6t77fftOVWDxz4+CMC+VtD8qzj4j4hck97XG8vvG4uIQC2OVzTgoQ+ye22NIZPFhqdWH8GjHx9As9mKqweFYe1vrkKU3qdXfp87YxCiLpsxLAprf3MVUqICUdVgxJ3/3o23vyno0XFDTSYL/r7lBOYt3wOT1YaZw+xrBfGTDhG5sn5Bvlh+3xXw16ixs6AaN7+5s8c/LJbWNuPWt7LwXtZpAMAj0wbhv/eNRYi/pkd/j6eQhCutAuWC6urqoNfrYTAYoNPp5C7HpTSbrPj954exan8JAGDWsCi8dEs6An28u/0zLVYbPt5XjFc3n8DZevvstAmJofjPvCs4TZ6IFOOb42fx0AfZaDTZd6m/JiUCT85KQXLU5a3r831+FX7zv/2oaTRB5+OFv902ElNTInqiZLfT2fdvBqFLYBDqmBACH+wuwrNrc2C2CiSG+bf2k3ftyS6EwKajFXhxQy4KzjYCAOJD/PD4zGTckBbNaaBEpDhn643425bj+N+eYlhtAioJuHl0LBZeOxjRet8u/SybTeCNHQX466Y82AQwLEaHN+8ajbgQzg5rD4NQD2EQ6pz9Refwqw9/QJmhBb7eaizNSMOc4TGd6srKPl2D59flIvv0OQBAiL8Gv7lmIO4c1x8aL/beEpGynTzbgJc25mH9EfuCtFovFeZfNQAPTkmCrhMt6IZmMxZ9chCbj1UAAG4dE4tnb0zlJtOXwCDUQxiEOq+6wYjfrjiA7/KrAAB+GjUidT4ID9QiUueDyNb/Rui0iAj0gcZLhbe/KcDGHPuT28dbhV9elYgHJideVvcaEZEryj59DkvXH8PeQvuHvmA/b/z6mkEYNyAElfUtqKgzoqLO/t+z531d1WCETdhnpj07Zxhu4/T4TmEQ6iEMQl1jtQm88vVxvPVNAczWzv1pqSTg1jFxeHT6YM54ICK3JoTA5mOVeGFDLvIrGzp9XkKoH167fRTSYvW9WJ17YRDqIQxC3dNssrZ+smlBZb3R+d/K1k87FfUtqGk0YWxCCB6fmYxBXRxTRESkZBarDZ9mn8GbOwrQZLLaW8sDtYjQ+SCytdU8Uqd13h8WoOVYyS5iEOohDEJERETK09n3b45EJSIiIo/FIEREREQei0GIiIiIPBaDEBEREXksBiEiIiLyWAxCRERE5LEUE4QSEhIgSVKb29KlSzs8Z8qUKRec8+CDD/ZRxUREROTqvOQuoCueffZZLFiwwPl1YOClF+FbsGABnn32WefXfn7coI6IiIjsFBWEAgMDERUV1aVz/Pz8unwOEREReQbFdI0BwNKlSxEaGoqRI0fipZdegsViueQ5H374IcLCwpCamorMzEw0NTV1eLzRaERdXV2bGxEREbknxbQIPfLIIxg1ahRCQkKwc+dOZGZmoqysDC+//HK759xxxx3o378/YmJicOjQITz55JPIy8vDqlWr2j1nyZIleOaZZ3rjEoiIiMjFyLrX2OLFi/HCCy90eMyxY8eQkpJywf3/+c9/8MADD6ChoQFarbZTv2/r1q2YNm0a8vPzkZSUdNFjjEYjjEaj8+u6ujrExcVxrzEiIiIF6exeY7K2CC1atAjz5s3r8JjExMSL3j9u3DhYLBYUFhYiOTm5U79v3LhxANBhENJqtZ0OVkRERKRssgah8PBwhIeHd+vcAwcOQKVSISIiokvnAEB0dHS3ficRERG5F0WMEcrKysLu3bsxdepUBAYGIisrCwsXLsRdd92F4OBgAEBJSQmmTZuG9957D2PHjkVBQQE++ugjXH/99QgNDcWhQ4ewcOFCTJo0Cenp6Z3+3Y6eQw6aJiIiUg7H+/YlRwAJBcjOzhbjxo0Ter1e+Pj4iCFDhojnn39etLS0OI85deqUACC2bdsmhBCiqKhITJo0SYSEhAitVisGDhwoHn/8cWEwGLr0u4uLiwUA3njjjTfeeONNgbfi4uIO3+dlHSytBDabDaWlpQgMDIQkST32cx2DsIuLi912ELa7XyOvT/nc/Rrd/foA979GXl/3CSFQX1+PmJgYqFTtrxakiK4xOalUKsTGxvbaz9fpdG75x30+d79GXp/yufs1uvv1Ae5/jby+7tHr9Zc8RlELKhIRERH1JAYhIiIi8lgMQjLRarV4+umn3XrNIne/Rl6f8rn7Nbr79QHuf428vt7HwdJERETksdgiRERERB6LQYiIiIg8FoMQEREReSwGISIiIvJYDEK96C9/+QsmTpwIPz8/BAUFdeocIQSeeuopREdHw9fXF9OnT8eJEyfaHFNTU4M777wTOp0OQUFBmD9/PhoaGnrhCjrW1ToKCwshSdJFbytXrnQed7Hvr1ixoi8uqY3u/DtPmTLlgtoffPDBNscUFRXhhhtugJ+fHyIiIvD444/DYrH05qW0q6vXWFNTg9/85jdITk6Gr68v4uPj8cgjj8BgMLQ5Tq7H8PXXX0dCQgJ8fHwwbtw47Nmzp8PjV65ciZSUFPj4+CAtLQ3r1q1r8/3OPB/7Wleu8V//+heuvvpqBAcHIzg4GNOnT7/g+Hnz5l3wWM2aNau3L6NdXbm+//73vxfU7uPj0+YYV3sMu3J9F3s9kSQJN9xwg/MYV3r8vvnmG/zsZz9DTEwMJEnCF198cclztm/fjlGjRkGr1WLgwIH473//e8ExXX1ed1mXNt6iLnnqqafEyy+/LB577DGh1+s7dc7SpUuFXq8XX3zxhTh48KCYM2eOGDBggGhubnYeM2vWLDF8+HCxa9cu8e2334qBAweK22+/vZeuon1drcNisYiysrI2t2eeeUYEBASI+vp653EAxPLly9scd/7195Xu/DtPnjxZLFiwoE3t5+9vZ7FYRGpqqpg+fbrYv3+/WLdunQgLCxOZmZm9fTkX1dVrPHz4sJg7d65Ys2aNyM/PF1u2bBGDBg0SGRkZbY6T4zFcsWKF0Gg04j//+Y/IyckRCxYsEEFBQaKiouKix3///fdCrVaLF198URw9elT84Q9/EN7e3uLw4cPOYzrzfOxLXb3GO+64Q7z++uti//794tixY2LevHlCr9eLM2fOOI+59957xaxZs9o8VjU1NX11SW109fqWL18udDpdm9rLy8vbHONKj2FXr6+6urrNtR05ckSo1WqxfPly5zGu9PitW7dO/P73vxerVq0SAMTnn3/e4fEnT54Ufn5+4rHHHhNHjx4Vr732mlCr1WLDhg3OY7r6b9YdDEJ9YPny5Z0KQjabTURFRYmXXnrJeV9tba3QarXif//7nxBCiKNHjwoAYu/evc5j1q9fLyRJEiUlJT1ee3t6qo4RI0aIX/ziF23u68wTqLd19/omT54sfvvb37b7/XXr1gmVStXmxfqNN94QOp1OGI3GHqm9s3rqMfzkk0+ERqMRZrPZeZ8cj+HYsWPFww8/7PzaarWKmJgYsWTJkosef+utt4obbrihzX3jxo0TDzzwgBCic8/HvtbVa/wpi8UiAgMDxbvvvuu879577xU33nhjT5faLV29vku9trraY3i5j98rr7wiAgMDRUNDg/M+V3r8zteZ14AnnnhCDBs2rM19P//5z8XMmTOdX1/uv1lnsGvMhZw6dQrl5eWYPn268z69Xo9x48YhKysLAJCVlYWgoCCMGTPGecz06dOhUqmwe/fuPqu1J+rIzs7GgQMHMH/+/Au+9/DDDyMsLAxjx47Ff/7zH4g+Xu7qcq7vww8/RFhYGFJTU5GZmYmmpqY2PzctLQ2RkZHO+2bOnIm6ujrk5OT0/IV0oKf+lgwGA3Q6Hby82m5d2JePoclkQnZ2dpvnjkqlwvTp053PnZ/Kyspqczxgfywcx3fm+diXunONP9XU1ASz2YyQkJA292/fvh0RERFITk7GQw89hOrq6h6tvTO6e30NDQ3o378/4uLicOONN7Z5HrnSY9gTj98777yD2267Df7+/m3ud4XHrzsu9RzsiX+zzuCmqy6kvLwcANq8STq+dnyvvLwcERERbb7v5eWFkJAQ5zF9oSfqeOeddzBkyBBMnDixzf3PPvssrrnmGvj5+WHTpk341a9+hYaGBjzyyCM9Vv+ldPf67rjjDvTv3x8xMTE4dOgQnnzySeTl5WHVqlXOn3uxx9fxvb7UE49hVVUVnnvuOdx///1t7u/rx7CqqgpWq/Wi/7a5ubkXPae9x+L855rjvvaO6UvducafevLJJxETE9PmjWXWrFmYO3cuBgwYgIKCAvzud7/Dddddh6ysLKjV6h69ho505/qSk5Pxn//8B+np6TAYDFi2bBkmTpyInJwcxMbGutRjeLmP3549e3DkyBG88847be53lcevO9p7DtbV1aG5uRnnzp277L/5zmAQ6qLFixfjhRde6PCYY8eOISUlpY8q6lmdvb7L1dzcjI8++gh//OMfL/je+feNHDkSjY2NeOmll3rkTbS3r+/8QJCWlobo6GhMmzYNBQUFSEpK6vbP7Yq+egzr6upwww03YOjQofjTn/7U5nu9+RhS9yxduhQrVqzA9u3b2wwovu2225z/n5aWhvT0dCQlJWH79u2YNm2aHKV22oQJEzBhwgTn1xMnTsSQIUPw1ltv4bnnnpOxsp73zjvvIC0tDWPHjm1zv5IfP1fBINRFixYtwrx58zo8JjExsVs/OyoqCgBQUVGB6Oho5/0VFRUYMWKE85jKyso251ksFtTU1DjPvxydvb7LrePTTz9FU1MT7rnnnkseO27cODz33HMwGo2XvR9NX12fw7hx4wAA+fn5SEpKQlRU1AUzHioqKgCgRx4/oG+usb6+HrNmzUJgYCA+//xzeHt7d3h8Tz6GFxMWFga1Wu38t3SoqKho91qioqI6PL4zz8e+1J1rdFi2bBmWLl2KzZs3Iz09vcNjExMTERYWhvz8/D59I72c63Pw9vbGyJEjkZ+fD8C1HsPLub7GxkasWLECzz777CV/j1yPX3e09xzU6XTw9fWFWq2+7L+JTumx0UbUrq4Oll62bJnzPoPBcNHB0vv27XMes3HjRtkGS3e3jsmTJ18w06g9f/7zn0VwcHC3a+2Onvp3/u677wQAcfDgQSHEj4Olz5/x8NZbbwmdTidaWlp67gI6obvXaDAYxPjx48XkyZNFY2Njp35XXzyGY8eOFb/+9