{ "cells": [ { "cell_type": "markdown", "id": "07e00571", "metadata": {}, "source": [ "Three examples demonstrate the solving of initial value problems. " ] }, { "cell_type": "markdown", "id": "43138a24", "metadata": {}, "source": [ "# 1. A model of a pendulum" ] }, { "cell_type": "markdown", "id": "77f17552", "metadata": {}, "source": [ "The second order ODE \n", "$$\n", " \\theta''(t) + \\alpha \\sin(\\theta(t)) = 0\n", "$$\n", "\n", "is solved as a system of two coupled first order ODEs:\n", "\n", "$$\n", " \\theta'(t) = v(t)\n", "$$\n", "\n", "$$\n", " v'(t) = -\\alpha \\sin(\\theta(t))\n", "$$\n", "\n", "with initial conditions $\\theta(0) = \\theta_0$, $v(0) = v_0$.\n", "\n", "The parameter $\\alpha$ equals $g/L$, where\n", "\n", "* $g$ is the gravitational constant, and\n", "* $L$ is the length of the pendulum.\n", "\n", "Following appendix C.4 of the text book we use SciPy\n", "to compute an approximate solution for this problem.\n", "The angle and its velocity are plotted with matplotlib." ] }, { "cell_type": "code", "execution_count": 1, "id": "0c57c40d", "metadata": {}, "outputs": [], "source": [ "import scipy as sp\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "id": "0d33fe11", "metadata": {}, "outputs": [], "source": [ "def pendulum(tmax, nstep, theta0, veloc0, alpha):\n", " \"\"\"\n", " Return the motion (theta, v, t) of\n", " a pendulum, governed by the ODE:\n", " theta''(t) + alpha*sin(theta(t)) = 0,\n", " where the parameters are\n", " tmax : time t ranges from 0 to tmax,\n", " nstep : the number of time steps,\n", " theta0 : angle at t = 0,\n", " veloc0 : velocity at t = 0,\n", " alpha : value for the parameter.\n", " \"\"\"\n", " tstep = tmax/float(nstep)\n", " tspan = np.linspace(0, tmax, nstep+1)\n", " veloc = np.zeros(nstep+1)\n", " theta = np.zeros(nstep+1)\n", " veloc[0] = veloc0\n", " theta[0] = theta0\n", " for k in range(nstep):\n", " theta[k+1] = theta[k] + tstep*veloc[k]\n", " veloc[k+1] = veloc[k] - alpha*tstep*np.sin(theta[k+1])\n", " return theta, veloc, tspan" ] }, { "cell_type": "code", "execution_count": 3, "id": "b28163a2", "metadata": {}, "outputs": [], "source": [ "def test_values():\n", " \"\"\"\n", " Returns values for the input data:\n", " tmax, nstep, theta0, veloc0, and alpha.\n", " \"\"\"\n", " theta0 = sp.pi/6\n", " nstep = 1000\n", " tmax = 10\n", " veloc0 = 0\n", " alpha = 5\n", " return tmax, nstep, theta0, veloc0, alpha" ] }, { "cell_type": "markdown", "id": "d27c7270", "metadata": {}, "source": [ "We are now ready to define the test values and\n", " compute the trajectory of\n", " the pendulum." ] }, { "cell_type": "code", "execution_count": 4, "id": "d57ba964", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tmx, dim, pos0, vel0, alp = test_values()\n", "theta, vel, tspan = pendulum(tmx, dim, pos0, vel0, alp)\n", "fig = plt.figure()\n", "fig.add_subplot(211)\n", "plt.plot(tspan, theta)\n", "plt.title('angle as function of time')\n", "fig.add_subplot(212,)\n", "plt.plot(tspan, vel, label='velocity(t)')\n", "plt.title('velocity as function of time')\n", "plt.subplots_adjust(hspace=0.5)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f8b18788", "metadata": {}, "source": [ "# 2. Celestial Mechanics" ] }, { "cell_type": "markdown", "id": "7164ad7b", "metadata": {}, "source": [ "The script plots the figure eight arising from the trajectories of three\n", "masses, in a simulation of the n-body problem from celestial mechanics.\n", "\n", "The parameters and initial values make a figure eight.\n", "Read \"Strange Orbits\" by Ivars Petersen, in Science News 168(7), 2005.\n", "http://www.sciencenews.org/articles/20050813/mathtrek.asp" ] }, { "cell_type": "markdown", "id": "eb74e736", "metadata": {}, "source": [ "### 2.1 drawing a figure eight" ] }, { "cell_type": "code", "execution_count": 5, "id": "59a17168", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 6, "id": "3f4409cb", "metadata": {}, "outputs": [], "source": [ "def fun(zvr, time):\n", " \"\"\"\n", " zvar is a vector with 12 entries\n", " arranged in blocks of 4:\n", " x[k](time), x'[k](time), y[k](time), y'[k](time)\n", " for the three masses k = 1, 2, 3.\n", " \"\"\"\n", " zeros = [0 for k in range(12)]\n", " rhs = np.array(zeros, float)\n", " # take three equal masses\n", " mass = [1, 1, 1]\n", " # relabel input vector zvr\n", " (x1p, u1x, y1p, v1y) = (zvr[0], zvr[1], zvr[2], zvr[3])\n", " (x2p, u2x, y2p, v2y) = (zvr[4], zvr[5], zvr[6], zvr[7])\n", " (x3p, u3x, y3p, v3y) = (zvr[8], zvr[9], zvr[10], zvr[11])\n", " # u and v are first derivatives of x and y\n", " (rhs[0], rhs[2]) = (u1x, v1y)\n", " (rhs[4], rhs[6]) = (u2x, v2y)\n", " (rhs[8], rhs[10]) = (u3x, v3y)\n", " # compute squared distances\n", " dx12 = x1p - x2p\n", " sdx12 = dx12**2\n", " dx13 = x1p - x3p\n", " sdx13 = dx13**2\n", " dx23 = x2p - x3p\n", " sdx23 = dx23**2\n", " dy12 = y1p - y2p\n", " sdy12 = dy12**2\n", " dy13 = y1p - y3p\n", " sdy13 = dy13**2\n", " dy23 = y2p - y3p\n", " sdy23 = dy23**2\n", " # denominators\n", " d12 = (sdx12 + sdy12)**1.5\n", " d13 = (sdx13 + sdy13)**1.5\n", " d23 = (sdx23 + sdy23)**1.5\n", " # righthandside for second order\n", " rhs[1] = - mass[1]*dx12/d12 - mass[2]*dx13/d13\n", " rhs[3] = - mass[1]*dy12/d12 - mass[2]*dy13/d13\n", " rhs[5] = - mass[0]*(-dx12)/d12 - mass[2]*dx23/d23\n", " rhs[7] = - mass[0]*(-dy12)/d12 - mass[2]*dy23/d23\n", " rhs[9] = - mass[0]*(-dx13)/d13 - mass[1]*(-dx23)/d23\n", " rhs[11] = - mass[0]*(-dy13)/d13 - mass[1]*(-dy23)/d23\n", " return rhs" ] }, { "cell_type": "markdown", "id": "b2cabc1b", "metadata": {}, "source": [ "The code below plots the trajectories of 3 equal masses forming a figure 8." ] }, { "cell_type": "code", "execution_count": 7, "id": "c80a5b6f", "metadata": {}, "outputs": [ { "data": { "image/png": 