a+dX1utVtGvX78OB0vPnj27zX0TJky4YLB0R8/HvtbVaxRCiBdeeEHodDqRlZXVqd9RXFwsJEkSq1evvux6u6o713c+i8UikpOTxcKFC4UQrvcYdvf6li9fLrRaraiqqrrk75Dz8TsfOjlYOjU1tc19t99++wWDpS/nb6JTtfbYT6ILnD59Wuzfv985RXz//v1i//79baaKJycni1WrVjm/Xrp0qQgKChKrV68Whw4dEjfeeONFp8+PHDlS7N69W3z33Xdi0KBBsk2f76iOM2fOiOTkZLF79+425504cUJIkiTWr19/wc9cs2aN+Ne//iUOHz4sTpw4If75z38KPz8/8dRTT/X69fxUV68vPz9fPPvss2Lfvn3i1KlTYvXq1SIxMVFMmjTJeY5j+vyMGTPEgQMHxIYNG0R4eLis0+e7co0Gg0GMGzdOpKWlifz8/DZTdi0WixBCvsdwxYoVQqvViv/+97/i6NGj4v777xdBQUHOGXp33323WLx4sfP477//Xnh5eYlly5aJY8eOiaeffvqi0+cv9XzsS129xqVLlwqNRiM+/fTTNo+V4zWovr5e/L//9/9EVlaWOHXqlNi8ebMYNWqUGDRoUJ8H8+5c3zPPPCM2btwoCgoKRHZ2trjtttuEj4+PyMnJcR7jSo9hV6/P4aqrrhI///nPL7jf1R6/+vp65/scAPHyyy+L/fv3i9OnTwshhFi8eLG4++67ncc7ps8//vjj4tixY+L111+/6PT5jv7NegKDUC+69957BYALbtu2bXMeg9b1VhxsNpv44x//KCIjI4VWqxXTpk0TeXl5bX5udXW1uP3220VAQIDQ6XTivvvuaxOu+sql6jh16tQF1yuEEJmZmSIuLk5YrdYLfub69evFiBEjREBAgPD39xfDhw8Xb7755kWP7W1dvb6ioiIxadIkERISIrRarRg4cKB4/PHH26wjJIQQhYWF4rrrrhO+vr4iLCxMLFq0qM3U877U1Wvctm3bRf+mAYhTp04JIeR9DF977TURHx8vNBqNGDt2rNi1a5fze5MnTxb33ntvm+M/+eQTMXjwYKHRaMSwYcPEV1991eb7nXk+9rWuXGP//v0v+lg9/fTTQgghmpqaxIwZM0R4eLjw9vYW/fv3FwsWLOjRN5mu6sr1Pfroo85jIyMjxfXXXy9++OGHNj/P1R7Drv6N5ubmCgBi06ZNF/wsV3v82nt9cFzTvffeKyZPnnzBOSNGjBAajUYkJia2eT906OjfrCdIQvTxvGQiIiIiF8F1hIiIiMhjMQgRERGRx2IQIiIiIo/FIEREREQei0GIiIiIPBaDEBEREXksBiEiIiLyWAxCRERE5LEYhIiIiMhjMQgRERGRx2IQIiIiIo/FIEREHuXs2bOIiorC888/77xv586d0Gg02LJli4yVEZEcuOkqEXmcdevW4aabbsLOnTuRnJyMESNG4MYbb8TLL78sd2lE1McYhIjIIz388MPYvHkzxowZg8OHD2Pv3r3QarVyl0VEfYxBiIg8UnNzM1JTU1FcXIzs7GykpaXJXRIRyYBjhIjIIxUUFKC0tBQ2mw2FhYVyl0NEMmGLEBF5HJPJhLFjx2LEiBFITk7Gq6++isOHDyMiIkLu0oiojzEIEZHHefzxx/Hpp5/i4MGDCAgIwOTJk6HX6/Hll1/KXRoR9TF2jRGRR9m+fTteffVVvP/++9DpdFCpVHj//ffx7bff4o033pC7PCLqY2wRIiIiIo/FFiEiIiLyWAxCRERE5LEYhIiIiMhjMQgRERGRx2IQIiIiIo/FIEREREQei0GIiIiIPBaDEBEREXksBiEiIiLyWAxCRERE5LEYhIiIiMhj/X+xjgCPrJZhugAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Let's check graphically the range of -pi*x*sin(pi*x) + cos(pi*x) - 3\n", "x_range = np.linspace(-1,1,50)\n", "y_range = -np.pi*x_range*np.sin(np.pi*x_range) + np.cos(np.pi*x_range) - 3\n", "plt.figure()\n", "plt.plot(x_range,y_range)\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "\n", "#Looks like no sign change for our domain of -1" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Let's check graphically the range of -pi*x*sin(pi*x) + cos(pi*x) - 3\n", "the_range = np.linspace(-0.1,0.1,50)\n", "y_range = -3*the_range**2 - 0.1*np.pi*np.sin(0.1*np.pi)+np.cos(0.1*np.pi)\n", "x_range = -np.pi*the_range*np.sin(np.pi*the_range)+np.cos(np.pi*the_range)-0.03\n", "plt.figure()\n", "plt.plot(the_range,x_range, the_range, y_range)\n", "plt.legend(['X-Range', 'Y-Range'])\n", "plt.xlabel('Domain (x or y)')\n", "plt.ylabel('Range (y or x)')\n", "\n", "#Looks like no sign change for our domain of -1" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xdot = P\n", "ydot = Q\n", "alpha_val = 0.5\n", "\n", "#Create Functions\n", "P = lambda x, y: y + x*(alpha_val - x**2 - y**2)\n", "Q = lambda x, y: -x + y*(1 - x**2 - y**2)\n", "def dX_dt(X, t, args = (P,Q)):\n", " return [P(X[0], X[1]), Q(X[0], X[1])]\n", "\n", "#Initial Conditions\n", "ts = np.linspace(0, 5, 30)\n", "ic = np.linspace(-1.2, 1.2, 7)\n", "\n", "#Make a vectorfield\n", "X, Y = np.mgrid[ic[0]:ic[-1]:20j, ic[0]:ic[-1]:20j]\n", "u = P(X,Y)\n", "v = Q(X,Y)\n", "plt.quiver(X, Y, u, v, color = 'red')\n", "\n", "#plot trajectories\n", "plt.title(f'Phase Portrait for $\\\\dot x = $ {xdot} and $\\\\dot y = $ {ydot}')\n", "plt.xlabel('x'); plt.ylabel('y'); plt.grid('both')\n", "plt.xlim((ic[0],ic[-1])); plt.ylim((ic[0],ic[-1]))\n", "\n", "for r in ic:\n", " for s in ic:\n", " X0 = [r,s]\n", " Xs = odeint(dX_dt,X0,ts)\n", " plt.plot(Xs[:,0],Xs[:,1], \"royalblue\",linewidth = 0.75)\n", "\n" ] }, { "cell_type": "markdown", "id": "759a57ff-d8a3-49c1-9556-2d41a34d78b8", "metadata": {}, "source": [ "From calculating the algabraeic expressions for the critical points and looking at the plot, it's pretty clear there is one critical point inside the potential limit cycle and the rest are outside of the potential limit cycle. \n", "\n", "It also looks like this limit cycle is **stable**. That is because the vectors point in towards the limit cycle. Let me prove this:" ] }, { "cell_type": "code", "execution_count": 16, "id": "4b004f14-5c8e-4eb4-88bd-a93666b11602", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dV/dt Expression: \n", "alpha - 4*x**2 - 4*y**2 + 1\n", "\n", "dV/dt Simplified:\n", "alpha - 4*x**2 - 4*y**2 + 1\n", "\n", "Sign Changes: \n", "[(-sqrt(alpha - 4*y**2 + 1)/2, y), (sqrt(alpha - 4*y**2 + 1)/2, y)]\n" ] } ], "source": [ "#Guess a psi for Poincare - Bendixson Theorem\n", "psi = 1\n", "def sign_change_test(xdot, ydot, psi):\n", " div_psiX = sm.diff(psi*xdot,x) + sm.diff(psi*ydot, y)\n", " print(f'dV/dt Expression: \\n{div_psiX}')\n", " print(f'\\ndV/dt Simplified:\\n{sm.simplify(div_psiX)}\\n')\n", " \n", " sign_changes = sm.solve(sm.Eq(0,div_psiX),x,y)\n", " print(f'Sign Changes: \\n{sign_changes}')\n", " return div_psiX\n", "\n", "expr = sign_change_test(xdot, ydot, psi)" ] }, { "cell_type": "markdown", "id": "063e52d9-875c-4dc9-83b6-6dca251ffa43", "metadata": {}, "source": [ "Now let me draw a rectangle around this limit cycle the same as the last problem. A rectangle at points (-1, -1), (-1, 1), (1, -1), (1, 1), and a smaller internal rectangle at (-0.1, -0.1), (-0.1, 0.1), (0.1, 0.1), (0.1, -0.1). " ] }, { "cell_type": "code", "execution_count": 17, "id": "a854e3d8-dee6-4084-be05-89e0686557b1", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\alpha - 4 y^{2} - 3$" ], "text/plain": [ "alpha - 4*y**2 - 3" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr.subs(x,-1)\n", "#This is clearly always < 0. No sign change" ] }, { "cell_type": "code", "execution_count": 18, "id": "488b307d-1f03-4f33-8a0c-76dffc194d2b", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\alpha - 4 x^{2} - 3$" ], "text/plain": [ "alpha - 4*x**2 - 3" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr.subs(y,-1)" ] }, { "cell_type": "code", "execution_count": 19, "id": "9b011142-9718-447e-ae43-9d30cff58568", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\alpha - 4 y^{2} - 3$" ], "text/plain": [ "alpha - 4*y**2 - 3" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr.subs(x,1)" ] }, { "cell_type": "code", "execution_count": 20, "id": "8b82bc08-3e2d-4db8-8424-0678fc762a68", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\alpha - 4 x^{2} - 3$" ], "text/plain": [ "alpha - 4*x**2 - 3" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr.subs(y,1)" ] }, { "cell_type": "markdown", "id": "ee28ae38-576e-4bc5-8c53-45e8dea3de1a", "metadata": {}, "source": [ "For $0 < \\alpha < 1$ these are all clearly always negative." ] }, { "cell_type": "code", "execution_count": 21, "id": "31752100-ae0a-4a84-8ba9-ef4d7147a5e7", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\alpha - 4 y^{2} + 0.96$" ], "text/plain": [ "alpha - 4*y**2 + 0.96" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr.subs(x,-0.1)" ] }, { "cell_type": "code", "execution_count": 22, "id": "7dc2aee7-f0f7-40d6-bad3-aee37f7b550a", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\alpha - 4 y^{2} + 0.96$" ], "text/plain": [ "alpha - 4*y**2 + 0.96" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr.subs(x,0.1)" ] }, { "cell_type": "code", "execution_count": 23, "id": "3c9c2d41-f3b5-4026-a8e7-d782388d7686", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\alpha - 4 x^{2} + 0.96$" ], "text/plain": [ "alpha - 4*x**2 + 0.96" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr.subs(y,-0.1)" ] }, { "cell_type": "code", "execution_count": 24, "id": "126023fa-4546-4fa4-a4a8-70de4ef70cfa", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\alpha - 4 x^{2} + 0.96$" ], "text/plain": [ "alpha - 4*x**2 + 0.96" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr.subs(y,0.1)" ] }, { "cell_type": "markdown", "id": "519cbcda-bcf9-4e05-8d99-4356d16ffd5c", "metadata": {}, "source": [ "For x or y = 0.1, it's clear this is always positive for $ 0 < \\alpha < 1 $.\n", "As a result, there must be a limit cycle between these two rectangles that is stable, as flow enters the region on all boundaries." ] }, { "attachments": { 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" } }, "cell_type": "markdown", "id": "0bc31580-8784-4e92-bbc8-93ee06cd9bf2", "metadata": {}, "source": [ "![image.png](attachment:a49d2138-fa02-44c3-bad9-c574795b9cc7.png)" ] }, { "cell_type": "markdown", "id": "44598ad7-a1a8-486a-8d27-839c657966c3", "metadata": {}, "source": [ "**Problem A**" ] }, { "cell_type": "code", "execution_count": 25, "id": "5b6610b7-3ae1-474e-bdcd-99f29fa603bb", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - x^{4} - x^{2} - 1$" ], "text/plain": [ "-x**4 - x**2 - 1" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xdot = y\n", "ydot = -x - (1+x**2+x**4)*y\n", "zeta = 1\n", "fun = sm.simplify(sm.diff(zeta*xdot,x) + sm.diff(zeta*ydot,y))\n", "fun" ] }, { "cell_type": "markdown", "id": "ce9a8a1a-4790-4825-8ddb-89145a4260f9", "metadata": {}, "source": [ "This function cannot change sign for all real numbers. Therefore, there is no limit cycle in the 2d plane.\n", "\n", "**Problem B**" ] }, { "cell_type": "code", "execution_count": 26, "id": "03ed9400-4f8a-4d93-95c4-8dc567a802dc", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 2 - x$" ], "text/plain": [ "2 - x" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xdot = x - x**2 + 2*y**2\n", "ydot = y*(x+1)\n", "\n", "zeta = 1\n", "\n", "fun = sm.simplify(sm.diff(zeta*xdot,x) + sm.diff(zeta*ydot,y))\n", "fun" ] }, { "cell_type": "code", "execution_count": 27, "id": "ef02629e-77eb-4876-b1bf-a14c4167818e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Create Functions\n", "P = lambda x, y: x - x**2 + 2*y**2\n", "Q = lambda x, y: y*(x+1)\n", "def dX_dt(X, t, args = (P,Q)):\n", " return [P(X[0], X[1]), Q(X[0], X[1])]\n", "\n", "#Initial Conditions\n", "ts = np.linspace(0, 0.1, 30)\n", "ic = np.linspace(-1.2, 1.2, 7)\n", "\n", "#Make a vectorfield\n", "X, Y = np.mgrid[ic[0]:ic[-1]:20j, ic[0]:ic[-1]:20j]\n", "u = P(X,Y)\n", "v = Q(X,Y)\n", "plt.quiver(X, Y, u, v, color = 'red')\n", "\n", "#plot trajectories\n", "plt.title(f'Phase Portrait for $\\\\dot x = $ {xdot} and $\\\\dot y = $ {ydot}')\n", "plt.xlabel('x'); plt.ylabel('y'); plt.grid('both')\n", "plt.xlim((ic[0],ic[-1])); plt.ylim((ic[0],ic[-1]))\n", "\n", "for r in ic:\n", " for s in ic:\n", " X0 = [r,s]\n", " Xs = odeint(dX_dt,X0,ts)\n", " plt.plot(Xs[:,0],Xs[:,1], \"royalblue\",linewidth = 0.75)\n", " " ] }, { "cell_type": "markdown", "id": "eca4d569-15b4-4167-a4ae-5360acd6e256", "metadata": {}, "source": [ "Now we know we can't just use Bendixson's criterion. But! The x axis looks invariant. Let's take a closer look." ] }, { "cell_type": "code", "execution_count": 28, "id": "98e0ce12-6e96-4b4c-825f-56d39aad8478", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dV/dt Expression: \n", "2 - x\n", "\n", "dV/dt Simplified:\n", "2 - x\n", "\n", "Sign Changes: \n", "[(2, y)]\n" ] }, { "data": { "text/latex": [ "$\\displaystyle 2$" ], "text/plain": [ "2" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Guess a psi for Poincare - Bendixson Theorem\n", "psi = 1\n", "def sign_change_test(xdot, ydot, psi):\n", " div_psiX = sm.diff(psi*xdot,x) + sm.diff(psi*ydot, y)\n", " print(f'dV/dt Expression: \\n{div_psiX}')\n", " print(f'\\ndV/dt Simplified:\\n{sm.simplify(div_psiX)}\\n')\n", " \n", " sign_changes = sm.solve(sm.Eq(0,div_psiX),x,y)\n", " print(f'Sign Changes: \\n{sign_changes}')\n", " return div_psiX\n", "\n", "expr = sign_change_test(xdot, ydot, psi)\n", "\n", "expr.subs(x,0)" ] }, { "cell_type": "markdown", "id": "826ecb2a-a9aa-4617-b1fc-9fb207b84622", "metadata": {}, "source": [ "So we know the x axis is invariant. Now to know if we have a limit cycle or not, we just need to be sure there are no critical points on the x axis." ] }, { "cell_type": "code", "execution_count": 29, "id": "899989af-6470-4837-9674-2784f372be09", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(-1, -1), (-1, 1), (0, 0), (1, 0)]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Peqn = sm.Eq(xdot, 0)\n", "Qeqn = sm.Eq(ydot, 0)\n", "\n", "criticalpoints = sm.solve((Peqn,Qeqn),x,y)\n", "display(criticalpoints)" ] }, { "cell_type": "markdown", "id": "fed0883c-3a2e-457b-8fa7-1a837bbafc2d", "metadata": {}, "source": [ "We have one troublesome critical point. Let's check if this is the right sign for us to say there's no limit cycle." ] }, { "cell_type": "code", "execution_count": 30, "id": "a27622ff-ab8e-4d8a-ab98-03631d28ff24", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 2 y^{2}$" ], "text/plain": [ "2*y**2" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xdot.subs(x, 0)" ] }, { "cell_type": "markdown", "id": "770cfd39-1620-4284-8115-202953c1c9b3", "metadata": {}, "source": [ "This is always positive, just like our other information about the x axis. Therefore there is no limit cycle." ] }, { "cell_type": "markdown", "id": "e023c7ab-7b27-4897-a378-5268d3d2c38d", "metadata": {}, "source": [ "**Problem C**" ] }, { "cell_type": "code", "execution_count": 31, "id": "e800d1c1-5823-47b7-8425-c73fc5a07bf5", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - 2 x^{2} - 6$" ], "text/plain": [ "-2*x**2 - 6" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xdot = y**2 - 2*x\n", "ydot = 3 - 4*y - 2*x**2*y\n", "\n", "zeta = 1 \n", "\n", "fun = sm.simplify(sm.diff(zeta*xdot,x) + sm.diff(zeta*ydot,y))\n", "fun" ] }, { "cell_type": "markdown", "id": "92bc04df-6400-470f-9c08-f39b992ce675", "metadata": {}, "source": [ "This function does not change sign for all real numbers. Therefore there is no limit cycle thanks to Bendixson's Criterion." ] }, { "cell_type": "markdown", "id": "77be06d4-3205-4c4f-b989-22ae7f906db4", "metadata": {}, "source": [ "**Problem D**" ] }, { "cell_type": "code", "execution_count": 32, "id": "b7cd9c6d-1552-4295-b68e-d8025d393e5b", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - x^{2} - 3$" ], "text/plain": [ "-x**2 - 3" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xdot = -x + y**3 - y**4\n", "ydot = 1 - 2*y - x**2*y + x**4\n", "\n", "zeta = 1\n", "\n", "fun = sm.simplify(sm.diff(zeta*xdot,x) + sm.diff(zeta*ydot,y))\n", "fun" ] }, { "cell_type": "markdown", "id": "7c0bb802-bc3d-475d-ba8e-15576cda7926", "metadata": {}, "source": [ "This function also does not change sign for all real numbers. There is no limit cycle thanks to Bendixson's Criterion." ] }, { "attachments": { "7767ef13-07dc-41ce-a54e-beef95d98016.