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e8MMPUrjo9tRTMH++2v/009R98R92LV6uXLlCcnIy+fLlu+v+fPnyERERcd/HRUVFkT17dry9vWnWrBlTp07lueeeu+ex48aNw9/fP+VWqFAhm34PzmDijoksPbIUL7MXS1svJX+O/LojuT2TycSUJlPoWa0nBgZvrnyTeeEyHbhwEMnJan6R779XfS6WLVN9LYR+LVvC0KFqv2tXCAvTm8dBOeRooxw5chAeHs6ePXsYM2YM/fr1Y8uWLfc8dtCgQURFRaXczp49m7lhNdt8ajMDN6rLb583/pxahWppTiSsTCYTU5tMpUfVHhio1rHvD3+vO5ZwdxaLml9k4ULVx2XJEllc0dGMGKFaweLjVf8XN7yi8DB2XZwid+7ceHh4EBkZedf9kZGRBAUF3fdxZrOZEiVKAFCxYkWOHj3KuHHjqF+//n+O9fHxwcdNl2K/eusqr614DYthoWPFjrxd9W3dkcS/mEwmvmj6BclGMl+FfcVry18jwDeAhsUb6o4m3JFhQN++alFADw9YtAiaN9edSvyb2azOUcWKauj022+rjtQmk+5kDsOuLS/e3t5UqVKFjRs3ptxnsVjYuHEjNWvWTPPzWCwW4uPj7RHRaRmG6ktxIeYCpXOX5osmX2CSH2yHZDKZmNZ0Gm3KtSHRkshLi1+SmXiFHmPHwlQ1eSXz58PLMnmlw8qZUy2C6eGhtrKI413sftmoX79+zJo1i3nz5nH06FG6d+9ObGwsnTqp0RcdOnRg0KBBKcePGzeODRs28Ndff3H06FEmTZrEt99+y2uvvWbvqE5lxu8zWPnHSrw9vFnYciHZvLPpjiQewMPswfyX5tOweENuJd6i6YKmHL50WHcs4U5mzoQP1eSVfP45vPqq3jzi4WrVgtGj1X6vXnD0qN48DsTua5q3adOGy5cvM2zYMCIiIqhYsSLr1q1L6cR75swZzObUGio2NpYePXpw7tw5smTJQunSpfnf//5HmzZt7B3VaRy5fIR+P/cDYHyD8VTKX0lzIpEW3h7eLG+9nJBvQ9h5bicN/9eQ7W9up0hAEd3RhKtbvhy6d1f7Q4ZA795684i0e/99tbbUhg2qk/WOHaqvkpuz+zwvmc3V53lJsiTx9Oyn2X1+N41LNGb1q6sxmxyy37W4j2u3r1F3Tl0OXz5M2Txl2f7mdgJ8A3THEq5q61Y1/Xx8PHTpombPlUvMzuX8eShXDqKi1KW/O65WuBKHmedF2N6noZ+y+/xu/H38+fqFr6VwcUKBWQJZ/9p6CuYoyJHLR3jl+1dISE7QHUu4ouPHoUULVbi0aAHTp0vh4owKFoQpU9T+8OFqMjs3J+98TuSPK38wdLMa/z+50WQK+hXUnEhkVEG/gqx6dRXZvLKx8dRGuq/qjos1ggrdrl5VQ6CvX4fg4NSh0cI5vf46vPiimhW5Y0e1dWNSvDiJZEsyb/74JvHJ8TQq3ohOFWW6eWdXMagii19ZjNlkZnb4bMb/Nl53JOEqEhLUZGd//gmPPw4rV0IWmXXbqVkXzAwMhL171arfbkyKFycx4/cZ7Di7g+ze2Zn5wkwZFu0impVsxpTGqjl48KbBLD60WHMi4fQMQ83MunWrWvBv1Sr41yznwkkFBamRYgCjRsGpU3rzaCTFixO4FHuJIZuGAGp0UWH/wpoTCVvqWb0n79Z4F4BOKzux7+I+zYmEUxs/PnUSuiVL4MkndScSttS+PTz7LMTFwTvvqGLVDUnx4gTe3/A+UfFRVM5fWWbRdVGfPPcJTUo04XbSbVosbsGl2Eu6IwlntHq1GgoNqoNno0Z68wjbM5lg2jS1JtXq1WpBTTckxYuD++3Mb8zbrxb0m950Oh5mD82JhD14mD1Y+PJCngh8gjNRZ2i9pDWJye7dIU+k059/qk/lhqGmk+/RQ3ciYS+lS6v5X0DN2XPzpt48Gkjx4sCSLEn0XNMTgLcqvUXwY8GaEwl7CvAN4Ie2P5DdOzu//v0r/db30x1JOIuYGDUUOipKzcpq7RchXNeQIVC0KJw7B+PG6U6T6aR4cWCzwmZxIPIAgVkCGRfifj+c7qhsnrL876X/AfDFni+YvW+25kTC4RmGGjp75AgUKABLl4K3t+5Uwt6yZIFPP1X7kyfDmTN682QyKV4cVEx8DCN+HQHAyPojyZ01t95AItM0L92ckfVHAtB9dXf2XtyrOZFwaOPGqen/vbxg2TLIn193IpFZXnwR6tVTnXcHD9adJlNJ8eKgPtnxCZdiL/FE4BN0q9JNdxyRyT6s+yEvlHyBhOQEWi1pxY24G7ojCUe0cWPqYovTpkGNGnrziMxlMqlWF5MJFiyAPXt0J8o0Urw4oAsxF5gUOgmA8SHj8fLw0pxIZDazycy8FvMoElCEv67/xZsr35QZeMXdIiJSO+i++aZat0i4n8qV1ey7AP36uc3QaSleHNCwzcO4lXiLWoVq8VLpl3THEZrkzJKT71/5Hm8Pb1YcW8FnOz/THUk4iuRkePVViIxU87hMnao7kdBpzBjVB+a339Rsym5AihcHc+TyEeaEzwHU3B8yk657q1awGpMbTgbg/V/eJ/RsqOZEwiGMHAmbN0O2bGoiuqxZdScSOj32GLyrJrpk2DCwWPTmyQRSvDiYj379CIthoUXpFtQqVEt3HOEAelTrQetyrUmyJNF6aWuu3LqiO5LQacMGGD1a7X/1lZrzQ4j+/cHfX604vXSp7jR2J8WLAzl86TDfH/4eIGW0iRAmk4mvX/iakrlKci76HJ1WdpL+L+7qwoXUfi5duqh9IQBy5lR9XgBGjFCXFl2YFC8O5KOtH2Fg8HKZlymfr7zuOMKB5PDJwZJWS/Dx8GHV8VVM3zNddySR2SwW1THz8mUoX14mohP/1aePKmKOHoXvvtOdxq6keHEQhy4dYsnhJQAMqzdMcxrhiMrnK8+EkAkA9N/Qn8OXDmtOJDLV5MmwaZPq3/L996qDphB38veHAQPU/siRkJSkN48dSfHiID76VbW6vFL2FWl1EffVO7g3jUs0Ji4pjnbL2hGXFKc7ksgM4eGpk5B99hmUKqUzjXBk77wDuXPDiROqyHVRUrw4gGNXjrHkiGp1GV5vuOY0wpGZTCbmNp9Lnqx5OHjpIAN/Gag7krC3W7fUsOjERGjeHN56S3ci4ciyZ4e+fdX+hAkuO++LFC8O4ImcpVjZdiVD6gzhybxP6o4jHFy+7PmY22IuAJ/v+px1J9bpDSTs6/33VR+GoCD4+ms1m6oQD9KjhypiDhyAda7590GKF83OnoUSJUwcW/kiH9UfrTuOcBJNn2jKO9XfAeCNH97gcuxlzYmEXaxZo6b9B5g3T10OEOJhcuaEbv8sKzN+vN4sdiLFi2ZTp8Lp07B2LZjlbIh0+Pi5j3ky75Ncir1EjzU9ZPi0q7l8GTp1Uvt9+0LDhlrjCCfz7rtqsc6tWyHU9Sa3lLdLjWJiYOZMtf/ee3qzCOfj6+nL/Bbz8TR7svTIUhYfXqw7krClnj3h0iU1/f+4cbrTCGdTsCC89pra//hjvVnsQIoXjebMgagoNXCgaVPdaYQzqpS/Eh/WUasK91zTk4ibEZoTCZv4/ns17b+nJ8yfD76+uhMJZ2QdNv3jj/D333qz2JgUL5pYLKmXsvv0kUtGIuMG1xlMpaBKXLt9ja4/dZXLR84uMlJ1uAQ1PLpSJb15hPMqUwZCQtQbznTXmthS3jI1+eUXOH4c/PxSVzMXIiO8PLyY12IeXmYvfjr+E/P3z9cdSWSUYajC5epVqFABhgzRnUg4u1691Pbrr+H2bb1ZbEiKF02srS5vvKFGtAnxKJ7K91TKelh91vXhXPQ5zYlEhixeDMuXq8tFc+eCt7fuRMLZPf88FCkC167BwoW609iMFC8a/P03rFql9q2tw0I8qgFPD6B6wepExUfR+cfOcvnI2UREqE66AB9+CBUrao0jXISHR+obzdSpLjNpnRQvGsyYoS5BNmggq9kL2/E0ezKvxTx8PX35+eTPzNs/T3ckkVaGAd27q0/HFSumLgUghC107qzWwtq/H7Zv153GJqR4yWTx8erSI6R+yBLCVkrnLp1y+ajf+n5E3ozUnEikyZIl8MMPal6OefPUVghbCQyEdu3UvvUNyMlJ8ZLJfvwRrlyBAgXghRd0pxGuqF/NflQKqsT1uOv0Xd9XdxzxMNevQ+/ean/wYCgvC7MKO+jcWW2XLIHoaL1ZbECKl0w2Z47aduyo+uQJYWueZk9mvTALs8nMokOLWHV8le5I4kHef18Njy5TBgYN0p1GuKqaNVU/hVu3YNEi3WkemRQvmej8eVi/Xu137Kg1inBxVQpUoV+NfgB0X92dmPgYzYnEPf36a2oz/syZ4OOjN49wXSZTauvLN9/ozWIDUrxkovnzVUfd2rXhiSd0pxGubuQzIymWsxjnos8xZJPMF+Jw4uKga1e1362b+sMghD116KCa/HfvhkOHdKd5JJlSvEybNo0iRYrg6+tLcHAwu3fvvu+xs2bNok6dOuTMmZOcOXMSEhLywOOdhWGkXjJ68029WYR7yOqVlRnNZgDwxe4vCD3reouzObUxY9RMlfnzu+zKv8LB5M2b2tnSyVtf7F68LF68mH79+jF8+HD27t1LhQoVaNSoEZcuXbrn8Vu2bKFdu3Zs3ryZ0NBQChUqRMOGDTl//ry9o9rV9u3w55+QLRu0aqU7jXAXzxV/jjcqvIGBwVs/vUVCcoLuSALUp15rwTJ1KgQEaI0j3Ij10/N330FSkt4sj8DuxcvkyZPp0qULnTp1omzZssyYMYOsWbMye/bsex6/YMECevToQcWKFSldujRff/01FouFjRs32juqXS1YoLavvCIz6orMNanhJPJkzcORy0f4NPRT3XGExaIuFyUlwYsvQsuWuhMJd9KoEeTKpTqJb96sO02G2bV4SUhIICwsjJCQkNQXNJsJCQkhNDRtTdi3bt0iMTGRwMBAe8W0u8REWLpU7b/6qt4swv3kypqLT577BICPtn7EmagzmhO5uW++gdBQ9Slm2jTVkVKIzOLlldr8/913erM8ArsWL1euXCE5OZl8+fLddX++fPmIiIhI03N88MEHFChQ4K4C6E7x8fFER0ffdXM0mzapuV3y5IFnn9WdRrijDhU6UKdwHW4l3qLvur6647ivq1dh4EC1P2oUPPaY3jzCPVknrFu2THUcd0IOPdpo/PjxLFq0iBUrVuDr63vPY8aNG4e/v3/KrVChQpmc8uGsQ+pbtZK5XYQeJpOJaU2n4WHyYMWxFaz9c63uSO5p8GC1BMBTT6Wu9itEZqtdWxXO0dGw1jn/Fti1eMmdOzceHh5ERt49RXlkZCRBQUEPfOzEiRMZP348P//8M+UfMOPkoEGDiIqKSrmdPXvWJtltJT5eLRIL0Lat3izCvT2V7yn61ugLQK+1vbideFtvIHezezfMmqX2p02TTzJCH7M59Q3JSVeatmvx4u3tTZUqVe7qbGvtfFuzZs37Pu7jjz9m1KhRrFu3jqpVqz7wNXx8fPDz87vr5kjWrlXFbcGC8PTTutMIdze83nAK5CjAX9f/YsL2CbrjuI/kZLWyr2GouTbq1NGdSLg7awfMVasgxvkmsbT7ZaN+/foxa9Ys5s2bx9GjR+nevTuxsbF06tQJgA4dOjDojimxJ0yYwNChQ5k9ezZFihQhIiKCiIgIbt68ae+odrF4sdq2aaOKXSF0yuGTg08bqRFH438bz4lrJzQnchOzZkFYGPj7w8cf604jhFq9vEQJ1edl3TrdadLN7m+nbdq0YeLEiQwbNoyKFSsSHh7OunXrUjrxnjlzhosXL6Yc/+WXX5KQkMArr7xC/vz5U24TJ060d1Sbi4+H1avVvsztIhxFq7KteK7Yc8Qnx/PO2ncwDEN3JNd2+bLq6wIwejT8awCDEFqYTPDSS2p/xQq9WTLAZLjYX67o6Gj8/f2JiorSfglp/Xpo3FhNoHnunLS8CMdx/OpxnvryKRKSE1jeejkvlXlJdyTX1bkzzJ6tPunu2SN9XYTjCA2FWrXAz08V2d7eWuOk5/1b3k7t6Icf1PbFF6VwEY6lZK6SDKg1AID3fn6PuCTnHC7p8EJDVeECMH26FC7CsQQHQ1CQ6pi5aZPuNOkib6l2YrHAjz+q/ebN9WYR4l4G1R5EwRwFOXXjFJNDJ+uO43osFujdW+136gQPGKQghBZmc+oblJNdOpLixU7CwuDCBTWJpkxMJxxRNu9sTAhRI47GbhvL+WjnXj/M4Xz7Lfz+O+TIAePG6U4jxL1Z+72sXKlGxTkJKV7sxHrJqEkT8PHRGkWI+3r1qVep+VhNYhNjGbRx0MMfINLm5k2wjqL88EPppCsc1zPPqD4vkZGqT5aTkOLFTn76SW3lkpFwZCaTic8bfw7Atwe+Zee5nZoTuYhx4+DiRSheHPr00Z1GiPvz9oaGDdW+Ew2ZluLFDs6fh4MH1Ui0xo11pxHiwaoVrEbHih0B6LOuDxbDojeQszt1CiZNUvuTJknTq3B81jcqKV7c288/q221amrlcSEc3dhnx5LdOzu7z+/mfwf+pzuOc3v/fTXJU4MGaqihEI7OWrzs3q0WD3UCUrzYwfr1atuokd4cQqRV/hz5+bDOhwAM/GUgMfHON124Q/j1V1i6VI3i+PRT1fwqhKMrWFAtFmoYsGGD7jRpIsWLjSUnp557KV6EM