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "fe2f9eb3-0261-4dd9-bd11-b9f235651b41", "metadata": {}, "source": [ "![image.png](attachment:7767ef13-07dc-41ce-a54e-beef95d98016.png)" ] }, { "cell_type": "code", "execution_count": 33, "id": "658651a7-69e8-4852-bb1f-8f767c3715b7", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\epsilon^{3} \\left(\\omega^{2} \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + x_{1}^{2}{\\left(t \\right)}\\right) + \\epsilon^{2} \\left(\\omega^{2} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + 2 \\omega \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + 2 x_{0}{\\left(t \\right)} x_{1}{\\left(t \\right)}\\right) + \\epsilon \\left(2 \\omega \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + x_{0}^{2}{\\left(t \\right)} + x_{1}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)}\\right) + x_{0}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)}$" ], "text/plain": [ "epsilon**3*(omega**2*Derivative(x_1(t), (t, 2)) + x_1(t)**2) + epsilon**2*(omega**2*Derivative(x_0(t), (t, 2)) + 2*omega*Derivative(x_1(t), (t, 2)) + 2*x_0(t)*x_1(t)) + epsilon*(2*omega*Derivative(x_0(t), (t, 2)) + x_0(t)**2 + x_1(t) + Derivative(x_1(t), (t, 2))) + x_0(t) + Derivative(x_0(t), (t, 2))" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = sm.Function('x')\n", "x0 = sm.Function('x_0')\n", "x1 = sm.Function('x_1')\n", "\n", "t = sm.Symbol('t')\n", "eps = sm.Symbol('epsilon')\n", "omega = sm.Symbol('omega')\n", "\n", "#Set up series expansion\n", "x = x0(t) + eps*x1(t)\n", "dt = (1+eps*omega)\n", "\n", "expr = dt**2*x.diff(t,t) + x + eps*x**2 \n", "sm.collect(sm.expand(expr),eps)" ] }, { "cell_type": "code", "execution_count": 34, "id": "965b5c7f-cd15-4d86-9b17-cecbfa77ec0a", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle x_{0}{\\left(t \\right)} = C_{1} \\sin{\\left(t \\right)} + C_{2} \\cos{\\left(t \\right)}$" ], "text/plain": [ "Eq(x_0(t), C1*sin(t) + C2*cos(t))" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solve for O(1)\n", "O_1 = sm.dsolve(x0(t) + x0(t).diff(t,t))\n", "O_1" ] }, { "cell_type": "code", "execution_count": 35, "id": "b507187a-0c37-4f67-a10c-2237fa3538fb", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle x_{1}{\\left(t \\right)} = \\frac{- 2 C_{1} \\omega \\left(\\epsilon \\omega + 1\\right)^{2} \\sin{\\left(t \\right)} - 2 C_{2} \\omega \\left(\\epsilon \\omega + 1\\right)^{2} \\cos{\\left(t \\right)} - \\left(C_{1} \\sin{\\left(t \\right)} + C_{2} \\cos{\\left(t \\right)}\\right)^{2}}{\\left(\\epsilon \\omega + 1\\right)^{2} + 1}$" ], "text/plain": [ "Eq(x_1(t), (-2*C1*omega*(epsilon*omega + 1)**2*sin(t) - 2*C2*omega*(epsilon*omega + 1)**2*cos(t) - (C1*sin(t) + C2*cos(t))**2)/((epsilon*omega + 1)**2 + 1))" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solve for O(eps)\n", "x0 = O_1.rhs #extract x0 solution\n", "\n", "#Solve for x1\n", "O_eps = sm.dsolve(sm.simplify(2*omega*dt**2*x0 + x0**2 + x1(t) + dt**2*x1(t)), x1(t))\n", "O_eps" ] }, { "cell_type": "code", "execution_count": 36, "id": "102fc8da-f0c6-43a9-99c2-64580071b3ef", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle x_{1}{\\left(t \\right)} = - \\frac{\\left(C_{1} \\sin{\\left(t \\right)} + C_{2} \\cos{\\left(t \\right)}\\right)^{2}}{2}$" ], "text/plain": [ "Eq(x_1(t), -(C1*sin(t) + C2*cos(t))**2/2)" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Now a hiccup. We need to make sure we have no secular terms. By inspection, we can do this by setting $\\omega$ = 0.\n", "O_eps = O_eps.subs(omega, 0)\n", "O_eps.simplify()" ] }, { "cell_type": "code", "execution_count": 37, "id": "2be9ea31-fb5a-49cc-888f-45b79d8fa22e", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 0 = C_{1} \\sin{\\left(t \\right)} + C_{2} \\cos{\\left(t \\right)} - \\frac{\\epsilon \\left(C_{1} \\sin{\\left(t \\right)} + C_{2} \\cos{\\left(t \\right)}\\right)^{2}}{2}$" ], "text/plain": [ "Eq(0, C1*sin(t) + C2*cos(t) - epsilon*(C1*sin(t) + C2*cos(t))**2/2)" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Now plug everything back into our expression for x:\n", "xsoln = sm.Eq(0, x0 + eps*O_eps.rhs)\n", "xsoln" ] }, { "attachments": { "f74938ea-d577-425c-b7b1-70a42814e493.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "80d5238b-e994-4493-82b9-66a90fe9251e", "metadata": {}, "source": [ "![image.png](attachment:f74938ea-d577-425c-b7b1-70a42814e493.png)" ] }, { "cell_type": "code", "execution_count": 38, "id": "e6c41e17-6b70-425a-8b9d-10c83f4b3e94", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\epsilon^{9} \\omega_{2} x_{2}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + \\epsilon^{8} \\left(\\omega_{1} x_{2}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + 2 \\omega_{2} x_{1}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + \\omega_{2} x_{2}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)}\\right) + \\epsilon^{7} \\left(2 \\omega_{1} x_{1}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + \\omega_{1} x_{2}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + 2 \\omega_{2} x_{0}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + \\omega_{2} x_{1}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + 2 \\omega_{2} x_{1}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + \\omega_{2} x_{2}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + x_{2}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)}\\right) + \\epsilon^{6} \\left(2 \\omega_{1} x_{0}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + \\omega_{1} x_{1}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + 2 \\omega_{1} x_{1}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + \\omega_{1} x_{2}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + \\omega_{2}^{2} \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)} + 2 \\omega_{2} x_{0}{\\left(t \\right)} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + 2 \\omega_{2} x_{0}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + \\omega_{2} x_{1}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + 2 \\omega_{2} x_{1}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + 2 x_{1}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + x_{2}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)}\\right) + \\epsilon^{5} \\left(2 \\omega_{1} \\omega_{2} \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)} + 2 \\omega_{1} x_{0}{\\left(t \\right)} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + 2 \\omega_{1} x_{0}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + \\omega_{1} x_{1}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + 2 \\omega_{1} x_{1}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + \\omega_{2}^{2} \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + \\omega_{2} x_{0}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + 2 \\omega_{2} x_{0}{\\left(t \\right)} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + 2 \\omega_{2} x_{0}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + \\omega_{2} x_{1}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} - \\omega_{2} \\frac{d}{d t} x_{2}{\\left(t \\right)} + 2 x_{0}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + x_{1}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + 2 x_{1}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + x_{2}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)}\\right) + \\epsilon^{4} \\left(\\omega_{1}^{2} \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)} + 2 \\omega_{1} \\omega_{2} \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + \\omega_{1} x_{0}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + 2 \\omega_{1} x_{0}{\\left(t \\right)} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + 2 \\omega_{1} x_{0}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + \\omega_{1} x_{1}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} - \\omega_{1} \\frac{d}{d t} x_{2}{\\left(t \\right)} + \\omega_{2}^{2} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + \\omega_{2} x_{0}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + 2 \\omega_{2} x_{0}{\\left(t \\right)} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} - \\omega_{2} \\frac{d}{d t} x_{1}{\\left(t \\right)} + 2 \\omega_{2} \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)} + 2 x_{0}{\\left(t \\right)} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + 2 x_{0}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + x_{1}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + 2 x_{1}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)}\\right) + \\epsilon^{3} \\left(\\omega_{1}^{2} \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + 2 \\omega_{1} \\omega_{2} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + \\omega_{1} x_{0}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + 2 \\omega_{1} x_{0}{\\left(t \\right)} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} - \\omega_{1} \\frac{d}{d t} x_{1}{\\left(t \\right)} + 2 \\omega_{1} \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)} + \\omega_{2} x_{0}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} - \\omega_{2} \\frac{d}{d t} x_{0}{\\left(t \\right)} + 2 \\omega_{2} \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + x_{0}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + 2 x_{0}{\\left(t \\right)} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + 2 x_{0}{\\left(t \\right)} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + x_{1}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} - \\frac{d}{d t} x_{2}{\\left(t \\right)}\\right) + \\epsilon^{2} \\left(\\omega_{1}^{2} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + \\omega_{1} x_{0}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} - \\omega_{1} \\frac{d}{d t} x_{0}{\\left(t \\right)} + 2 \\omega_{1} \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + 2 \\omega_{2} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + x_{0}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + 2 x_{0}{\\left(t \\right)} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + x_{2}{\\left(t \\right)} - \\frac{d}{d t} x_{1}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)}\\right) + \\epsilon \\left(2 \\omega_{1} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + x_{0}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + x_{1}{\\left(t \\right)} - \\frac{d}{d t} x_{0}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)}\\right) + x_{0}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)}$" ], "text/plain": [ "epsilon**9*omega_2*x_2(t)**2*Derivative(x_2(t), t) + epsilon**8*(omega_1*x_2(t)**2*Derivative(x_2(t), t) + 2*omega_2*x_1(t)*x_2(t)*Derivative(x_2(t), t) + omega_2*x_2(t)**2*Derivative(x_1(t), t)) + epsilon**7*(2*omega_1*x_1(t)*x_2(t)*Derivative(x_2(t), t) + omega_1*x_2(t)**2*Derivative(x_1(t), t) + 2*omega_2*x_0(t)*x_2(t)*Derivative(x_2(t), t) + omega_2*x_1(t)**2*Derivative(x_2(t), t) + 2*omega_2*x_1(t)*x_2(t)*Derivative(x_1(t), t) + omega_2*x_2(t)**2*Derivative(x_0(t), t) + x_2(t)**2*Derivative(x_2(t), t)) + epsilon**6*(2*omega_1*x_0(t)*x_2(t)*Derivative(x_2(t), t) + omega_1*x_1(t)**2*Derivative(x_2(t), t) + 2*omega_1*x_1(t)*x_2(t)*Derivative(x_1(t), t) + omega_1*x_2(t)**2*Derivative(x_0(t), t) + omega_2**2*Derivative(x_2(t), (t, 2)) + 2*omega_2*x_0(t)*x_1(t)*Derivative(x_2(t), t) + 2*omega_2*x_0(t)*x_2(t)*Derivative(x_1(t), t) + omega_2*x_1(t)**2*Derivative(x_1(t), t) + 2*omega_2*x_1(t)*x_2(t)*Derivative(x_0(t), t) + 2*x_1(t)*x_2(t)*Derivative(x_2(t), t) + x_2(t)**2*Derivative(x_1(t), t)) + epsilon**5*(2*omega_1*omega_2*Derivative(x_2(t), (t, 2)) + 2*omega_1*x_0(t)*x_1(t)*Derivative(x_2(t), t) + 2*omega_1*x_0(t)*x_2(t)*Derivative(x_1(t), t) + omega_1*x_1(t)**2*Derivative(x_1(t), t) + 2*omega_1*x_1(t)*x_2(t)*Derivative(x_0(t), t) + omega_2**2*Derivative(x_1(t), (t, 2)) + omega_2*x_0(t)**2*Derivative(x_2(t), t) + 2*omega_2*x_0(t)*x_1(t)*Derivative(x_1(t), t) + 2*omega_2*x_0(t)*x_2(t)*Derivative(x_0(t), t) + omega_2*x_1(t)**2*Derivative(x_0(t), t) - omega_2*Derivative(x_2(t), t) + 2*x_0(t)*x_2(t)*Derivative(x_2(t), t) + x_1(t)**2*Derivative(x_2(t), t) + 2*x_1(t)*x_2(t)*Derivative(x_1(t), t) + x_2(t)**2*Derivative(x_0(t), t)) + epsilon**4*(omega_1**2*Derivative(x_2(t), (t, 2)) + 2*omega_1*omega_2*Derivative(x_1(t), (t, 2)) + omega_1*x_0(t)**2*Derivative(x_2(t), t) + 2*omega_1*x_0(t)*x_1(t)*Derivative(x_1(t), t) + 2*omega_1*x_0(t)*x_2(t)*Derivative(x_0(t), t) + omega_1*x_1(t)**2*Derivative(x_0(t), t) - omega_1*Derivative(x_2(t), t) + omega_2**2*Derivative(x_0(t), (t, 2)) + omega_2*x_0(t)**2*Derivative(x_1(t), t) + 2*omega_2*x_0(t)*x_1(t)*Derivative(x_0(t), t) - omega_2*Derivative(x_1(t), t) + 2*omega_2*Derivative(x_2(t), (t, 2)) + 2*x_0(t)*x_1(t)*Derivative(x_2(t), t) + 2*x_0(t)*x_2(t)*Derivative(x_1(t), t) + x_1(t)**2*Derivative(x_1(t), t) + 2*x_1(t)*x_2(t)*Derivative(x_0(t), t)) + epsilon**3*(omega_1**2*Derivative(x_1(t), (t, 2)) + 2*omega_1*omega_2*Derivative(x_0(t), (t, 2)) + omega_1*x_0(t)**2*Derivative(x_1(t), t) + 2*omega_1*x_0(t)*x_1(t)*Derivative(x_0(t), t) - omega_1*Derivative(x_1(t), t) + 2*omega_1*Derivative(x_2(t), (t, 2)) + omega_2*x_0(t)**2*Derivative(x_0(t), t) - omega_2*Derivative(x_0(t), t) + 2*omega_2*Derivative(x_1(t), (t, 2)) + x_0(t)**2*Derivative(x_2(t), t) + 2*x_0(t)*x_1(t)*Derivative(x_1(t), t) + 2*x_0(t)*x_2(t)*Derivative(x_0(t), t) + x_1(t)**2*Derivative(x_0(t), t) - Derivative(x_2(t), t)) + epsilon**2*(omega_1**2*Derivative(x_0(t), (t, 2)) + omega_1*x_0(t)**2*Derivative(x_0(t), t) - omega_1*Derivative(x_0(t), t) + 2*omega_1*Derivative(x_1(t), (t, 2)) + 2*omega_2*Derivative(x_0(t), (t, 2)) + x_0(t)**2*Derivative(x_1(t), t) + 2*x_0(t)*x_1(t)*Derivative(x_0(t), t) + x_2(t) - Derivative(x_1(t), t) + Derivative(x_2(t), (t, 2))) + epsilon*(2*omega_1*Derivative(x_0(t), (t, 2)) + x_0(t)**2*Derivative(x_0(t), t) + x_1(t) - Derivative(x_0(t), t) + Derivative(x_1(t), (t, 2))) + x_0(t) + Derivative(x_0(t), (t, 2))" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = sm.Function('x')\n", "x0 = sm.Function('x_0')\n", "x1 = sm.Function('x_1')\n", "x2 = sm.Function('x_2')\n", "\n", "t = sm.Symbol('t')\n", "eps = sm.Symbol('epsilon')\n", "omega_1 = sm.Symbol('omega_1')\n", "omega_2 = sm.Symbol('omega_2')\n", "\n", "#Set up series expansion\n", "x_expr = x0(t) + eps*x1(t) + eps**2*x2(t)\n", "dt = (1+eps*omega_1+eps**2*omega_2)\n", "\n", "expr = dt**2*x_expr.diff(t,t) + eps*(x_expr**2 - 1) * dt * x_expr.diff(t) + x_expr \n", "sm.collect(sm.expand(expr),eps)" ] }, { "cell_type": "code", "execution_count": 39, "id": "c70d7149-3628-4a60-b261-5eedc052e72b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Order 0: \n" ] }, { "data": { "text/latex": [ "$\\displaystyle x_{0}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)}$" ], "text/plain": [ "x_0(t) + Derivative(x_0(t), (t, 2))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Order 1: \n" ] }, { "data": { "text/latex": [ "$\\displaystyle 2 \\omega_{1} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + x_{0}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + x_{1}{\\left(t \\right)} - \\frac{d}{d t} x_{0}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)}$" ], "text/plain": [ "2*omega_1*Derivative(x_0(t), (t, 2)) + x_0(t)**2*Derivative(x_0(t), t) + x_1(t) - Derivative(x_0(t), t) + Derivative(x_1(t), (t, 2))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Order 2: \n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\omega_{1}^{2} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + \\omega_{1} x_{0}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} - \\omega_{1} \\frac{d}{d t} x_{0}{\\left(t \\right)} + 2 \\omega_{1} \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + 2 \\omega_{2} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + x_{0}^{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + 2 x_{0}{\\left(t \\right)} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + x_{2}{\\left(t \\right)} - \\frac{d}{d t} x_{1}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)}$" ], "text/plain": [ "omega_1**2*Derivative(x_0(t), (t, 2)) + omega_1*x_0(t)**2*Derivative(x_0(t), t) - omega_1*Derivative(x_0(t), t) + 2*omega_1*Derivative(x_1(t), (t, 2)) + 2*omega_2*Derivative(x_0(t), (t, 