+lboy/Fcxbn4s2LjPtNRsekW3Jyav+Wbt3Um4EQzsLa+uIkq0xL8WJjYWFqxXs/PzX/jxDOwsfTh0kNVV+NT3d+ypmoM5oTOZnZs2H/fggIgI8+0p1GiPRp0kRt169XcxQ5OClebMx6yahBA5lMUzifF0u9SN3H6xKXFMeHmz7UHcd5xMTA0KFqf/hwyJ1bbx4h0uvppyFbNjVkev9+3WkeSooXG7N21pVLRsIZmUwmJj6nFkH99sC37L24V3MiJzFxovqjX6IE9OihO40Q6eftDfXrq/0tW3QmSRMpXmzo1i3YtUvth4TozSJERlUrWI1Xn3oVgP4/95dVpx/mwgVVvICa30Xz4nZCZJgUL+4pNBQSE1XH7WLFdKcRIuPGPDsGHw8fNp/ezJo/1+iO49iGD1efXGrWhJdf1p1GiIyzFi9btzr8UgFSvNjQr7+qbb16MkJSOLciAUXoE6xGzgzYMIAkS5LmRA7q8OHUVaMnTpRffOHcKlZUo01u3HD4fi9SvNjQncWLEM5uUJ1B5MqSi6NXjjJ732zdcRzT+++rkRktW0KtWrrTCPFoPD2hTh217+CXjqR4sZG4uNT+LlK8CFcQ4BvA8HrDARi2eZhMXPdvmzbBmjXqD/748brTCGEbTtLvRYoXG9m1S80Ini8flCypO40QttGtajdKBJYgMjaST3Z8ojuO47BYoH9/tf/22/DEE3rzCGErTtLvRYoXG5H+LsIVeXt4MyFkAgATd0zkQswFzYkcxMKFsG+f6h8wbJjuNELYTqVKkD07REXBkSO609yXFC82smOH2lovFwrhKl4q/RJPF3qa20m3+ehXmTmWuDgYMkTtDxwIefLozSOELXl4QPXqan/nTr1ZHkCKFxswDLUYJ6jRkkK4EpPJxPgQ1afj671f8+fVPzUn0mzaNDhzBh57DPr21Z1GCNurUUNtQ0P15ngAKV5s4M8/4fp18PWF8uV1pxHC9moXrs3zJZ8n2Uhm6OahuuPoEx2tJqIDGDkSsmTRm0cIe7B+CpeWF9dmPb+VK4OXl94sQtjLmGfHYMLE4sOLCbsQpjuOHpMmwdWrULo0dOigO40Q9mFdVfjoUTXniwOS4sUGrEOkZRVp4crK5ytP+/LtARi8abDmNBpcuqSKF4BRo2TlVeG68uSB4sXVvvUNzsFI8WIDUrwIdzGy/ki8zF78fPJnNp3apDtO5ho7FmJjoUoVWQZAuD5rvxcHvXQkxcsjun07dRZl67kWwlUVy1mMblW6ATBo4yD3WbTx77/hyy/V/rhxMh+CcH0O3u9FipdHtG8fJCWpyekKF9adRgj7+7Duh2Tzysbu87v54dgPuuNkjhEjICEBnn1WlowX7qFqVbXdu1cNqXUwUrw8on371LZqVfkwJtxDvuz5eLfGu4Dq++LyizYeOQLz56v9sWPlF124h6eeArNZ9fWKiNCd5j+keHlE4eFqW7GizhRCZK7+tfqTK0sujl05xvz983XHsa+hQ9VyAC1aSMc24T6yZoVSpdS+9VO6A5Hi5RFZ+7tUqKA3hxCZyd/Xn8F11Iij4VuGE5cUpzmRnezeDcuXq0+go0frTiNE5qpUSW2tn9IdiBQvjyApCQ4eVPvS8iLcTY9qPXjM7zHORZ/jq9+/0h3HPgb/MyT89dehXDm9WYTIbNbiRVpeXMvx42qZk2zZUofEC+EufD19GVpXzbY77rdx3Eq8pTmRjW3cqG5eXqrDrhDuxvqpXFpeXIv1klH58qpVWQh306liJ4oGFCUyNpJpu6fpjmM7hgEffqj2334bihTRGkcILazFy4kTamkMByJvuY9AOusKd+fl4cWwesMAmLB9AjHxMZoT2cjatWp+iyxZUi8dCeFucudWC5ACHDigN8u/SPHyCKSzrhDwWvnXKJmrJFdvX+XzXZ/rjvPoDAOGqYKMXr0gKEhvHiF0evJJtT16VG+Of5Hi5RFYz6X04xPuzNPsyfB6wwGYFDqJG3E39AZ6VD/9BGFhqjPbgAG60wihV5kyanvkiN4c/5Ipxcu0adMoUqQIvr6+BAcHs3v37vsee/jwYV5++WWKFCmCyWTis88+y4yI6RYbC2fOqH3ruRXCXbUp14ayecpyI+4Gk0Mn646TcRZLaqtL795qgToh3FnZsmrrbi0vixcvpl+/fgwfPpy9e/dSoUIFGjVqxKVLl+55/K1btyhWrBjjx48nyIGba//4Q21z54ZcufRmEUI3D7MHH9X/CIDPdn7G1VtXNSfKoBUr1PXgHDngvfd0pxFCP3dteZk8eTJdunShU6dOlC1blhkzZpA1a1Zmz559z+OrVavGJ598Qtu2bfHx8bF3vAw7dkxtpdVFCOWlMi9RMagiMQkxfLLjE91x0s9igeHq8hfvviufSoSA1De5s2chxnE65Nu1eElISCAsLIyQOxYyM5vNhISEEBoaas+XtjtrC1rp0npzCOEozCZzSuvL1N1TibwZqTlROi1ZAocPg7+/Kl6EEBAYqFYehtRP7Q7ArsXLlStXSE5OJp/1G/9Hvnz5iLDRQk/x8fFER0ffdcsM0vIixH89X/J5qheszq3EW0zYPkF3nLRLTk6diO699yAgQGcaIRyLA/Z7cfrRRuPGjcPf3z/lVqhQoUx5XWvxIi0vQqQymUwprS/T90znfPR5zYnS6Lvv1C91YCD06aM7jRCOxfop3V1aXnLnzo2HhweRkXc3H0dGRtqsM+6gQYOIiopKuZ09e9Ymz/sgFgv8+afaty66KYRQGhZvyNOFniY+OZ6x28bqjvNwSUkwcqTaHzAA/Pz05hHC0VjXv/nrL7057mDX4sXb25sqVaqwcePGlPssFgsbN26kZs2aNnkNHx8f/Pz87rrZ24ULEB8Pnp5QuLDdX04Ip2IymRj9rFqB+et9X3Mu+pzmRA/x7bdq+vPcudWkdEKIuxUrprbuUrwA9OvXj1mzZjFv3jyOHj1K9+7diY2NpVOnTgB06NCBQYMGpRyfkJBAeHg44eHhJCQkcP78ecLDwzlx4oS9o6aZ9fwVLqwKGCHE3eoXqU+9x+uRkJzA+N/G645zf4mJ8JG6zMUHH0D27HrzCOGI3K3lBaBNmzZMnDiRYcOGUbFiRcLDw1m3bl1KJ94zZ85w8eLFlOMvXLhApUqVqFSpEhcvXmTixIlUqlSJt956y95R0+zUKbUtWlRvDiEcmXXW3Vl7Zzlu35e5c+H0aTWaokcP3WmEcEzWN7urVyEqSm+Wf2RKu0GvXr3odZ/m2C1bttz17yJFimAYRiakyjhr8WJtSRNC/Ff9IvWpU7gO285sY8L2CUxpMkV3pLslJMBodXmLgQMha1a9eYRwVNmzQ968cOmSan2pVEl3IucfbaSDtLwI8XAmkyml9WVm2EwuxFzQnOhfvv1WrfGRLx9066Y7jRCOzcH6vUjxkgHWcyfFixAP9mzRZ6lVqBbxyfF8vP1j3XFSJSbCmDFq//33IUsWvXmEcHQO1u9FipcMkJYXIdLmztaXr8K+4mLMxYc8IpMsWKB+kfPkkVYXIdJCWl6cW3y8GioNUrwIkRbPFXuOGo/VIC4pzjHWPEpKSm11GTAAsmXTm0cIZ2CdAPacY0x9IMVLOl28CIYBPj7qQ5sQ4sHubH2Z8fsM/WseLVqk5nXJlQu6d9ebRQhnUbCg2krx4pzO/zPis0ABMJn0ZhHCWTQq3ojqBatzO+k2E3dM1BckOTl1hNF778m8LkKklbV4Oe8Y0x5I8ZJO1ktGBQrozSGEM7mz9WX679O5FHtJT5AlS+CPPyBnTujZU08GIZyRtXi5fFn1n9BMipd0shYv1vMohEibJiWaULVAVW4l3mLSjkmZH8BigVGj1P6778oaRkKkR65cqr8EqP4Tmknxkk7S8iJExtzZ+jJtzzSu3LqSuQGWLYMjR8DfH955J3NfWwhnZzKlvvE5wKUjKV7SSYoXITKu2RPNqJy/MrGJsZnb+nJnq0ufPhAQkHmvLYSrcKB+L1K8pJMUL0JknMlkYljdYQB8secLrt66mjkvvHIlHDwIOXJA376Z85pCuBopXpzXnaONhBDp92KpF6kYVJGbCTeZHDrZ/i9oGKkrR/furTrrCiHSL39+tY3UPN0BUryk26V/BkkEBenNIYSzurP1ZeruqVy/fd2+L7hqFYSHq8no3n3Xvq8lhCvLnVttr2Ryf7V7kOIlHZKS4Po/f2dz5dKbRQhn1rx0c57M+yQxCTF8sfsL+73Qna0uvXrJL64Qj8JavFy+rDcHUryky/U7PiAGBurLIYSzM5vMDKkzBIDPdn3GzYSb9nmhtWvh998ha1bo188+ryGEu7BOKy8tL87Fer4CAsDTU2sUIZxeq7KteCLwCa7dvsaM32fY/gXubHXp3h3y5rX9awjhTuSykXO6+s/ACOv5E0JknIfZg0G1BwEwccdEbifetu0LbNwIu3aBry/072/b5xbCHVlbXuSykXOxFi9y2VwI23it/GsU9i9MZGwk3+z7xrZPbl05uksX6WEvhC1YP7lfv646gWokxUs6WFvKpOVFCNvw8vBi4NMDAfh4+8ckJCfY5om3b4ctW8DLCwYMsM1zCuHuAgNTVyS+dk1rFCle0kFaXoSwvU6VOpE/e37ORp/l2/3f2uZJra0ub7wBhQrZ5jmFcHceHqmzU1/NpAkm70OKl3SwFpoy0kgI2/H19KV/LdUnZdxv40iyPGJzdFiYGmVkNsPAgTZIKIRIYV3QNCZGawwpXtLBeq5y5NCbQwhX061KN3JlycXJ6yf5/vD3j/ZkY8eqbbt2ULz4o4cTQqSyvgFGR2uNIcVLOkjxIoR9ZPPORr+aah6WMdvGYDEsGXuiw4dh+XK1P3iwjdIJIVJIy4vzufnPPFpSvAhhez2r9cTfx58jl4/ww7EfMvYk48apbcuWULaszbIJIf5hLV6k5cV5SMuLEPbj7+vPO9XfAWD01tEYhpG+JzhxAr77Tu0PGWLjdEIIQC4bOSNr8ZI9u94cQriqPjX6kM0rG/si9rHuxLr0PXjCBLBYoEkTqFzZPgGFcHdy2cj5SMuLEPaVO2tuulftDsCoraPS3vpy9izMm6f2P/zQTumEENLy4oSkeBHC/vrV7IePhw+h50LZcnpL2h70ySeQmAj160OtWvaMJ4R7s74BSsuL87B22JXLRkLYT/4c+Xmr8lsAjN42+uEPiIyEWbPUvrS6CGFfvr5qGx+vNYYUL+mQ8M/M5dZzJ4Swj/effh9PsyebTm0i9Gzogw+ePBni4iA4GJ59NnMCCuGufHzUVooX52E9V97eenMI4eoK+xfmjQpvAGrel/u6dg2mT1f7H36Yuu6KEMI+pHhxLhZL6iKaUrwIYX8Daw/EbDKz+s/V7Lu4794HTZmirudWqADNmmVuQCHckRQvziUxMXVfihch7K9EYAnaPtkWgLG/jf3vAdHRqngBNa+LtLoIYX9SvDgXa38XSD13Qgj7GlxbTfG/7Mgyjlw+cvcXv/wSrl+HUqXUjLpCCPuT4sW53Fm8eHnpyyGEOymXtxwvlX4JA4Nxv41L/cKtW6qjLqg1jDw89AQUwt1I8eJcrMWLh4f8nRQiMw2po6b6/+7gd5y8dlLdmZAA7dtDuXJq9WghROZwp+Jl2rRpFClSBF9fX4KDg9m9e/cDj1+yZAmlS5fG19eXp556ijVr1mRGzAeyFi/S6iJE5qpSoApNSjQh2UhmwvYJ6s6AANXysn+//FIKkZmsn94tGVz53UbsXrwsXryYfv36MXz4cPbu3UuFChVo1KgRly5duufxO3bsoF27dnTu3Jl9+/bRokULWrRowaFDh+wd9YGs50laXYTIfNbWl7nhczkbdTb1C/ILKYQe6V041cbsXrxMnjyZLl260KlTJ8qWLcuMGTPImjUrs2fPvufxn3/+OY0bN2bAgAGUKVOGUaNGUblyZb744gt7R00TzedLCLf0dOGnqV+kPomWRCbumKg7jhDuy0FG9dm1eElISCAsLIyQkJDUFzSbCQkJITT03rNmhoaG3nU8QKNGje57fHx8PNHR0XfdhBCuZ0idIXCkJdOGVmTn/iu64wjh3ly55eXKlSskJyeTL1++u+7Ply8fERER93xMREREuo4fN24c/v7+KbdChQrZJvy/WItNaXkRQo9nHm9Alu0TSA7rxIDJ95m0TghhX+7Q8pIZBg0aRFRUVMrt7NmzD3+QEMLprF5t4vb5EuAdzb7H3+Ta7Wu6Iwnhvly55SV37tx4eHgQGRl51/2RkZEEBQXd8zFBQUHpOt7Hxwc/P7+7bkII12IYMPqfBabzPrOEWI9zTNk1RW8oIdyRO7S8eHt7U6VKFTZu3Jhyn8ViYePGjdSsWfOej6lZs+ZdxwNs2LDhvsdnFrlsJIQ+v/wCe/ZAliwwZnAeAKbsmkJ0vPRxE8Id2f2yUb9+/Zg1axbz5s3j6NGjdO/endjYWDp16gRAhw4dGDRoUMrxffr0Yd26dUyaNIljx44xYsQIfv/9d3r16mXvqEIIB2VtdenWDTrVbkapXKW4HnedL/d8qTeYEO4mOVltNbfA2L14adOmDRMnTmTYsGFUrFiR8PBw1q1bl9Ip98yZM1y8eDHl+Fq1arFw4UJmzpxJhQoVWLp0KT/88ANPPvmkvaM+kHU6CevK0kKIzLFtG2zdqhZE7d8fPMweDK6j1jyavHMytxJvaU4ohBuxztiqeZE/k2G41oWQ6Oho/P39iYqKsmn/l8uXIW9etZ+cDGan7+oshHNo3BjWr1etLjNmqPsSkxMp+UVJTt84zeeNP6d3cG+9IYVwF8uXw8svw9NPw2+/2fSp0/P+LW/BaXRnkal5SQch3MaePapw8fCADz5Ivd/Lw4uBTw8E4OPtHxOfJL+UQmQKa8uLt7fWGFK8pNGdxcudK0wLIexnzBi1bd8eiha9+2sdK3akQI4CnI85z/z98zM/nBDuSIoX53LneZKWFyHs7+BBWLlS9Qu8o09/Ch9PHwbUGgDA+O3jSbJIhzQh7M5B+rxI8ZJGJlNqASPFixD2N3as2rZqBaVL3/uYLpW7kCdrHv66/heLDi3KvHBCuCtpeXE+1kJTihch7Ov4cVi8WO0PHnz/47J5Z+PdGu8CMGbbGCyGJRPSCeHGpHhxPlK8CJE5xo9XE0K+8AJUqPDgY3tW70mAbwDHrhxj+dHlmRNQCHcVF6e2Urw4D19ftb19W28OIVzZ6dPw7bdqf8iQhx/v5+NH7+pqqPSYbWNwsdkfhHAsMTFqmyOH1hhSvKSD9VzdvKk3hxCu7OOP1WSQISEQHJy2x/QO7k02r2yER4Sz5s819g0ohDuT4sX5WM9VtCynIoRdXLgAs2er/Q8/TPvjcmXNRY9qPQAYvW20tL4IYS/WT+/Zs2uNIcVLOlgn/LMWnkII25o0SfUpq10b6tZN32P71eyHj4cPO8/tZPPpzfYJKIS7k5YX5yMtL0LYz5UrqdP/f/hh+td9C8oeRJfKXQAYvXW0jdMJIQApXpyRtLwIYT+ffQa3bkGVKtCwYcaeY8DTA/Aye7H59GZ2nN1h03xCCFLfAOWykfOQlhch7OPGDZg6Ve1npNXFqrB/YTpU6ACokUdCCBuz9nmRlhfnIS0vQtjHF1+oDwVPPgkvvvhozzWw9kDMJjNr/lzDvov7bBNQCKFYP71L8eI8rMVLVJTeHEK4kps31SUjULPpmh/xr1KJwBK0fbItIK0vQtjc1atqGxioNYYUL+lgPVfXrunNIYQr+eor9ffwiSegdWvbPOfg2mpNgWVHl3Hk8hHbPKkQ7i4hIfXSQ+7cWqNI8ZIOefKo7eXLenMI4Sri4mDiRLU/aBB4eNjmecvlLUfLMi0BGPfbONs8qRDuzvrJ3WSCgACtUaR4SQdroXnlit4cQriK2bMhIgIKF4bXXrPtc1tbXxYeXMjJaydt++RCuKM7LxnZ6pNGBknxkg5SvAhhO4mJMGGC2v/gA/Dysu3zVylQhSYlmmAxLEzYPsG2Ty6EO7K++eXKpTcHUryki7V4uXFD/eEVQmTc//4HZ85AUBC8+aZ9XmNIHbWy49zwuZyNOmufFxHCXVhbXjT3dwEpXtIlZ87UkRDWcyiESL/kZBg7Vu3375+6YrutPV34aeoXqU+iJZFPdnxinxcRwl1Y3/ik5cW5eHikjjiSS0dCZNz338OJE+pvYLdu9n0ta+vLrL2ziLwZad8XE8KVyWUj52VtLZMRR0JkjMWS2ury7rv2n2W8QdEGBBcMJi4pjsmhk+37YkK4sogItQ0K0psDKV7SLV8+tbWeQyFE+qxcCYcOqUkfe/a0/+uZTCY+rPshANN/n8612zJRkxAZcuGC2hYooDcHUryk22OPqe25c3pzCOGMDAM++kjtv/NO5k0V0eyJZlTIV4GbCTf5fOfnmfOiQria8+fVVooX51OwoNpaz6EQIu1+/BHCw9WyKO++m3mvazKZUvq+TNk9hRtxNzLvxYVwFdaWF+sboUZSvKSTFC9CZIxhwIgRav+ddzK/z9/LZV+mbJ6y3Ii7wZRdUzL3xYVwdoYhl42cmRQvQmSMtdUle3bo1y/zX99sMjOs7jAAPt35qbS+CJEeV6+mTnAmHXadjxQvQqSfYcDIkWpfR6uL1StlX5HWFyEywtrqkicPeHvrzYIUL+lmLV4uXFBDPoUQD/fTT7Bvn75WFysPs8ddrS9RcVH6wgjhTByosy5I8ZJuQUFqQc2kJJnrRYi0uLPVpVcv/TOLS+uLEBlw5ozaWofcaibFSzp5eUH+/Gr/77/1ZhHCGaxaBXv3QrZs8N57utPc3foyeedkaX0RIi1OnVLbokX15viHFC8ZUKyY2lrPpRDi3u4cYeQIrS5Wr5R9hTK5y0jrixBpZX3Ds74BaibFSwZYz91ff+nNIYSjW73asVpdrDzMHgyrJ31fhEgzaXlxfsWLq+3Jk3pzCOHI7mx16dlTDVJwJK3KtqJM7jJcj7vO1N1TdccRwrFZP61L8eK8pOVFiIdbswbCwiBrVujfX3ea/7qz9WVyqPR9EeK+YmLUPC/g+sXLtWvXaN++PX5+fgQEBNC5c2du3rz5wMfMnDmT+vXr4+fnh8lk4saNG/aK90ikeBHiwRy91cVKWl+ESAPrJaPAQLWiqgOwW/HSvn17Dh8+zIYNG1i1ahVbt26la9euD3zMrVu3aNy4MYMHD7ZXLJuwFi9nz0JCgt4sQjiiNWvg998dt9XFysPswdC6QwHV+hIdH605kRAOyMH6u4CdipejR4+ybt06vv76a4KDg6lduzZTp05l0aJFXLDO0ncPffv2ZeDAgdSoUcMesWwmXz7IkkVNUifDpYW4253zuvToAXnz6s3zMK3LtaZ07tKq9WWXtL4I8R/WDp4OMtII7FS8hIaGEhAQQNWqVVPuCwkJwWw2s2vXLpu+Vnx8PNHR0Xfd7M1kSu20e+KE3V9OCKeydi3s2aMK/AEDdKd5uDvnfZkUOklaX4T4t2PH1LZ0ab057mCX4iUiIoK8//q45enpSWBgIBERETZ9rXHjxuHv759yK1SokE2f/36s5/Do0Ux5OSGcgmHA8OFqv2dPx291sbqz9UXmfRHiX6xvdM5avAwcOBCTyfTA2zFrhZZJBg0aRFRUVMrt7NmzmfK6ZcqorRQvQqRauVL1dcmWzTlaXaz+3foiK04LcQfr+7r1jc8BeKbn4Pfee4+OHTs+8JhixYoRFBTEpUuX7ro/KSmJa9euEWTjpbR9fHzw8fGx6XOmhfUcHjmS6S8thEOyWGCo6vtKnz7O0+pi1ebJNoz9bSyHLh1i0o5JjHp2lO5IQuh35Yq6AZQsqTfLHdJVvOTJk4c8aRjzWLNmTW7cuEFYWBhVqlQBYNOmTVgsFoKDgzOW1MHc2fJiGKofjBDu7Pvv4dAh8Pd37BFG92M2mfmo/ke0/L4ln+36jN7BvcmTzUHHeAuRWaytLoULqyZVB2GXPi9lypShcePGdOnShd27d7N9+3Z69epF27ZtKfDPctrnz5+ndOnS7N69O+VxERERhIeHc+KfXrAHDx4kPDyca9eu2SPmIylVShUs16/DvxqZhHA7SUmpfV3eew9y5tSbJ6NalG5BlfxVuJlwkwnbJ+iOI4R+DthZF+w4z8uCBQsoXbo0DRo0oGnTptSuXZuZM2emfD0xMZE//viDW7dupdw3Y8YMKlWqRJcuXQCoW7culSpV4scff7RXzAzLkiV1yLv0exHu7n//g+PHIVcudcnIWZlMJkY/OxqAaXumcSHm/lM7COEWHLC/C9ixeAkMDGThwoXExMQQFRXF7NmzyZ49e8rXixQpgmEY1K9fP+W+ESNGYBjGf24P62eji/R7EUJN1Gid12XgQIeZgDPDGhVvxNOFniYuKY4xW8fojiOEXocOqa27FC/uoFw5tT14UG8OIXT65hs4fRqCgtSkdM7OZDIx5llVtMzaO4vTN07rDSSETuHhaluxos4U/yHFyyOwnkvruRXC3dy+DaPVVRaGDFHLAbiCekXqEVIshERLIh/9+pHuOELoEREBkZGqg+eTT+pOcxcpXh6BtXg5cACSk7VGEUKLGTPgwgU1EOGfrmouY/Qzqiqbt38ex68e15xGCA3271fbkiUdaqQRSPHySEqWVB13b92CP//UnUaIzHXzJowbp/aHDQMN0y3ZVfBjwbxQ8gUshoURW0bojiNE5rNeVqhQQWuMe5Hi5RF4eED58mpfLh0JdzNlCly+DCVKQIcOutPYx0fPqEtGiw4t4mCkdG4Tbsba8uJg/V1AipdHVqmS2krxItzJjRvwySdqf8QI8PLSmcZ+KgZVpHW51hgYDNsyTHccITKXg3bWBSleHpn1nO7bpzWGEJlq4kRVwJQrB23b6k5jXyPrj8RsMvPDsR/YfX73wx8ghCu4fRv++EPty2Uj12Ntedm3Ty0TIISru3gRJk9W+6NHq8unrqx07tK8Xv51AAb+MhBDftGFO9i7Vy1Yli8f5M+vO81/SPHyiJ56Cjw91bX/M2d0pxHC/kaOVB/KataE5s11p8kcI+uPxNvDm82nN/PzyZ91xxHC/nbtUtvgYIdcvE+Kl0eUJUvqpaOdO7VGEcLu/vgDvv5a7U+Y4JB/0+zi8YDH6VWtFwAf/PIBFsOiOZEQdnZn8eKApHixgRo11FaKF+HqPvxQzWn0/PNQp47uNJlrcJ3B+Pn4sT9yP4sOLdIdRwj7kuLF9VmLl9BQvTmEsKddu2DpUtXaYp3fxZ3kypqLD57+AIAhm4YQnxSvOZEQdhIZCX//rX7Zq1XTneaepHixAWvxsm8fxMvfM+GCDEMtughqThcHmyk80/QJ7kP+7Pk5feM0X4V9pTuOEPZhbXUpU8ZhV1qV4sUGihWD3LnV6royZFq4ovXrYcsWNYvuR2681E8272yMqD8CgFFbRxEdH603kBD24OCXjECKF5swmaTfi3BdFgt8oK6W0KuXWsfInb1Z6U1K5irJlVtXmLhjou44Qtie9Y1MihfXV7Om2u7YoTeHELa2cKFafNTPDwYN0p1GP0+zJ2OfHQvA5NDJRNyM0JxICBtKSEjtwFm7tt4sDyDFi41Yz/HWrTJZnXAd8fEwdKjaHzgQcuXSm8dRtCzTkuoFqxObGMuoX0fpjiOE7fz+u5rIKXduKFtWd5r7kuLFRqpXB19f1UnbOqOyEM5uxgw4fVpNsNmnj+40jsNkMvFxyMcAzNw7kz+vyrLywkX8+qva1q3r0BM5SfFiI76+qZeOtmzRGkUIm7h+HUb906gwYgRkzao1jsOpV6QeTZ9oSpIliQ9++UB3HCFsw1q81KunN8dDSPFiQ/Xrq60UL8IVjBkDV6+qluM339SdxjF9HPIxZpOZFcdW8OvpX3XHEeLRJCXB9u1qv25dvVkeQooXG7qzeJF+L8KZnTwJU6ao/UmT1Ppd4r/K5S1H18pdAej3cz9ZNkA4t3374OZNCAhQC/c5MClebEj6vQhX8cEHkJgIjRpB48a60zi2kc+MJId3DvZe3MuCAwt0xxEi46yXjOrUcfjl4qV4saE7+71s3qw3ixAZtW0bLFsGZjNMlGlMHipvtrwMqTMEgEEbB3Er8ZbmREJk0IYNavvMM3pzpIEULzZmPefWnwEhnInFAv36qf0uXdx3GYD06lOjD4/7P875mPNM2jFJdxwh0u/2bTXXB6gmVwcnxYuNWZvYf/lFNbsL4UwWLlTTPOTIASNH6k7jPHw9fRkfMh6ACdsncDHmouZEQqTT1q0QFwePPabWNHJwUrzYWJUqam6fmBhZZVo4l1u3UmfQHTwY8uXTm8fZtCnXhhqP1SA2MZahm4fqjiNE+qxfr7aNGjn0/C5WUrzYmNkMDRuq/XXr9GYRIj0mT4Zz5+Dxx6FvX91pnI/JZGJyw8kAzN43m/0R+zUnEiId7ixenIAUL3ZgvXQkxYtwFhcvwnh11YPx41Xnc5F+NQvVpE25NhgYvPfzexgyZ4JwBmfPwpEj6tN3gwa606SJFC92YC1c9+2DCFmzTTiBQYMgNlYtItumje40zm1cg3H4ePiw8dRGfjj2g+44Qjzczz+rbbVqEBioN0saSfFiB3nzqr4vkPozIYSjCg2FefPU/pQpTnG526EVzVmUAbUGAGriutuJtzUnEuIhVq9WWyea1EmKFzux/gz89JPeHEI8SHIyvPOO2u/USU20KB7dwNoDKeRXiNM3TvPJjk90xxHi/m7fTu3v8uKLerOkgxQvdtK8udquXatGnwnhiObMgbAw8PODceN0p3Ed2byzMbGhmuFv3G/j+PvG35oTCXEfv/yihhoWKgSVKulOk2ZSvNhJ1apquHxsrPrZEMLRXL+eOjR65EgZGm1rrcq2on6R+sQlxdF/Q3/dcYS4t5Ur1bZ5c6e6ZizFi52YTNCihdpfsUJrFCHuafhwuHJFrRrds6fuNK7HZDIxpfEUzCYzS48sZeNfG3VHEuJuycmpfRuslwuchBQvdvTSS2r7449qpXEhHMXBgzB9utqfMgW8vPTmcVVP5XuKHlV7ANBnXR8Sk2XabeFAdu6ES5fA3x/q1dOdJl2keLGjOnUgZ0716XbHDt1phFAMA3r3Vh+6Xn7ZaaZ1cFofPfMRubLk4vDlw0zfM113HCFSWS8ZNWvmdJ9g7Fq8XLt2jfbt2+Pn50dAQACdO3fm5s2bDzz+nXfeoVSpUmTJkoXChQvTu3dvoqKi7BnTbry84IUX1P7y5XqzCGG1ZAls2aImopskawjaXc4sORnbYCwAw7cMJ/JmpOZEQqA+xXz/vdq3XiZwInYtXtq3b8/hw4fZsGEDq1atYuvWrXTt2vW+x1+4cIELFy4wceJEDh06xNy5c1m3bh2dO3e2Z0y7evlltV2yRH3SFUKn6Gh49121P3CgWgpA2F/nSp2pkr8KUfFR0nlXOIZdu+DvvyF7dmjaVHeadDMZdpq/+ujRo5QtW5Y9e/ZQtWpVANatW0fTpk05d+4cBQoUSNPzLFmyhNdee43Y2Fg8PT0fenx0dDT+/v5ERUXh5+f3SN+DLcTHQ1AQ3LgBmzdD/fq6Ewl31qeP6uNSvDgcOiTLAGSmPef3EPx1MAYGGzts5Nmiz+qOJNxZ377w+efQvj3873+60wDpe/+2W8tLaGgoAQEBKYULQEhICGazmV27dqX5eazfxP0Kl/j4eKKjo++6ORIfn9TWl+++05tFuLewMPjiC7X/5ZdSuGS2agWr0bOaGtbVfXV34pPiNScSbis5OfWSUdu2erNkkN2Kl4iICPLmzXvXfZ6engQGBhKRxgV/rly5wqhRox54qWncuHH4+/un3AoVKvRIue2hXTu1XbIEEhL0ZhHuKTkZ3n4bLBb18/jcc7oTuafRz44mKHsQx68eZ8L2CbrjCHe1datajTUgABo21J0mQ9JdvAwcOBCTyfTA27Fjxx45WHR0NM2aNaNs2bKMGDHivscNGjSIqKiolNvZs2cf+bVtrX59deno+nVZ60jo8eWX8PvvakTk5Mm607gvf19/Pmv0GQBjt43lz6t/6g0k3NOiRWr78svg7a03SwY9vBPJv7z33nt07NjxgccUK1aMoKAgLl26dNf9SUlJXLt2jaCgoAc+PiYmhsaNG5MjRw5WrFiB1wOGcPn4+ODj45Pm/Dp4eKiVej//HBYuhOef151IuJMLF2DwYLU/bpwqpIU+rcu1Zk74HNafXE/PNT1Z/9p6TE40s6lwcvHxsHSp2nfSS0aQCR12f//9d6r8s8Tyzz//TOPGjR/YYTc6OppGjRrh4+PDmjVryJo1a7pe19E67Frt3g3BwZA1K0REQI4cuhMJd9Gmjbq8Xb26mm/Iw0N3InHy2knKTS9HfHI8C1supN1T7XRHEu5i6VJo1QoKFFCjjdIwECazOESH3TJlytC4cWO6dOnC7t272b59O7169aJt27Yphcv58+cpXbo0u3fvTgnesGFDYmNj+eabb4iOjiYiIoKIiAiSnXyccbVqUKqUWv/K2k9KCHtbt079vJnN8NVXUrg4iuKBxfmw7ocAvLv+XW7E3dAbSLiPOXPUtkMHhypc0suu87wsWLCA0qVL06BBA5o2bUrt2rWZOXNmytcTExP5448/uHXrFgB79+5l165dHDx4kBIlSpA/f/6UmyP2ZUkPkwnefFPtf/ON3izCPcTGpq5Z1KcPVKyoNY74lwG1BlA6d2kiYyP5YMMHuuMId3DhgvpEA9Cpk94sj8hul410cdTLRqAuFz32mBr5ceQIlCmjO5FwZf36waefqp+5I0fkUqUj2vr3VurNVWvKbOqwiWeKPqM5kXBpEyao2Slr1YLt23Wn+Q+HuGwk/isoSC0hAdL6Iuxr50747DO1P3OmFC6Oqu7jdeletTsAb/30FrEJsZoTCZdlGDB7ttq3XgZwYlK8ZDLrSgfz50OiLDAr7CA+Xv1tMgx1WbtJE92JxIOMDxlPIb9C/HX9L4ZuHqo7jnBVO3bA8eNq1Ejr1rrTPDIpXjJZ06aqBebyZfjxR91phCsaNQqOHoV8+dRlI+HY/Hz8+Or5rwD4bOdn7Dy3U3Mi4ZKm/7OieevWLtEUK8VLJvP0TG2xmzZNbxbhesLDYfx4tT99OgQGao0j0qjJE014vfzrGBi8ufJNWTpA2FZkpJriHVJ78Ts5KV40ePttNXR182Y4fFh3GuEqEhNVYZycDK+8Ai1b6k4k0uPTRp+SN1tejl45yuito3XHEa7k66/VH4jq1eGO9QadmRQvGhQqBC1aqH3rQnlCPKpPPoF9+1Rri/xcOZ9cWXMxralqjh2/fTzhEeF6AwnXkJQEM2aofRdpdQEpXrR55x21nT8fbtzQGkW4gAMHYORItf/556q/i3A+r5R9hZZlWpJkSaLDig5y+Ug8up9+gnPnIHdul+ioayXFiyb16sGTT6oZd60THgqREfHx8PrrasXyF16A9u11JxKP4stmX5Inax4OXjrIsM3DdMcRzs7aDPvWW+DrqzeLDUnxoonJlNr6Mm2a6qcgREYMG6ZaXvLkgVmz1M+WcF55s+Vl1guzAPhkxyds+3ub5kTCae3dC5s2qXVB3n5bdxqbkuJFo/btIWdOOHkSVqzQnUY4o23bVF8XUIWLXC5yDc1LN6djxY4YGLzxwxvExMfojiSc0cSJatu6NTz+uN4sNibFi0bZskGvXmp/wgQ1qZgQaRUTA2+8oX5uOnWC5s11JxK29Hnjz3nc/3FO3TjFu+vf1R1HOJvTp1NXAR4wQGsUe5DiRbN33oEsWeD339XQaSHS6t134dQpKFIkdSkA4Tr8fPyY12IeJkx8s+8bfvrjJ92RhDP59FPVHyEkBCpV0p3G5qR40SxPntQlA6yTiwnxMD/+qNbHMplg3jxwsDVIhY3UK1KPfjX7AWrto8uxlzUnEk7h2jU1twvA++/rzWInUrw4gPfeU/2pNmxQ/auEeJCICDVwAKB/f6hbV28eYV+jnx1NuTzluBR7iTd/fBNDri+Lh/nySzWUtWJF1fLigqR4cQBFikDbtmp/zBitUYSDs1jgtdfU2ljly6t1jIRr8/X0ZUHLBfh4+LDq+Cqm7JqiO5JwdC1bqo5wAwe67PBDKV4cxODB6mds+XI1S6oQ9zJhAmzcqBaGXbwYfHx0JxKZoUJQBSY1nATA+7+8z96L0kQr7m3Sjkm88cd4Tk0aCm3a6I5jN1K8OIiyZaFdO7U/fLjeLMIxbd8OQ4eq/WnToHRpvXlE5upRrQctSrcgITmBtkvbyvBp8R9RcVGM2TaG+fvns+2Ma88PJMWLAxk+XC3Y+NNPsHu37jTCkVy7Bq++qgYPtG+vhkgL92IymfjmxW8o5FeIP6/9Sc81rrNOjbCNyaGTuR53nTK5y9D+KdeealuKFwdSsqSa5h3UrKlCgJrH5a234MwZKFFC9cVz0cvY4iECswSy8OWFmE1mvj3wLfP3z9cdSTiIK7euMHnnZAA+euYjPMwemhPZlxQvDmbYMDXyaP16+O033WmEI5g2Tc3A7OUFixZBjhy6Ewmdaheuzcj6ahXOHqt7cPTyUc2JhCMY/9t4bibcpHL+yrQs01J3HLuT4sXBFCuWOu9L//4y6667Cw2FfmqaDz7+GKpU0ZtHOIZBtQfRoGgDYhNjafl9S+n/4ubORJ1h2p5pAIx+ZjRmk+u/tbv+d+iERo5USwfs2pU6u7NwP5GR8MorkJgIrVpBnz66EwlH4WH2YOHLCymYoyDHrhyT+V/c3KCNg4hLiqN+kfo0LtFYd5xMIcWLAwoKgg8+UPsDB0JcnN48IvMlJalRjhcuQJkyqbPpCmGVN1telrZeipfZi6VHljI5dLLuSEKDXed2sfDgQkyYmNRwEiY3+UMhxYuDeu89KFBAra01daruNCKzDRoEv/4K2bOruX+kn4u4lxqP1eCzxp8B8MEvH7Dl9BateUTmMgwjZdHONyq+QeX8lTUnyjxSvDiorFlTZ9sdMwYuXdKbR2SepUtTV7KfO1fmcxEP1r1qd14v/zrJRjJtlrbhfPR53ZFEJllyZAmh50LJ6pWV0c+M1h0nU0nx4sA6dIDKlSEqymXX1hL/cviwmtUb1Cr2L7+sN49wfCaTiRnPz6B8vvJcir3Ey9+/TFySXGt2dTcTbtL/5/4AvF/rfQr6FdScKHNJ8eLAzGaYPj115eCtW3UnEvZ05Qq88ALcvAnPPANjx+pOJJxFVq+sLG+9nJy+Odl1fhdv/fiWdOB1cSO3jORs9FmKBBRhwNMDdMfJdFK8OLjgYOjaVe336KFGngjXk5Cg1lI7dUoNl1+yBDw9dacSzqR4YHGWtFqCh8mDBQcXMP638bojCTs5GHmQT3d+CsAXTb4gq1dWzYkynxQvTmDsWMidW11S+Pxz3WmErRkGdO8O27aBn59aHiJXLt2phDNqUKwBU5qoVacHbxrMD8d+0BtI2JzFsNB9dXeSjWRalmlJs5LNdEfSQooXJxAYqCYoA7X+0V9/6c0jbOvTT2H2bHWZcPFitUinEBnVo1oPelTtAcBry19jf8R+zYmELc3ZN4ftZ7eTzSsbnzX6THccbaR4cRJvvAH16sGtW2oGXotFdyJhCz/9pGZSBpg8GRq7x/xSws4+a/xZygy8L3z3AhdiLuiOJGzgXPQ5+v2sptweWX8khfwLaU6kjxQvTsJsVhOVZc0KW7aoxfmEc9u1S01EZxiqX1Pv3roTCVfh5eHFklZLKJmrJGejz9JkQROi4qJ0xxKPwDAM3vrxLaLjowkuGEyfGu495bYUL06keHEY/08fvA8+kMtHzuz4cWjWDG7fhiZN4IsvZAZdYVs5s+Rkbfu15MuWjwORB3j5+5dJSE7QHUtk0Ox9s1l/cj0+Hj7MbTEXT7N79+iX4sXJ9OwJdetCbKxcPnJWERHq8tDVq1C1qlq/ystLdyrhiorlLMaa9mvI7p2djac28ubKN7EY8kfD2ZyJOpMyk+6YZ8dQOrfMXCnFi5Mxm1XnTuvlI2tHXuEcYmJUi8upU6olbfVqtQSAEPZSOX9llrVehqfZkwUHFzDol0G6I4l0SLIk8dry14hJiKFWoVr0rdFXdySHIMWLEypePHXI9Icfws6devOItImLg5degr17IU8eWLcO8ubVnUq4g4bFG/LNi98A8PGOj5m4Y6LmRCKtRv06im1ntpHDOwfzW8zHw+yhO5JDsGvxcu3aNdq3b4+fnx8BAQF07tyZmzdvPvAx3bp1o3jx4mTJkoU8efLQvHlzjh07Zs+YTqlzZ2jdGpKToV07tYSAcFwJCdCqFWzcCNmyqRaXEiV0pxLupEOFDoxvoDrNDdgwgOl7pmtOJB5my+ktjN6m1iz66vmvKB5YXHMix2HX4qV9+/YcPnyYDRs2sGrVKrZu3UpX63Sx91GlShXmzJnD0aNHWb9+PYZh0LBhQ5KTk+0Z1emYTDBzJhQpolae7tpVjVoRjicpCV57DVatAl9fta1WTXcq4Y4+qP0Bg2sPBqDnmp7MC5+nOZG4nyu3rtB+eXsshoVOFTvR7ql2uiM5FJNhpwUwjh49StmyZdmzZw9Vq1YFYN26dTRt2pRz585RoECBND3PgQMHqFChAidOnKB48YdXndHR0fj7+xMVFYWfn98jfQ/OYNcuqF1bvUF++in07as7kbiTxaIWWpw/X3XK/fFHmctF6GUYBu+uf5fPd32O2WTmu5e/o3W51rpjiTskWZJosqAJv/z1C6VylSKsaxjZvLPpjmV36Xn/tlvLS2hoKAEBASmFC0BISAhms5ldu3al6TliY2OZM2cORYsWpVChe0/GEx8fT3R09F03dxIcDBP/uXzdvz9s3qw3j0hlsajRYfPng4eHmj1XChehm8lk4tNGn/JWpbewGBbaL2/PymMrdccSdxj0yyB++esXsnplZUmrJW5RuKSX3YqXiIgI8v6rN6KnpyeBgYFEREQ88LHTp08ne/bsZM+enbVr17Jhwwa8vb3veey4cePw9/dPud2vyHFlvXtDhw6q/0urVuoyktArORm6dYMZM9Qlvm+/VZ11hXAEJpOJGc/P4NWnXiXJksQrS15h6ZGlumMJYOHBhUwMVZ9I57WYx1P5ntKcyDGlu3gZOHAgJpPpgbdH7WDbvn179u3bx6+//krJkiVp3bo1cXFx9zx20KBBREVFpdzOnj37SK/tjEwm9SZZpYqaO+Sll9Q8MEKPpCTo2BG+/loNbZ8zR3WqFsKReJg9mNdiXkoB02ZpGxYcWKA7llvbe3EvnX/sDMCg2oN4pewrmhM5rnRP0ffee+/RsWPHBx5TrFgxgoKCuHTp0l33JyUlce3aNYKCgh74eGsryhNPPEGNGjXImTMnK1asoN093gF8fHzw8fFJ77fhcrJkgeXL1aRn4eHqzXL5cvB070kYM11CArRvD0uXqktFCxaoJQCEcESeZk/mt5iPj4cPc8Ln8PqK14lLiqNz5c66o7mdM1FneH7h88QlxdGkRBNGPTNKdySHlu63tjx58pAnT56HHlezZk1u3LhBWFgYVapUAWDTpk1YLBaCg4PT/HqGYWAYBvHx8emN6nYKF4YffoAGDdSCf717w7RpMu18ZomLU8PXf/pJdc79/nto0UJ3KiEezMPswdcvfo2Phw8zwmbw1k9vEZcUR8/qPXVHcxvXb1+nyYImXLx5kXJ5yrHw5YUyn8tD2K3PS5kyZWjcuDFdunRh9+7dbN++nV69etG2bduUkUbnz5+ndOnS7N69G4C//vqLcePGERYWxpkzZ9ixYwetWrUiS5YsNG3a1F5RXUqtWurTvsmkFm+UGXgzx/Xr0KiRKlx8fdWoIilchLMwm8xMbzadvsF9Aei1thdDNw3FToNRxR3ik+JpsbgFRy4foUCOAqxtv5YA3wDdsRyeXed5WbBgAaVLl6ZBgwY0bdqU2rVrM3PmzJSvJyYm8scff3Dr1i0AfH192bZtG02bNqVEiRK0adOGHDlysGPHjv90/hX317KlGjYNMHAgzJqlN4+rO3sW6tSBrVvBzw/WrJFRRcL5mEwmJjeazPB6wwEYvW00nX/sTGJyouZkrivJksSry19l699byeGdg7Xt11LI3/0GnWSE3eZ50cXd5nl5kAED1DBqkwnmzYPXX9edyPUcPKhWhT5/HgoUgLVroXx53amEeDSzwmbx9uq3sRgWmpRoIsN17SDZksxrK15j0aFFeHt4s+bVNTQo1kB3LK0cYp4Xod/HH0OPHmrm3Y4dVR8MYTvr16sWl/PnoUwZCA2VwkW4hi5VuvBDmx/I4pmFtSfWUnduXc5Gud9ITnuxGBY6/9iZRYcW4Wn2ZGmrpW5fuKSXFC8uzGSCqVPVOkgWixoFs3ix7lTOzzBg0iRo2lStKVWnDvz2m+owLYSreKHUC2x6YxO5s+Zm78W9VJtVjdCzobpjOb1kSzJdfuzCvP3z8DB5sPiVxbxQ6gXdsZyOFC8uzmyGr75Sl4ySktQQaukDk3FxcfDGG2o2Y4tFFYYbNkBgoO5kQthejcdqsKfLHsrnK09kbCT159Vnbvhc3bGcVnxSPG2XtWV2+GzMJjPfvvQtLcu01B3LKUnx4gY8PNREaW+/rVoNunaVUUgZ8fffUK+emi3XwwOmTFGFoEwzJFxZkYAibH9zOy3LtCQhOYFOKzvRe21v4pNk+or0uJlwkxe+e4GlR5bi7eHNklZLZLHFRyDFi5vw8IDp02HQIPXvDz6Afv3UNPbi4VauhIoVYfdu1cqyfj28847MoSPcQ3bv7CxptSRlJNLU3VN5evbT/HX9L83JnEPkzUhC5oew4a8NZPPKxupXV0uLyyOS4sWNmEwwdmxqq8unn6q5SGJitMZyaAkJaqXuFi3gxg2oXh3CwtREgEK4E7PJzIj6I1j96mpyZclF2MUwKn1ViWVHlumO5tD2R+yn+tfV2XV+Fzl9c7Kxw0ZCioXojuX0pHhxQwMGqI67vr6wahU8/bQs5ngvR46oSf8+/1z9u18/2LYNihTRGksIrZo+0ZR93fZRq1AtouOjeWXJK3T9qSsx8fIp6N9WHlvJ07Of5kzUGUrmKsnOt3YS/FjaZ5gX9yfFi5tq3Rp+/RWCgtRcJZUqqVlhhbqU9sknULmyamXJmVP930yaBPdZ3FwIt1LIvxBb3tjCB09/gAkTs/bOovyM8mw+tVl3NIeQmJzIwF8G0mJxC2ITY2lQtAE7O++kZK6SuqO5DCle3Fj16qoPR3CwuiTSvDm89566VOKujh9XQ5/ffx/i49UEdAcPwgsyklGIu3h5eDE+ZDyb39hM0YCinL5xmmfnP0vvtb25mXBTdzxtzkadpf68+kzYPgGAd6q/w9r2a8mZJafeYC5Gihc3V6iQmta+Xz/178mT1aWSQ4f05spst27B0KHw1FNqsrkcOeCbb2D1aihYUHc6IRxXvSL12P/2frpV6QaozrxlppVh2ZFlbrU2kmEYLDq0iIpfVWTH2R34+fixpNUSpjSZgpeHl+54LkeWBxApVq6ETp3UIoPe3jB8uGqB8Ez32uPOwzDUYop9+qT2+2nUCGbOlEnnhEiv9SfW0311d07dOAVAo+KNmNpkKk/kekJzMvuKuBlBj9U9WHFsBQBV8ldh8SuLKR5YXHMy5yLLA4gMad4cDh9Wl0gSEmDIEHVJaccO3cnsIyxMFSrNm6vCpVAhWLZMrU8khYsQ6deoRCMO9zjMsLrD8PbwZv3J9Tz55ZP0XdeXy7GXdcezuWRLMjPDZlJuejlWHFuBl9mLkfVHEto5VAoXO5OWF/EfhgELFkDv3qoVBuDVV2HCBHjsMb3ZbOH4cXWJyLrWk5eX6uvz4YeQTdaeE8ImTlw7wTtr32HdiXWAmiumf83+9KvZjxw+OTSne3S/nv6VPuv6sD9yPwCV81dmTvM5lM8nC5xlVHrev6V4Efd16ZJqffnmG1XQZM2qJmbr3x9y59adLv0OHFCjiL77To0oMpnUek8jR0KxYrrTCeGafvnrFwb+MpCwi2EA5MqSi3eqv0PP6j3JndX5/pCER4Qz8teR/HDsBwACfAMYWX8k3at2l74tj0iKFylebCosTLXCWC8fZc+uipg+fSBfPr3ZHsYwYNMmVbSsX596//PPw5gxsgq0EJnBYlhYdmQZQzYN4c9rfwKQ1SsrnSt1pm+NvhTL6fifHsIuhDFm25iUfi1mk5luVbrx0TMfOWUR5oikeJHixeasHVtHjIB9+9R9Xl7Qpo0qbKpV0xrvPy5ehHnzYPZs+FP9rcRshldeUZP0Va2qN58Q7ijJksTyo8uZsH0Cey/uTbm/QdEGvFX5LVqUboGvp6/GhHdLSE5g2ZFlfLHnC3acVZ/eTJho82QbhtYdStk8ZTUndC1SvEjxYjeGoSZsGz8edu5Mvb98edUv5tVXVcdXHa5dUwXWkiWwbl3quk3ZskHHjmo4uFweEkI/wzDYdGoTE0Mnsv7EegzU21BglkBalW1FyzIteabIM1ouwxiGwa7zu1h4cCGLDy/mUuwlADzNnrQu15ohdYZI0WInUrxI8ZIp9uyBqVPVUgN3TmwXHKwmd2vcWLVweHjY5/WTk2HvXti8GX7+GbZsuXuhyVq1oHNnaNVKzdsihHA8p2+cZs6+OcwJn8PZ6LMp9wf4BtCkRBNCioXwbNFnKRJQxG4ZYuJj2Hx6M+tPrGfNiTWcvnE65WtB2YN4u8rbdK3Slfw58tstg5DiRYqXTHb9OixdqkYo/frr3V/z91eXlKy30qWhaFG1rlJ6xMaq4cyHDqmCZd8+NTtwVNTdx5UvDy+9pC5nlSnzSN+WECITJVuS2XRqE8uOLmPFsRUpLR5WRQKKULVAVSoHVaZS/kqUzFWSwv6F8TSnbyKq67ev89f1v9gfuZ/fL/zOngt72B+xn0RLYsox2byy8VKZl2j3ZDueK/acdMTNJFK8SPGizfnz6pLNunWwYcN/iwtQo3wKFlS3nDkhIEAVOSaTuixlsajHXb+ubmfOqJFP9+LvD/XqwTPPqE64JUrY9dsTQmSCZEsyO87u4OeTP7Pp9CZ2ndtFspH8n+M8TB48HvA4+bLlIzBLIIFZAsnimQWzyYzZZCYuKY6o+ChuxN3g6u2rnL5xmhtxN+75msVyFqNR8UY0Kt6IkGIhZPOWeRMymxQvUrw4hKQktS7Qnj2qlWTvXjhxAmIyuPisvz+UKqUWkaxcGapUgYoV7XdZSgjhGGLiY9h9fjd7L+5lb8RewiPCOXX9FPHJ8Rl6vqDsQZTKVYpqBapRrWA1qhWoRtGcRW2cWqSXFC9SvDgsw4ArV+DkSYiMVAtCXr8O0dHqayaTGhWUI4dqlcmZU7XQFC2q9oUQAtTw64sxFzl14xRXbl3h2u1rXL11lfjkeCyGBYthwdvDmwDfgJTb4/6PUySgiLSqOKj0vH+78Ko1whGZTJAnj7oJIURGmU1mCvoVpKCfrJzqjmRtIyGEEEI4FSlehBBCCOFUpHgRQgghhFOR4kUIIYQQTkWKFyGEEEI4FSlehBBCCOFUpHgRQgghhFOR4kUIIYQQTkWKFyGEEEI4FSlehBBCCOFUpHgRQgghhFOR4kUIIYQQTkWKFyGEEEI4FZdbVdowDEAtrS2EEEII52B937a+jz+IyxUvMTExABQqVEhzEiGEEEKkV0xMDP7+/g88xmSkpcRxIhaLhQsXLpAjRw5MJpPuOP8RHR1NoUKFOHv2LH5+frrjiH+R8+PY5Pw4PjlHjs2Rz49hGMTExFCgQAHM5gf3anG5lhez2cxjjz2mO8ZD+fn5OdwPjkgl58exyflxfHKOHJujnp+HtbhYSYddIYQQQjgVKV6EEEII4VSkeMlkPj4+DB8+HB8fH91RxD3I+XFscn4cn5wjx+Yq58flOuwKIYQQwrVJy4sQQgghnIoUL0IIIYRwKlK8CCGEEMKpSPEihBBCCKcixYudjRkzhlq1apE1a1YCAgLS9BjDMBg2bBj58+cnS5YshISE8Oeff9o3qBu7du0a7du3x8/Pj4CAADp37szNmzcf+Jj69etjMpnuur399tuZlNi1TZs2jSJFiuDr60twcDC7d+9+4PFLliyhdOnS+Pr68tRTT7FmzZpMSuq+0nOO5s6d+5/fFV9f30xM6z62bt3KCy+8QIECBTCZTPzwww8PfcyWLVuoXLkyPj4+lChRgrlz59o9py1I8WJnCQkJtGrViu7du6f5MR9//DFTpkxhxowZ7Nq1i2zZstGoUSPi4uLsmNR9tW/fnsOHD7NhwwZWrVrF1q1b6dq160Mf16VLFy5evJhy+/jjjzMhrWtbvHgx/fr1Y/jw4ezdu5cKFSrQqFEjLl26dM/jd+zYQbt27ejcuTP79u2jRYsWtGjRgkOHDmVycveR3nMEajbXO39X/v7770xM7D5iY2OpUKEC06ZNS9Pxp06dolmzZjzzzDOEh4fTt29f3nrrLdavX2/npDZgiEwxZ84cw9/f/6HHWSwWIygoyPjkk09S7rtx44bh4+NjfPfdd3ZM6J6OHDliAMaePXtS7lu7dq1hMpmM8+fP3/dx9erVM/r06ZMJCd1L9erVjZ49e6b8Ozk52ShQoIAxbty4ex7funVro1mzZnfdFxwcbHTr1s2uOd1Zes9RWv/2CdsCjBUrVjzwmPfff98oV67cXfe1adPGaNSokR2T2Ya0vDiYU6dOERERQUhISMp9/v7+BAcHExoaqjGZawoNDSUgIICqVaum3BcSEoLZbGbXrl0PfOyCBQvInTs3Tz75JIMGDeLWrVv2juvSEhISCAsLu+tn32w2ExISct+f/dDQ0LuOB2jUqJH8rthJRs4RwM2bN3n88ccpVKgQzZs35/Dhw5kRVzyEM//+uNzCjM4uIiICgHz58t11f758+VK+JmwnIiKCvHnz3nWfp6cngYGBD/z/fvXVV3n88ccpUKAABw4c4IMPPuCPP/5g+fLl9o7ssq5cuUJycvI9f/aPHTt2z8dERETI70omysg5KlWqFLNnz6Z8+fJERUUxceJEatWqxeHDh51iEV1Xdr/fn+joaG7fvk2WLFk0JXs4aXnJgIEDB/6nA9q/b/f7RRaZw97nqGvXrjRq1IinnnqK9u3bM3/+fFasWMHJkydt+F0I4fxq1qxJhw4dqFixIvXq1WP58uXkyZOHr776Snc04cSk5SUD3nvvPTp27PjAY4oVK5ah5w4KCgIgMjKS/Pnzp9wfGRlJxYoVM/Sc7iit5ygoKOg/HQ2TkpK4du1ayrlIi+DgYABOnDhB8eLF051XQO7cufHw8CAyMvKu+yMjI+97LoKCgtJ1vHg0GTlH/+bl5UWlSpU4ceKEPSKKdLjf74+fn59Dt7qAFC8ZkidPHvLkyWOX5y5atChBQUFs3LgxpViJjo5m165d6Rqx5O7Seo5q1qzJjRs3CAsLo0qVKgBs2rQJi8WSUpCkRXh4OMBdBadIH29vb6pUqcLGjRtp0aIFABaLhY0bN9KrV697PqZmzZps3LiRvn37pty3YcMGatasmQmJ3U9GztG/JScnc/DgQZo2bWrHpCItatas+Z+pBZzm90d3j2FX9/fffxv79u0zRo4caWTPnt3Yt2+fsW/fPiMmJiblmFKlShnLly9P+ff48eONgIAAY+XKlcaBAweM5s2bG0WLFjVu376t41tweY0bNzYqVapk7Nq1y/jtt9+MJ554wmjXrl3K18+dO2eUKlXK2LVrl2EYhnHixAnjo48+Mn7//Xfj1KlTxsqVK41ixYoZdevW1fUtuIxFixYZPj4+xty5c40jR44YXbt2NQICAoyIiAjDMAzj9ddfNwYOHJhy/Pbt2w1PT09j4sSJxtGjR43hw4cbXl5exsGDB3V9Cy4vvedo5MiRxvr1642TJ08aYWFhRtu2bQ1fX1/j8OHDur4FlxUTE5PyHgMYkydPNvbt22f8/fffhmEYxsCBA43XX3895fi//vrLyJo1qzFgwADj6NGjxrRp0wwPDw9j3bp1ur6FNJPixc7eeOMNA/jPbfPmzSnHAMacOXNS/m2xWIyhQ4ca+fLlM3x8fIwGDRoYf/zxR+aHdxNXr1412rVrZ2TPnt3w8/MzOnXqdFdxeerUqbvO2ZkzZ4y6desagYGBho+Pj1GiRAljwIABRlRUlKbvwLVMnTrVKFy4sOHt7W1Ur17d2LlzZ8rX6tWrZ7zxxht3Hf/9998bJUuWNLy9vY1y5coZq1evzuTE7ic956hv374px+bLl89o2rSpsXfvXg2pXd/mzZvv+X5jPR9vvPGGUa9evf88pmLFioa3t7dRrFixu96LHJnJMAxDS5OPEEIIIUQGyGgjIYQQQjgVKV6EEEII4VSkeBFCCCGEU5HiRQghhBBORYoXIYQQQjgVKV6EEEII4VSkeBFCCCGEU5HiRQghhBBORYoXIYQQQjgVKV6EEEII4VSkeBFCCCGEU5HiRQghhBBO5f/ASvDm2ZRttgAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# initial positions\n", "ip1 = [0.97000436, -0.24308753]\n", "ip2 = [-ip1[0], -ip1[1]]\n", "ip3 = [0, 0]\n", "# initial velocities\n", "iv3 = [-0.93240737, -0.86473146]\n", "iv2 = [-iv3[0]/2, -iv3[1]/2]\n", "iv1 = iv2\n", "# input for initial righthandside vector\n", "initz = [ip1[0], iv1[0], ip1[1], iv1[1], \\\n", " ip2[0], iv2[0], ip2[1], iv2[1], \\\n", " ip3[0], iv3[0], ip3[1], iv3[1]]\n", "# solving the IVP\n", "period = 2*sp.pi/3\n", "dim = 1000\n", "tspan = np.linspace(0, period, dim+1)\n", "path = odeint(fun, initz, tspan)\n", "# extracing the trajectories\n", "(x1p, y1p) = (path[:, 0], path[:, 2])\n", "(x2p, y2p) = (path[:, 4], path[:, 6])\n", "(x3p, y3p) = (path[:, 8], path[:, 10])\n", "# plotting the trajectories\n", "plt.figure()\n", "plt.plot(x1p, y1p, 'r', x2p, y2p, 'g', x3p, y3p, 'b')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "caf6f102", "metadata": {}, "source": [ "### 2.1 defining an animation" ] }, { "cell_type": "markdown", "id": "d5f6aba8", "metadata": {}, "source": [ "Runs an animation to plots the trajectories of 3 equal masses\n", "forming a figure 8.To run the animation in the notebook, the first line in the code cell below needed to be added." ] }, { "cell_type": "markdown", "id": "86736720-a79e-4ffe-b0fb-48e9fc37f075", "metadata": {}, "source": [ "Runs an animation to plots the trajectories of 3 equal masses\n", "forming a figure 8." ] }, { "cell_type": "code", "execution_count": 8, "id": "ea1708b3-0f5a-46e2-8160-9f30a0376b2e", "metadata": {}, "outputs": [], "source": [ "# initial positions\n", "ip1 = [0.97000436, -0.24308753]\n", "ip2 = [-ip1[0], -ip1[1]]\n", "ip3 = [0, 0]\n", "# initial velocities\n", "iv3 = [-0.93240737, -0.86473146]\n", "iv2 = [-iv3[0]/2, -iv3[1]/2]\n", "iv1 = iv2\n", "# input for initial righthandside vector\n", "initz = [ip1[0], iv1[0], ip1[1], iv1[1], \\\n", " ip2[0], iv2[0], ip2[1], iv2[1], \\\n", " ip3[0], iv3[0], ip3[1], iv3[1]]\n", "# solving the IVP\n", "period = 2*np.pi/3\n", "dim = 1000\n", "tspan = np.linspace(0, period, dim+1)\n", "path = odeint(fun, initz, tspan)" ] }, { "cell_type": "code", "execution_count": 9, "id": "8ceb1a15-b3c1-4ae7-b613-459c1449b029", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1001" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(path[:,0])" ] }, { "cell_type": "code", "execution_count": 10, "id": "f3be6e80-2e52-44a0-b58c-4456cf240e3b", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "MovieWriter ffmpeg unavailable; using Pillow instead.\n" ] }, { "data": { "image/png": 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LkrxH58ILL4ypU6fGvHnzYt26dfHEE0/E/Pnz49prry1+4uqFF16IMWPGxLp16yLijci58sorY//+/fG9730vCoVC5PP5yOfz0dHRUYoxAYDE9egVnZ647777Yv78+TFlypQoLy+PD33oQ/H1r3+9+OevvfZabNu2LQ4cOBARERs2bCh+Iuv888/vcq0dO3bEyJEjSzUqAJCoknyPTl/yPToAcOI5ob5HBwCgPxA6AECyhA4AkCyhAwAkS+gAAMkSOgBAsoQOAJAsoQMAJEvoAADJEjoAQLKEDgCQLKEDACRL6AAAyRI6AECyhA4AkCyhAwAkS+gAAMkSOgBAsoQOAJAsoQMAJEvoAADJEjoAQLKEDgCQLKEDACRL6AAAyRI6AECyhA4AkCyhAwAkS+gAAMkSOgBAsoQOAJAsoQMAJEvoAADJEjoAQLKEDgCQLKEDACRL6AAAyRI6AECyhA4AkCyhAwAkS+gAAMkSOgBAsoQOAJAsoQMAJEvoAADJEjoAQLKEDgCQLKEDACRL6AAAyRI6AECyhA4AkCyhAwAkS+gAAMkSOgBAsoQOAJAsoQMAJEvoAADJEjoAQLKEDgCQLKEDACRL6AAAyRI6AECyhA4AkKyShc7evXtj1qxZUVlZGdXV1TF37tx49dVXu3VulmXxgQ98IMrKyuLhhx8u1YgAQOJKFjqzZs2KzZs3x6pVq+KRRx6Jxx57LG688cZunbts2bIoKysr1WgAwEliYCkuumXLlli5cmU8+eSTMXHixIiI+MY3vhHTpk2LpUuXxogRI4547qZNm+KrX/1qPPXUUzF8+PBSjAcAnCRK8opOa2trVFdXFyMnIqKxsTHKy8tj7dq1RzzvwIED8bGPfSyWL18etbW13bqvgwcPRqFQ6HIDAIgoUejk8/kYNmxYl2MDBw6MwYMHRz6fP+J5//qv/xqTJ0+Oa665ptv31dzcHFVVVcVbXV3dMc8NAKSlR6GzcOHCKCsrO+pt69atxzTIL37xi1i9enUsW7asR+ctWrQo2tvbi7ddu3Yd0/0DAOnp0Xt0br311rjhhhuOumbUqFFRW1sbu3fv7nL89ddfj7179x7xn6RWr14d27dvj+rq6i7HP/ShD8Vll10Wa9asOex5uVwucrlcd38FAOAk0qPQGTp0aAwdOvRt1zU0NMQrr7wS69evjwkTJkTEGyHT2dkZ9fX1hz1n4cKF8YlPfKLLsbFjx8bdd98dV199dU/GBACIiBJ96urCCy+MqVOnxrx582LFihXx2muvxfz58+Paa68tfuLqhRdeiClTpsQPf/jDmDRpUtTW1h721Z6zzz47zj333FKMCQAkrmTfo3PffffFmDFjYsqUKTFt2rR473vfG9/+9reLf/7aa6/Ftm3b4sCBA6UaAQA4yZVlWZb19RC9qVAoRFVVVbS3t0dlZWVfjwMAdEOpnr/9v64AgGQJHQAgWUIHAEiW0AEAkiV0AIBkCR0AIFlCBwBIltABAJIldACAZAkdACBZQgcASJbQAQCSJXQAgGQJHQAgWUIHAEiW0AEAkiV0AIBkCR0AIFlCBwBIltABAJIldACAZAkdACBZQgcASJbQAQCSJXQAgGQJHQAgWUIHAEiW0AEAkiV0AIBkDezrAXpblmUREVEoFPp4EgCgu9583n7zeby3JBc6L7/8ckRE1NXV9fEkAEBPvfzyy1FVVdVr10sudAYPHhwRETt37uzVjToZFQqFqKuri127dkVlZWVfj3NCs5e9wz72HnvZe+xl72hvb4+zzz67+DzeW5ILnfLyN952VFVV5QHXSyorK+1lL7GXvcM+9h572XvsZe9483m8167Xq1cDAOhHhA4AkKzkQieXy8WSJUsil8v19SgnPHvZe+xl77CPvcde9h572TtKtY9lWW9/jgsAoJ9I7hUdAIA3CR0AIFlCBwBIltABAJKVROj8+7//e0yePDlOO+20qK6u7tY5N9xwQ5SVlXW5TZ06tbSDngCOZS+zLIvFixfH8OHD49RTT43Gxsb44x//WNpB+7m9e/fGrFmzorKyMqqrq2Pu3Lnx6quvHvWcK6644i2PyX/+538+ThP3H8uXL4+RI0dGRUVF1NfXx7p16466/sEHH4wxY8ZERUVFjB07Nn75y18ep0n7v57s5b333vuWx19FRcVxnLZ/euyxx+Lqq6+OESNGRFlZWTz88MNve86aNWvi0ksvjVwuF+eff37ce++9JZ/zRNDTvVyzZs1bHpNlZWWRz+d7dL9JhM6hQ4fiIx/5SHzqU5/q0XlTp06N//7v/y7efvKTn5RowhPHsezlXXfdFV//+tdjxYoVsXbt2viHf/iHaGpqir/+9a8lnLR/mzVrVmzevDlWrVoVjzzySDz22GNx4403vu158+bN6/KYvOuuu47DtP3HAw88EAsWLIglS5bEhg0bYty4cdHU1BS7d+8+7Prf/va3MXPmzJg7d25s3Lgxpk+fHtOnT49nnnnmOE/e//R0LyPe+Gbf//34e+65547jxP3T/v37Y9y4cbF8+fJurd+xY0dcddVV8U//9E+xadOmuOWWW+ITn/hE/OpXvyrxpP1fT/fyTdu2bevyuBw2bFjP7jhLyA9+8IOsqqqqW2tnz56dXXPNNSWd50TW3b3s7OzMamtrs6985SvFY6+88kqWy+Wyn/zkJyWcsP/6wx/+kEVE9uSTTxaP/dd//VdWVlaWvfDCC0c87/LLL89uvvnm4zBh/zVp0qTsX/7lX4o/d3R0ZCNGjMiam5sPu/6jH/1odtVVV3U5Vl9fn33yk58s6Zwngp7uZU/+/jxZRUT20EMPHXXNv/3bv2Xvete7uhybMWNG1tTUVMLJTjzd2ctHH300i4jsf/7nf/6u+0riFZ1jtWbNmhg2bFiMHj06PvWpTxX/z+d0344dOyKfz0djY2PxWFVVVdTX10dra2sfTtZ3Wltbo7q6OiZOnFg81tjYGOXl5bF27dqjnnvffffFkCFD4uKLL45FixbFgQMHSj1uv3Ho0KFYv359l8dSeXl5NDY2HvGx1Nra2mV9RERTU9NJ+9h707HsZUTEq6++Guecc07U1dXFNddcE5s3bz4e4ybFY7L3jR8/PoYPHx7vf//744knnujx+cn9Tz27a+rUqfHBD34wzj333Ni+fXt8/vOfjw984APR2toaAwYM6OvxThhv/ltpTU1Nl+M1NTU9/nfUVOTz+be8tDpw4MAYPHjwUffkYx/7WJxzzjkxYsSI+P3vfx+f+9znYtu2bfGzn/2s1CP3C3v27ImOjo7DPpa2bt162HPy+bzH3mEcy16OHj06vv/978cll1wS7e3tsXTp0pg8eXJs3rw53vGOdxyPsZNwpMdkoVCIv/zlL3Hqqaf20WQnnuHDh8eKFSti4sSJcfDgwfjud78bV1xxRaxduzYuvfTSbl+n34bOwoUL48477zzqmi1btsSYMWOO6frXXntt8b/Hjh0bl1xySZx33nmxZs2amDJlyjFds78q9V6eLLq7j8fqf7+HZ+zYsTF8+PCYMmVKbN++Pc4777xjvi50R0NDQzQ0NBR/njx5clx44YXxrW99K26//fY+nIyT1ejRo2P06NHFnydPnhzbt2+Pu+++O370ox91+zr9NnRuvfXWuOGGG466ZtSoUb12f6NGjYohQ4bEs88+m1zolHIva2trIyKira0thg8fXjze1tYW48ePP6Zr9lfd3cfa2tq3vOHz9ddfj7179xb3qzvq6+sjIuLZZ589KUJnyJAhMWDAgGhra+tyvK2t7Yj7Vltb26P1J4tj2cv/65RTTol3v/vd8eyzz5ZixGQd6TFZWVnp1ZxeMGnSpHj88cd7dE6/DZ2hQ4fG0KFDj9v9Pf/88/Hyyy93ebJORSn38txzz43a2tpoaWkphk2hUIi1a9f2+FNw/V1397GhoSFeeeWVWL9+fUyYMCEiIlavXh2dnZ3FeOmOTZs2RUQk+Zg8nEGDBsWECROipaUlpk+fHhERnZ2d0dLSEvPnzz/sOQ0NDdHS0hK33HJL8diqVau6vDJxMjqWvfy/Ojo64umnn45p06aVcNL0NDQ0vOUrDjwme8+mTZt6/nfi3/VW5n7iueeeyzZu3Jjddttt2emnn55t3Lgx27hxY7Zv377imtGjR2c/+9nPsizLsn379mWf+cxnstbW1mzHjh3Zb37zm+zSSy/NLrjgguyvf/1rX/0a/UJP9zLLsuyOO+7Iqqurs5///OfZ73//++yaa67Jzj333Owvf/lLX/wK/cLUqVOzd7/73dnatWuzxx9/PLvggguymTNnFv/8+eefz0aPHp2tXbs2y7Ise/bZZ7Mvf/nL2VNPPZXt2LEj+/nPf56NGjUqe9/73tdXv0KfuP/++7NcLpfde++92R/+8IfsxhtvzKqrq7N8Pp9lWZZdd9112cKFC4vrn3jiiWzgwIHZ0qVLsy1btmRLlizJTjnllOzpp5/uq1+h3+jpXt52223Zr371q2z79u3Z+vXrs2uvvTarqKjINm/e3Fe/Qr+wb9++4t+DEZF97WtfyzZu3Jg999xzWZZl2cKFC7PrrruuuP5Pf/pTdtppp2Wf/exnsy1btmTLly/PBgwYkK1cubKvfoV+o6d7effdd2cPP/xw9sc//jF7+umns5tvvjkrLy/PfvOb3/TofpMIndmzZ2cR8Zbbo48+WlwTEdkPfvCDLMuy7MCBA9mVV16ZDR06NDvllFOyc845J5s3b17xL4CTWU/3Msve+Ij5F7/4xaympibL5XLZlClTsm3bth3/4fuRl19+OZs5c2Z2+umnZ5WVldmcOXO6xOKOHTu67OvOnTuz973vfdngwYOzXC6XnX/++dlnP/vZrL29vY9+g77zjW98Izv77LOzQYMGZZMmTcp+97vfFf/s8ssvz2bPnt1l/U9/+tPsne98ZzZo0KDsXe96V/af//mfx3ni/qsne3nLLbcU19bU1GTTpk3LNmzY0AdT9y9vfsT5/97e3LvZs2dnl19++VvOGT9+fDZo0KBs1KhRXf6+PJn1dC/vvPPO7LzzzssqKiqywYMHZ1dccUW2evXqHt9vWZZl2d/1OhIAQD91Un+PDgCQNqEDACRL6AAAyRI6AECyhA4AkCyhAwAkS+gAAMkSOgBAsoQOAJAsoQMAJEvoAADJEjoAQLL+H3ZZdzPWUz0DAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "from matplotlib import animation\n", "\n", "def animate(frame):\n", " \"\"\"\n", " Makes a plot of the sine function\n", " for the given frequence in freq.\n", " \"\"\"\n", " dim = len(path[:,0])\n", " showframe = frame*dim//35\n", " (x1p, x2p, x3p) = (path[:, 0], path[:, 4], path[:, 8])\n", " (y1p, y2p, y3p) = (path[:, 2], path[:, 6], path[:, 10])\n", " plt.clf()\n", " (s1x, s1y) = (x1p[1:showframe], y1p[1:showframe])\n", " (s2x, s2y) = (x2p[1:showframe], y2p[1:showframe])\n", " (s3x, s3y) = (x3p[1:showframe], y3p[1:showframe])\n", " axs = plt.axes(xlim=(-1.5, 1.5), ylim=(-0.5, 0.5))\n", " plt.plot(s1x, s1y, 'r', s2x, s2y, 'g', s3x, s3y, 'b')\n", "\n", "fig = plt.figure()\n", "anim = animation.FuncAnimation(fig, animate, frames=35)\n", "# anim.save('animatedsine.gif', writer='imagemagick')\n", "anim.save('animatedeight.gif')\n", "# plt.show()" ] }, { "cell_type": "markdown", "id": "c9055311", "metadata": {}, "source": [ "# 3. The Tractrix Problem" ] }, { "cell_type": "markdown", "id": "93fb564f", "metadata": {}, "source": [ "A tractor is connected to a trailer by a rigid bar of unit length.\n", "The tractor moves in a circle. The path of the trailer is the solution\n", "of a system of ordinary differential equations." ] }, { "cell_type": "code", "execution_count": 11, "id": "d13474ac", "metadata": {}, "outputs": [], "source": [ "import scipy as sp\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 12, "id": "b26e2666", "metadata": {}, "outputs": [], "source": [ "def tractor(time):\n", " \"\"\"\n", " Returns a 4-tuple xp, yp, xv, yv\n", " the coordinates xp, yp of the position and\n", " the components xv, yv of the velocity vector\n", " for the tractor at the given time.\n", " \"\"\"\n", " xpos = np.cos(time)\n", " ypos = np.sin(time)\n", " xvel = -np.sin(time)\n", " yvel = np.cos(time)\n", " return xpos, ypos, xvel, yvel" ] }, { "cell_type": "code", "execution_count": 13, "id": "be35bc9e", "metadata": {}, "outputs": [], "source": [ "def trailer(yval, time):\n", " \"\"\"\n", " Defines the right hand side of\n", " the system for the trailer.\n", " \"\"\"\n", " rhs = np.array([0, 0], float)\n", " x1p, x2p, x1v, x2v = tractor(time)\n", " rhs[0] = yval[0] - x1p\n", " rhs[1] = yval[1] - x2p\n", " rhs = rhs/np.linalg.norm(rhs)\n", " vtu = x1v*rhs[0] + x2v*rhs[1]\n", " rhs = vtu*rhs\n", " return rhs" ] }, { "cell_type": "markdown", "id": "f50c16dc", "metadata": {}, "source": [ "We can now define the setup for the system\n", " for the trailer and solve it." ] }, { "cell_type": "code", "execution_count": 14, "id": "f2cab46c", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "endtime = 20\n", "dim = 100\n", "tspan = np.linspace(0, endtime, dim+1)\n", "initc = np.array([2, 0])\n", "path = odeint(trailer, initc, tspan)\n", "xtrail = path[:, 0]\n", "ytrail = path[:, 1]\n", "xtrac, ytrac, x1v, x2v = tractor(tspan)\n", "plt.figure()\n", "plt.plot(xtrac, ytrac, 'r', xtrail, ytrail, 'g')\n", "for i in range(0, dim, 6):\n", " plt.plot(np.array([xtrac[i], xtrail[i]]), \\\n", " np.array([ytrac[i], ytrail[i]]), 'b')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "6c2dd5b0", "metadata": {}, "outputs": [], "source": [] } ], "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": "3.10.10" } }, "nbformat": 4, "nbformat_minor": 5 }