2)) + x_0(t)**2*Derivative(x_1(t), t) + 2*x_0(t)*x_1(t)*Derivative(x_0(t), t) + x_2(t) - Derivative(x_1(t), t) + Derivative(x_2(t), (t, 2))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#getting the first 3 orders:\n", "eps_ords = sm.collect(sm.expand(expr),eps,evaluate=False)\n", "eps_list= []\n", "for order in range(3):\n", " eps_list.append(eps_ords[eps**order])\n", " print(f'\\nOrder {order}: ')\n", " display(eps_list[order])\n", " " ] }, { "cell_type": "code", "execution_count": 40, "id": "d071eaab-7b56-4a69-bc0d-9d231fb780cc", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle x_{0}{\\left(t \\right)} = C_{1} \\sin{\\left(t \\right)} + C_{2} \\cos{\\left(t \\right)}$" ], "text/plain": [ "Eq(x_0(t), C1*sin(t) + C2*cos(t))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Solve 0th order\n", "ord_0 = sm.dsolve(eps_list[0],x0(t))\n", "display(ord_0)" ] }, { "cell_type": "code", "execution_count": 41, "id": "7d7fd828-c8d1-4773-9f43-8f4cb9ba51f4", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle x_{1}{\\left(t \\right)} = - \\frac{C_{1} \\left(C_{1}^{2} - 3 C_{2}^{2}\\right) \\cos^{3}{\\left(t \\right)}}{8} + \\frac{\\left(3 C_{1}^{3} - C_{1}^{2} C_{2} t - 9 C_{1} C_{2}^{2} - 8 C_{1} \\omega_{1} t - C_{2}^{3} t + 4 C_{2} t + 8 C_{3}\\right) \\cos{\\left(t \\right)}}{8} + \\frac{\\left(- C_{1}^{3} t + 4 C_{1}^{2} C_{2} - C_{1} C_{2}^{2} t + 8 C_{1} \\omega_{1} + 4 C_{1} t + 8 C_{2} \\omega_{1} t + C_{2} \\left(3 C_{1}^{2} - C_{2}^{2}\\right) \\cos^{2}{\\left(t \\right)} - 4 C_{2} + 8 C_{4}\\right) \\sin{\\left(t \\right)}}{8}$" ], "text/plain": [ "Eq(x_1(t), -C1*(C1**2 - 3*C2**2)*cos(t)**3/8 + (3*C1**3 - C1**2*C2*t - 9*C1*C2**2 - 8*C1*omega_1*t - C2**3*t + 4*C2*t + 8*C3)*cos(t)/8 + (-C1**3*t + 4*C1**2*C2 - C1*C2**2*t + 8*C1*omega_1 + 4*C1*t + 8*C2*omega_1*t + C2*(3*C1**2 - C2**2)*cos(t)**2 - 4*C2 + 8*C4)*sin(t)/8)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Solve 1st Order\n", "ord_1 = sm.dsolve(eps_list[1].subs(x0(t),ord_0.rhs),x1(t))\n", "display(ord_1.simplify())" ] }, { "cell_type": "code", "execution_count": 42, "id": "84909933-3519-43c8-90a2-94dc13511795", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(-C1**3*sin(t) - C1**2*C2*cos(t) - C1*C2**2*sin(t) + 4*C1*sin(t) - C2**3*cos(t) + 4*C2*cos(t))/(8*(C1*cos(t) - C2*sin(t)))]" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Collect t terms to solve for omega\n", "ord_1_terms = sm.collect(sm.expand(ord_1.rhs), t, evaluate=False)\n", "\n", "#Solve for omega that makes that t term equal to 0.\n", "omega_1_soln = sm.solve(sm.Eq(0,ord_1_terms[t]), omega_1)\n", "omega_1_soln" ] }, { "cell_type": "code", "execution_count": 43, "id": "5f46858f-7448-47d4-8f65-588728554a40", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Eq(x_1(t), (-C1**4*cos(2*t)**2 + 6*C1**4*cos(2*t) + 3*C1**4 + 4*C1**3*C2*sin(2*t) + 2*C1**3*C2*sin(4*t) + 6*C1**2*C2**2*cos(2*t)**2 - 2*C1**2*C2**2*cos(2*t) - 28*C1**2*C2**2 - 8*C1**2*cos(2*t) + 8*C1**2 + 12*C1*C2**3*sin(2*t) - 2*C1*C2**3*sin(4*t) + 16*C1*C3*cos(2*t) + 16*C1*C3 + 16*C1*C4*sin(2*t) - C2**4*cos(2*t)**2 + C2**4 - 8*C2**2*cos(2*t) + 8*C2**2 - 16*C2*C3*sin(2*t) + 16*C2*C4*cos(2*t) - 16*C2*C4)/(32*C1*cos(t) - 32*C2*sin(t)))\n" ] } ], "source": [ "#Plug this solved omega_1 back into our expression for the order 1 terms\n", "ord_1 = sm.simplify(ord_1.subs(omega_1, list(omega_1_soln)[0]))\n", "ord_1\n", "print(ord_1)" ] }, { "cell_type": "code", "execution_count": 44, "id": "4eb17f76-b2d2-4a56-a6df-78555443aa41", "metadata": {}, "outputs": [ { "ename": "SyntaxError", "evalue": "closing parenthesis ')' does not match opening parenthesis '{' (3522621134.py, line 2)", "output_type": "error", "traceback": [ "\u001b[0;36m Cell \u001b[0;32mIn[44], line 2\u001b[0;36m\u001b[0m\n\u001b[0;31m ord_2 = sm.simplify(sm.dsolve(eps_list[2].subs({x1(t): ord_1.rhs), x0(t): ord_0.rhs},x2(t)))\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m closing parenthesis ')' does not match opening parenthesis '{'\n" ] } ], "source": [ "#Again for order 2\n", "ord_2 = sm.simplify(sm.dsolve(eps_list[2].subs({x1(t): ord_1.rhs), x0(t): ord_0.rhs},x2(t)))\n", "ord_2\n", "print(ord_2)" ] }, { "cell_type": "code", "execution_count": null, "id": "64f88151-64b0-4a6f-90df-6d33be83aa65", "metadata": {}, "outputs": [], "source": [ "#Collect t terms to solve for omega_2\n", "ord_2_temrs = sm.collect(sm.expand(ord_w.rhs), t, evaluate=False)\n", "\n", "#Solve for omega_2 that makes that t term equal to 0.\n", "omega_2_soln = sm.solve(sm.Eq(0,ord_2_terms[t]), omega_2)\n", "omega_2_soln" ] }, { "cell_type": "code", "execution_count": null, "id": "b215845a-9b51-4aea-b947-c6d530a05a27", "metadata": {}, "outputs": [], "source": [ "#Plug this solved omega_2 back into the expression for the order 2 terms:\n", "ord_2 = sm.simplify(ord_2.subs(omega_2, list(omega_2_soln)[0]))\n", "ord_2\n", "print(ord_2)" ] }, { "cell_type": "code", "execution_count": null, "id": "32cbfb5c-7e61-431c-b7e7-e06c2ee05bb4", "metadata": {}, "outputs": [], "source": [ "x_soln = sm.Eq(x(t), ord_0.rhs + eps*ord_1.rhs + eps**2*ord_2.rhs" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }