{ "cells": [ { "cell_type": "code", "execution_count": 4, "id": "bec17a8e", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import quad" ] }, { "cell_type": "markdown", "id": "83411453-6cde-4a2f-ad1c-833ac21554d2", "metadata": {}, "source": [ "

Use scipy.integrate.quad to evaluate the following definite integrals (which can also be expressed in closed form over the range given but are awkward).

\n", "

\n", "$$\n", "\\int_0^1 \\frac{x^4(1-x)^4}{1+x^2}\\;\\mathrm{d}x.\n", "$$\n", "(Compare with $22/7 - \\pi$).

\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "170e08b6-75ee-4bd5-92f9-d6b0095a7fdc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0.0012644892673496185, 1.1126990906558069e-14)\n", "0.0012644892673496777\n" ] } ], "source": [ "f1 = lambda x: x**4 * (1 - x)**4/(1 + x**2)\n", "print(quad(f1, 0, 1))\n", "print(22/7 - np.pi)" ] }, { "cell_type": "markdown", "id": "c7177654-38f9-41ce-8bde-8e58202cfbbc", "metadata": {}, "source": [ "

The following integral appears in the Debye theory of the heat capacity of crystals at low temperature\n", "$$\n", "\\int_0^\\infty \\frac{x^3}{e^x-1}\\;\\mathrm{d}x\n", "$$\n", "(Compare with $\\pi^4/15$).

\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "189c630d-d033-450e-ac6f-41f697d4abef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(6.49393940226683, 2.628470027132503e-09)\n", "6.493939402266828\n" ] } ], "source": [ "f2 = lambda x: x**3/(np.exp(x) - 1)\n", "\n", "print(quad(f2, 0, np.inf))\n", "print(np.pi**4/15)" ] }, { "cell_type": "markdown", "id": "1b97ab5b-9482-4cf6-b117-add283248804", "metadata": {}, "source": [ "

The integral sometimes known as the Sophomore's dream:\n", "$$\n", "\\int_0^1 x^{-x}\\;\\mathrm{d}x\n", "$$\n", "(Compare the value you obtain from the summation $\\sum_{n=1}^\\infty n^{-n}$).

" ] }, { "cell_type": "code", "execution_count": 7, "id": "d9615549-1562-4536-ab28-e4e556e025d3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1.2912859970626633, 3.668398917966442e-11)\n", "1.2912859970626636\n" ] } ], "source": [ "f3 = lambda x: x**-x\n", "\n", "print(quad(f3, 0, 1))\n", "\n", "n, I, TOL = 0, 0, 1.e-16\n", "while True:\n", " Iold = I\n", " n += 1\n", " I += n**-n\n", " if I-Iold < TOL:\n", " break\n", "\n", "print(I)" ] }, { "cell_type": "markdown", "id": "fd89ea5d-e024-4718-a7ae-6cd2d479f961", "metadata": {}, "source": [ "

\n", "$$\n", "\\int_0^1 [\\ln(1/x)]^p\\;\\mathrm{d}x\n", "$$\n", "(Compare with $p!$ for integer $0 \\le p \\le 10$).

\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "558a4a0e-653e-4aef-ace3-6dff92535b58", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0 1.0\n", "0.9999999999999999 1.0\n", "1.9999999999999978 2.0\n", "5.999999999999848 6.0\n", "23.99999999999799 24.0\n", "120.0000000000472 120.0\n", "719.9999999995489 720.0\n", "5040.000000415095 5040.0\n", "40320.000004345224 40320.0\n", "362880.0000102735 362880.0\n" ] } ], "source": [ "from scipy.special import factorial\n", "f4 = lambda x, p: np.log(1/x)**p\n", "for p in range(10):\n", " print(quad(f4, 0, 1, args=(p,))[0], factorial(p))" ] }, { "cell_type": "markdown", "id": "0efe3dff-4798-4882-bab0-944416f2a174", "metadata": {}, "source": [ "

\n", "$$\n", "\\int_0^{2\\pi} e^{z\\cos\\theta}\\;\\mathrm{d}\\theta\n", "$$\n", "(Compare with $2\\pi I_0(z)$, where $I_0(z)$ is a modified Bessel function of the first kind, for $0 \\le z \\le 2$).\n", "Here we find the maximum deviation from the Bessel function $I_0(z)$\n", " for 100 values of $z$\n", " between 0 and 2:\n", "

" ] }, { "cell_type": "code", "execution_count": 9, "id": "2abfd3c9-3455-4a9e-9942-abc4a03da661", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.4796610037801656e-12\n" ] } ], "source": [ "from scipy.special import i0\n", "z = np.linspace(0,2,100)\n", "y1 = i0(z)\n", "f5 = lambda theta, z: np.exp(z*np.cos(theta))\n", "y2 = np.array([quad(f5, 0, 2*np.pi, args=(zz,))[0] for zz in z])\n", "y2 /= 2 * np.pi\n", "print(np.max(abs(y2-y1)))" ] }, { "cell_type": "markdown", "id": "77ca028b-d060-4a6d-b253-e03bf7e4e677", "metadata": {}, "source": [ "\n", "---\n", "\n", "

The trajectory of a projectile in the $xz$-plane launched from the origin at an angle $\\theta_0$ from the (horizontal) $x$-axis with speed $v_0 = 25\\;\\mathrm{m\\,s^{-1}}$ is\n", "$$\n", "z = x\\tan\\theta_0 - \\frac{g}{2v_0^2\\cos^2\\theta_0}x^2.\n", "$$

\n", "\n", "During its flight, the projectile is subject to a constant acceleration $\\ddot{\\boldsymbol{r}} = -g\\hat{\\boldsymbol{k}}$. Integrating,\n", "$$\n", "\\begin{align*}\n", "\\boldsymbol{v} = \\dot{\\boldsymbol{r}} = -gt\\hat{\\boldsymbol{k}} + \\boldsymbol{v_0}\\\\\n", "\\boldsymbol{r} = \\textstyle -\\frac{1}{2}gt^2\\hat{\\boldsymbol{k}} + \\boldsymbol{v_0}t + \\boldsymbol{r_0}\n", "\\end{align*}\n", "$$\n", "where $\\boldsymbol{v_0} = (v_0\\cos\\theta)\\hat{\\boldsymbol{i}} + v_0(\\sin\\theta)\\hat{\\boldsymbol{k}}$ and $\\boldsymbol{r_0}=0$ (the projectile starts at the origin).\n", "\n", "Therefore, $x = v_0t\\cos\\theta$ and $z = v_0t\\sin\\theta - \\frac{1}{2}gt^2$. Eliminating $t$ from these expressions gives the formula for $z$ above.\n", "\n", "\n", "

If the projectile passes through the point $(5, 15)$, use Brent's method to determine the possible values of $\\theta_0$.

\n", "\n", "

In general, there are two (physically distinct) possible angles $\\theta_0$ corresponding to the projectile passing through the specified point, $(x_1, y_1) = (5,15)$, on the way up or on the way down. These values are the roots in $(0, \\pi/2)$ of the function\n", "$$\n", "f(\\theta_0; x_1, z_1) = x_1\\tan\\theta_0 - \\frac{g x_1^2}{2v_0^2\\cos^2\\theta_0} - z_1\n", "$$\n", "After bracketing the roots with a rough plot of $f(\\theta_0)$, we can use brentq:

" ] }, { "cell_type": "code", "execution_count": 28, "id": "58a4582d-ec35-4964-9a2d-2eb83c4fa196", "metadata": {}, "outputs": [ { "data": { "image/png": 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RFgPD6uPJdioE1jPCLyREBsAAQ4ZzO1Y//sVYVOHAWW7qSTVXpNHit/M38X9Hk3DuRg56BNXFKz0D0SvY26KnI9exs8agsAYYFNYARRotDl3JwC9nUvHY5wcR1tAVo9r7YmBofTjYcjIFSYfl/h9LhqXOAvJvAXWbG+8aDcP1i9kVZAJOnsa7Dpmdq+n5WH8sCRtPp8DTyRajOzTGivHt4OZo4NlyZsDeRolewd7oFeyN7IISbPn7Bpbvv4r3t17A4DYNMCrCFy0buopdJhEDDBlIWhzg0hBwcDPeNRzcAc8AfTdSs37Guw6ZhVKtDjsv3ML/HU3CqaRs9G/hg2Vjw9HB34PjO6rI3ckWEzv7Y8Kjfvg7+Q42HE/Gk98cQUDdOniuiz8GhtaHtVISC7qTBWKAIcNIiwXqBRv/OqoI/c7UDDBUiSKNFptOp2DZX1cBAGM7NMaXo9vAsw6n39eUQqFAW193tPV1x5zHQ7DpVAo+/v0SPvnjEiZ1aYKR4Y3YvUQmxwBDhpEWB9QLMf51GoYDl3YY/zokOwXFpVh3LAnfHkiAu6Mt3ugbxBYCI6hjZ43xnfwwpoMvomNuYtlfCfh092U808kP4x5pzG45MhkGGDKMtFig7XjjX0fVDvhzPqDTGW6zSJK17IISrDp8HasOX4eflxMWDg1Fr+b1jLYCLulZK60wuHVDPNGqAfZfzsCyfVex7K+rGBXhi8ndm6Ces/TXyyF5Y4Ch2hME03UhebcESouBzCtA3WbGvx5JVn5xKZbvT8B3BxLQ2tcNX49pi0cCPDm+xcQUCgW6NauLbs3q4mzyHXy59wq6f7wPz3X2x6SuTSxiSjqJgwGGai/vJlCUC9QNMv61lDZA/db6gbwMMBapVKvDjyeS8enuy2js6YjVE9ujnZ+H2GURgFaN3PDtuHY4lZiN//12EWuPJeGVHoEY09EXdtYcI0OGxQBDtZcWq1/q38bBNNdTtdMP5G092jTXI0kQBAG7Ym/jw50XAQFYMKQl+rXwZouLBIU3dseGFzpi76U0fLTzElYeuobX+jTD4NYNoWTXHhkIAwzVXloc4G2CAbxlGoYDhz413fVIdH8nZWPRjotIyMjHtN7NMCqiEWw4OFfSFAoFejb3Rrdm9fDL3zew+I94LN+fgHcfD0GnAC+xyyMzwABDtXc71jQzkMqo2gG3LwAlasDW0XTXJZPLzC/Gwh1x2Hn+Fp7r7I+VEyIsesVcOVJaKTA8XIVBrepj9eHrmLT6JPqEeGP2wGAO9KVa4a8wVHumGsBbxrUR4OAB3DxrumuSSel0An48noSei/+CuliLPa93w2t9gxheZMzOWonnuwZg9+vdoNEK6LX4L6w+fB1anSB2aSRT/DSg2tFpgfRLpm2BUSj+3dix8SOmuy6ZRPztPLy9JQapd4oQ9WQr9Ar2FrskMqD6rg74akxb7I9Px7u/nsfPp5KxYEgoWjdyE7s0khm2wFDtZF8HBK1+EK8pqcL1A3nJbBSWaPG/nRfxxJcH0dbXHbte68rwYsa6NquLna92Rd8QHzy1/Chmb4lBjlojdlkkIwwwVDtpcYBXkH56syk1bAfcOGXaa5LRHLicjr6f/oVjCZnY8tKjmPVYMBxt2UBs7uxtlJjaqyl2vtoFN7IL0ffTv7DvUprYZZFM8BOCasfU41/KNGgD5KQAebcAZx/TX58MorBEi0W/xWHz6Rt4a0BzjG7vyxV0LVBjTyesmhCBn04m45V1f+OJ1g0w+7FgjnmiB2ILDNWOWAHG3kV/XXYjydbZ5DsY+PkBxKbmYsfULhjbsTHDiwVTKBSIjPDFb9O6ICE9HwM+249jCZlil0USxgBDtWOqTRzvp2G4fiAvyYpGq8Onu+MRufwIRrRTYcMLj8DXk9PhSa+RhyPWPdcREx/1x4RVJ7BgeyyKNFqxyyIJYoChmivbk0iMFhjg3xV5STaupudjxNeHsSPmJja92AkvdQ/kyqx0DysrBSY86o9tUzrjZGI2Bn1xEDEpOWKXRRLDAEM1l3kFsLbXr8sihobtgBun9VO5SdIEQcDao4l4/IuDiPDzwNZXOqNFA1exyyKJC6hbBxsnP4IhrRvgyW+OYPXh6xAErhtDehwhRTV3+5/xL1Yi5eC6zQFtMZCTDLj7iVMDPVRBcSlmbY7B0YRMrBjXDp0CuYw8VZ210gqv9GyKDk08MWXd3zh+LQuLhofChbtcWzy2wFDNiTWAt4zSGnDzBbISxKuBHujy7TwM/uoQ0vOKsX1qZ4YXqrEIPw9ET+2MvOJSPP7FQZy/wS4lS8cAQzUn5gDeMh5NgKxr4tZA9/XrmRsY8tUh9GvhjTXPtue+N1RrnnXssOqZCDzZrhFGLjuCNUcT2aVkwdiFRDWXFgt0nCxuDe7+QDYDjJQUl2oxf3sstp29iS9Gt0HP5lxNlwzHykqBl3sEIryxO6au/xvHEjLx4fAwrhljgdgCQzVTnA/cSZRAC4w/W2AkJDlLjZHLjuBcSg62T+nM8EJG07GJJ6KndsEdtQZPfHkQ1zIKxC6JTIwBhmom/SLg6AXUqSduHexCkowjVzPx+JcHEaZyxc+TH0EjD67tQsZV19kOqye2R59gbwz+8iAOXE4XuyQyIba5Uc2IPYC3TFkXkiDod6kmUWw4kYS5W2Px3uMhGNXeV+xyyIIorRSY9Vgwmno74/kfTmFm/yCM7+QHBT8PzB4DDNWMFAbwAoB7Y0CjBvJvc08kEWh1Aj78LQ4/n0rBymci8EiAp9glkYUaEa6Cv5cTXlhzCpdu5+H9J1rC1pqdDOaM/3WpZqTSAmPjALg0ZDeSCPKLS/H8Dyfx58U0/PLSowwvJLrwxu7Y+sqjOJeSg7HfHUNWQYnYJZERMcBQzUilBQbQdyNxLRiTSslWY8TXh1Gi1WHzS4/Cz8tJ7JKIAAAN3Bzw8+RH4Olkiye+PIiLt3LFLomMhAGGqq8gU99lI4UWGADw8ONUahM6lZiFIV8dQoSfB75/JgKuDlwRlaTF0dYaX41ui+FtVRj59REcupIhdklkBAwwVH1psfr9j+xdxK5EjzORTGbn+Zt4+rvjmNqrKeYPaQlrJT9CSJqsrBSY3qcZ3nuiBZ5bfRJbz6aKXRIZGAfxUvWlxUmn9QXQdyHFbRe7CrO37lgSFkTH4vNRbdA7hOu7kDyMCFfBs44tXvm/00jPK8aznf3FLokMRLRfnxITE9GvXz84OzujTZs22Lt3b4Xn582bB4VCUf7nxIkTIlVK95DKAN4yHlyN15gEQcDney7jw9/isHpie4YXkp0eQfXwf5M64qu9V7BoRxx0Om4/YA5ECTCCIGDSpEno3bs3li5dCkEQMGjQIFy9ehUAUFRUhNOnT2PJkiVYsmQJli9fjoiICDFKpfuR0gBeQN8CU5it/0MGpdMJeG/rBfzfsUT8NPkRRPh5iF0SUY20buSGTS92wo7zN/H6z2dRUqoTuySqJYUgwk5YMTExSEtLQ69evQAAaWlpaNKkCRYuXIhp06Zh2bJlCAwMRO/evR94ntzcXLi6uiInJwcuLhIZj2HuBAH4sDHwzDagfiuxq/nX//yBsZuAhm3FrsRsFJdq8fpPZxGbmovVE9tzZV0yC2l5RZjw/Ql4ONni67Hh3ENJJIb4/halBSYoKKg8vABAvXr1EBISAjs7O+h0OkRFRWHIkCEYPnw4Ll26JEaJVJncG0BJHuAVJHYlFbEbyaDyi0vx7KqTSMpSc1sAMiv1nO3x4/MdoRMEPLX8KNeKkTFRAoytre09j2VnZ2PQoEEoLCzEwoULMWPGDJw4cQLh4eHYs2fPA88XHBwMlUoFlUqFqKgoY5VNgL77yCMAsLEXu5KKPJpwLRgDySoowehvjwIA1k3qCM86diJXRGRYzvY2+P6Z9mjk4YDR3x5Fel6x2CVRDYjShXS3/fv3Izo6Gv/73/8qPK5WqzF48GDEx8cjISEBSqWywvPsQhLBoc+AlJNA5BqxK6noz4VAbiow5CuxK5G1jPxijF1xDP5eTvh0VGvYWSsf/iIimSrV6vD6z2dx/kYO1k3qCG8Xif1iZsZk24X0XxqNBuvXr8e8efPuec7R0RFr1qxBWloa4uPjRaiO7iG1Abxl2IVUa+l5xXhq+VE09XbGF0+1YXghs2ettELUk63R1tcdkd8cQeqdQrFLomoQPcAsXrwYs2fPhp3d/ZupfXx8EBISguJiNvFJQlosUK+52FXci11ItZKWW4RRy4+gZUNXLHmyFReoI4uhtFLgf8PD8GigF5785giSs9Ril0RVJOqn1IoVK9C/f380atQIAFBcXAytVlvhGK1WC1tbW4SGhopRIt0t+7o+LEiNuz+QdxPQ8Deo6rqVU4RRy4+idSN3fDKS4YUsj5WVAguGtESfEG88+c0RXMsoELskqgLRPqmWLl2KhIQE3Lp1Czt37sTmzZvx3HPPYc+ePZg7dy4KCgpQWlqKWbNmYcGCBfeMfyERFOUCRTn6bQSkpk49wMZJH7CoylLvFCJy+RFE+Hng4xFhUFopxC6JSBQKhQLvDgrBE60b4MlvjuBKWp7YJdFDiDIBfuXKlXj55ZcBAIsWLSp/fMqUKbCyssLy5cvx1VdfoWPHjnj33Xe5iJ1U5KToQ4KDu9iV3Euh0I+DyUqQ1irBEpacpcboFUfRpWldLBjcElYML2ThFAoF3urfHHbWSkR+cxTrn++IZt7OYpdFlRAlwEycOBETJ06s9PnUVG66JUk5KYBbI31YkCJ3P27qWEXJWWqMWn4UvYLr4f0nWkAh1f+mRCamUCjwWp9msFIAY1Ycw08vPAJ/Lyexy6L7YGc3VV1OEuCqEruKynk04UykKridW4QxK46hN8MLUaWm9WqKYW0aYsy3R5GSzYG9UsQAQ1WXkyLN8S9lyrqQqFJZBSUYs+IYOvh74L3HGV6IKqNQKPDWgOboHeKN0d8ew+3cIrFLorswwFDV3UmWdguMuz+7kB4gt0iDcSuPIcjbGR8OD+OYF6KHUCgUmPt4C3Tw98CYFceQmc/lPKSEAYaqLicFcPMVu4rKeTQB7iQBWo3YlUiOuqQUE78/gXrO9lgS2ZqzjYiqyMpKgQ+HhyG4vgvGfnccOWp+vkgFAwxVXY7EW2BcVYDCSl8nlSvSaPH8D6dgrVRg6Zi2sLXm//ZE1aG0UiDqyVZQuTtg3PfHkVfEECMF/CSjqtFq9AvFSXkMjJVS30LEbqRyGq0OU9b/jfziUqwYHwF7G66nRFQTNkorfDm6DVwdbPDsqpNQl5SKXZLFY4Chqsm7CUABONcXu5IH45YC5XQ6AW/8fBbJWWqsntAedexEWTWByGzYWSvxzdhwQAG8su5vlGp1Ypdk0RhgqGruJAMuDQClxL8EPfy5Gi8AQRAwd9sFxKTkYM2zHeDqaCN2SURmwcFWiW/HtUPqnULM3hIDQRDELsliMcBQ1eSkSHv8SxnORAIAfP3XVew8fws/PNsedZ3vv1EqEdWMq4MNVk1oj0NXMhG1K17sciwWAwxVTU6StMe/lGEXEjafTsHXe6/i+wkRULk7il0OkVnycbXH6okRWHM0EWuPJopdjkVigKGqkUsLTFkXkoU26x68nIG3t5zH0rFt0aKBq9jlEJm1wHrO+G58O3ywIw47z98SuxyLU+0BDTdv3sSePXsQExOD9PR0KJVKNGjQAOHh4ejTpw8cHByMUSeJ7U4yUL+V2FU8nFtjoLQIyLsFuEh8wLGBXUjNwYtrT2Hh0Jbo0rSu2OUQWYTwxh74NLI1Xt1wBp512iPCz0PskixGlVtgYmJiMHToUDRq1Aivv/46du3ahfj4eMTFxeHXX3/FM888Ax8fH7zxxhvIzc01Zs0kBqlvI1DGxh5waWhx3Ugp2WpM+P4EJncPwLC2MmgpIzIjfVv44J2BIXhu9UnE384TuxyLUaUWmKVLl2Lfvn144YUXsHr1ari4uNz3uNTUVOzZswcTJkzA22+/jbZt2xq0WBKJIPyziJ0MAgzwTzfSNcDvUbErMYk76hI88/0J9G3hjZe6B4hdDpFFGt3BF7dzizB+5XFsfqkT6ruyN8LYHtoCs3HjRvj7++Onn35C//79Kw0vANCgQQM8/fTT2LRpE06cOIFr1zgbxCwUZgMatTzGwACAu5/FtMCUrbLr7+WE959oyc0ZiUT0au+m6NasLiauOomCYi50Z2wPDTDNmjXDgAEDqn3iF154AWo1tyA3C3eSAAd3wK6O2JVUjUcTi5hKrdMJeP3ns9DodPh8VBvub0QkMoVCgflDWsLd0QbTfjwDrc4yJxOYykMDTFhYWIWfU1NTkZqaipycHADA6dOnMW3aNHzxxRfQarUVjm3RooUBSyXRyGUGUpmyLiQz99meyzibfAcrxrWDgy23CCCSAhulFb4eE46E9Hx8tPOi2OWYtWpPo/b19cXHH3+MW7duISYmBl26dMH+/ftx7do1vPHGG8aokcQmp/EvgEWsBbP9XCpWHryG78ZHwLMOF6ojkhJXRxt890wENpxMxoYTSWKXY7aqPY169OjRWLJkCQCgd+/e8PLywl9//QUXFxe8++67Bi+QJEAuM5DKuPsDRTmAOgtwNL8pjWeT7+DNjefw5eg2CPJxFrscIroPfy8nfD0mHBNXnYCvhxMeCfAUuySzU+0WGJVK35WwadMm/Pnnn1i8eHH5wN4jR44YtjqShjtJ8upCsncBHD3NshvpVk4RJv1wEtN7N0PP5t5il0NED/BIgCfeezwEL/7fKVzPKBC7HLNT7QATFhaGrl27YvTo0Zg8eTJGjBiBEydOYNSoUfjzzz+NUSOJLScFcJNRCwxglgN5C0u0mPTDSXRrVhfPdfEXuxwiqoJR7X0xMlyFiatPIEetEbscs6IQqrmV5o0bN2BjYwNra2t4eOib57Ozs1FSUgIA8PY23W+Fubm5cHV1RU5OzgOnd1MtfRwIPPUjoGondiVVt2kS4NUM6DZD7EoMQqcTMGX930jPK8aa59rDzpqDdonkQqsT8MKakyjUaLFqQnvYKLmLjyG+v6t9F8PDwzF79uzy8AIA7u7u8Pb2Nml4IRPRFAIF6fIaAwPoZyKZ0UDez/ZcxtmUO/h6bFuGFyKZUVop8NmoNsjML8H72y6IXY7ZqHaAeeKJJzB8+PD7Prd79+5aF0QSk3MDUNoCTjLbW8ejidmMgeGMIyL5c7Kzxorx7bAj5hZ+OpEsdjlmodqzkBo1aoT58+fjzz//hLPzvzMgSkpK8OOPP+LKlSsGLZBElpOsH8BrJbMmT3d/sxgDE3czF29uPIcvnuKMIyK5U7k74sun2uDZ1ScR5OOMVo3cxC5J1qodYE6fPo3U1FQcP34cVv/5UhMEAZmZmQYtjiRAbovYlfHwB/JvASUFgK2T2NXUSI5agxfWnMILXQPQK5jds0TmoFOgF6b3aYrJa09h25TO8GKrao1VO8DMmDEDrq6u911l95dffjFETSQlOcmAq6/YVVSfU13Atg6QfR3wlt+K0DqdgFc3/I2m9epgSs9AscshIgOa1KUJzqXk4JV1p7H22Q6w5qDeGqn2XevUqROKi4vLw0pWVhaio6Oh0WgwZMgQA5dHopNrC4xCoa87N1XsSmrk8z8vIyGjAFGRrWHFPY6IzIpCocBHI8JwR63Bot+43UBNVTvAfPfdd4iIiMDSpUsBAB4eHggNDcWIESNw+fJlgxdIIruTJL81YMo4+wB5N8Wuotr2XkzDt/sT8M3T4XB1sBG7HCIyAkdba3zzdDh+PpmMX8/cELscWap2gPniiy+we/dudO3atfwxX19f9OnTB88884whayMpkGsLDAA41wfyboldRbUkZhZg2o9/44NhoWjuw7WNiMxZY08nfPZUG8zeHIPY1Fyxy5GdageY1q1bo0ePHrCxqfibYXx8PM6ePWuwwkgCdDog94b81oApI7MWmMISLV5YcwrDw1UY3Lqh2OUQkQn0CKqHyd0C8MLak7ijLhG7HFmpdoDx8vJCeno6FAp9v3x+fj4WLlyIpUuXokePHgYvkERUkAZoSwAXmX6ZyqgFRhAEzNp8Di72Npj9WLDY5RCRCb3cIxDNfVww9ccz0OmqtTi+Rat2gHnnnXcwY8YMLF26FC1btoS3tzfmzJmDXr16YcWKFcaokcRyJxmo4w3Y2ItdSc3IqAVm9eHrOJKQiS/HtOEy40QWxspKgagnWyEpswBf/3VV7HJko9rTqN3c3LBq1SokJCQgLi4OGo0GQUFBCA7mb41mp2wRO7mSSQvM30nZ+N/OS1j7XHvUc5ZpWCSiWnG2t8GXo9ti5LIjaNfYHR2aeIpdkuRV+1e9OXPmAACaNGmCgQMHYsiQIQgODsauXbuwfv16gxdIIspJlu/4F0DfApN/G9Bpxa6kUjlqDV5Z9zde69MM4Y09Hv4CIjJbLRu6YvbAYEz98W9k5BeLXY7kVakFJikpCdevXwcAxMTE4MCBA7h7E+ukpCTMnDkTTz31lMGLJJHIeQYSoO/+EnT6zSidfcSu5h6CIGDmpnMI8nHGs539xS6HiCRgbAdfHE3IxPQNZ7B6QnuuA/UAVQowdevWRXR0NGbOnIn8/Hxs3br1nmMcHR0xZcqUKl84MTERzz//PA4fPozAwEBERUWVDwJWq9WYNm0aHBwckJWVhYULF6Jx48ZVPjcZyJ1kIEDGA7Ot7QBHT/04GAkGmB+OJOJM8h3smNaFH1JEBEC/yN2Hw0Ix6IuDWLrvCl7p2VTskiSrSl1IDg4OePHFF3H48GG8+eab0Ol09/zJz8/HokWLqnRRQRAwadIk9O7dG0uXLoUgCBg0aBCuXtUPXho3bhy6dOmCzz//HDNnzsTjjz8OjUZT878l1YzcW2AAyY6DOX8jBx/+dhFfjG4DDydbscshIglxtrfBV6Pb4qu9V3E0gXsMVqZaY2BatmyJefPmoaioCNeu6Xf6zc/PR1ZWVrUuev78ecycORMzZszA008/jT/++AMKhQLbt2/HqVOnEB0djcjISABAaGgoFAoFx9eIISdJ3mNgAEnORMor0uDldafxSs9ARPhx3AsR3at8PMx6joepTLUH8Z46dQp+fn544YUXAOhbZ3bt2oVXX30VBQUFVTpHUFAQevXqVf5zvXr1EBISAjs7O2zduhWBgYGws/t3h85WrVph27Zt1S2VaqMoFyjKMYMWGB9JtcDo13uJga+HI17sFiB2OUQkYWM7+KK9vwembzgDLdeHuUe1A8zUqVPxwgsvICwsDACgVCoRGRmJunXrYtKkSVU6h63tvU3m2dnZGDRoEGJjY+Hl5VXhOXd3d8THx1d6vuDgYKhUKqhUKkRFRVXjb0OVyknR7+bs4C52JbXjXF9SLTA/nkjGsWtZiHqSmzQS0YMpFAosGhaK5Cw1lu69InY5klPtAOPn54f3338fdevWrfC4QqFAdHR0jYrYv38/hg0bBpVKhZycHHh4VGxWt7Ozg1qtrvT1cXFxSElJQUpKCl577bUa1UB3KRv/opD5l6yEWmDibuZi/vZYfBbZGnWd7R7+AiKyeGXrwyzddxUnr1dvuIa5q3aA8fb2BoDyrQQA4NChQ1i8eDGaNGlS7QI0Gg3Wr1+PefPmAdDvbl1cXLG/r7CwEO7uMm8JkBtzGP8CSKYFRl1SilfWncakLk3QKdDr4S8gIvpHy4aueKNfEF7dcAa5RZzQUqbaAeaFF17AyJEjsXPnTrzyyivo0qULunTpAqVSiW+++abaBSxevBizZ88uH/MSEBCAjIyMCsekp6cjKCio2uemWjCHGUiAZFpg5m+Pg6eTHab24pRIIqq+CZ384O/lhHd/OS92KZJR7QATGhqKNWvW4Omnn4aDgwPCw8OxdOlSXL16Fe3bt6/WuVasWIH+/fujUSP9b/rFxcUYNmwYzp07V6EVJjY2FgMHDqxuqVQbd5IBNzNpgSlIB7Ti/dayK/Y2tp9LRVRkKyg57oWIasDKSoHFI1vhr/h0/PL3DbHLkYRq74UEAPb29pgwYcI9jx8+fBidOnWq0jmWLl2KlJQUqFQq7Ny5E2q1Glu2bMHq1avRuXNn7Ny5E4MHD8aZM2dgZWWFkSNH1qRUqqmcFKBZP7GrqD2negAU+i0FRGhRSssrwsxN5zB/cEuo3B1Nfn0iMh/1XOzxv+FheP2nswhv7I5GHpb9mVLtAJOZmYlvv/0W165dq7C4nFarxf79+8vXh3mQlStX4uWXXwaACovfTZkyBVZWVli3bh2mT5+OQ4cOISMjAzt27IBSqaxuqVQb5tKFpLQG6tTTdyOZ+O8jCAJm/HwOnQO9MKRNQ5Nem4jMU98WPni8dTqmbziDH5/vCGsL3r2+2gGmX79+yMzMRKdOnSpMh1ZUY7bKxIkTMXHixEqf9/Lywpo1a6pbGhmKVgPkpZrHIF5AtMXs1hxNxOXbefjt1a4mvzYRma93BgZj0BcH8fW+q5hiwePqqh1gEhIScOHCBdSvX/+e53bv3m2QokhkeTcBKPTjR8yBCNsJXL6dhw9/u4iVz0TA1cHGpNcmIvPmaGuNz0e1wYhlh9G5qRfa+FrmLN1qtz3NmjULsbGx933u7vVbSKbuJAMuDfTdL+bAxC0wxaVaTPvxDMY94oeOTTxNdl0ishwtG7pieu9mmPbjGeQXl4pdjiiq/Q31yiuv4Nlnn8WhQ4cqPK7T6RAdHY0TJ04YrDgSibmMfynjXB+4k2Syy0XtiodCAbzWp5nJrklElmdSlyb4Kz4dc7dewCcjW4ldjslVO8AMHToU+/fvR6tWrWBvb1/+uCAIuHz5skGLI5GYyyJ2ZZx9gORjJrnUkauZWHMkEVtfeRS21pY7uI6IjM/KSoHFT7ZC/08PYOf5m+jf0ky6/auo2gHm2LFjOHr0aPleSP+1ceNGgxRFIjPHFhgTjIHJUWvw2k9n8NaA5gis52z06xER1Xd1wLzBLfD2lvOI8POAZx3L2aak2r8iTpw4ETY29x+UWN2F7EiizGURuzImGgPz/vYLaObtjKc7Njb6tYiIyjzRqgEi/Dzwzi/nIQiWs2t1tVtgBg4ciC+//BKRkZEVHtfpdFi5ciV++OEHgxVHIslJMbMupPpAYTagKQJs7B9+fA3sir2N3bG38cf0btVaUoCIqLYUCgUWDG2Jfkv2Y+vZVAxubRnrTlU7wMyYMQN///03vv7663ueUygUDDByJwjm14Xk6AUolED+LcDdz+Cnzy4owewtMXjv8RbwcTVOQCIiehCvOnZYOLQlZm6KQccmnvB2Mf/Pomp3Ib3xxhvYtWsXSktLodPpyv9oNJryHaVJxorzAE2B+awBAwBWVkbd1HHutgtopXLFsLaW8VsPEUlT/5b10T2oLmZtjrGIrqSHBpirV69W+DkyMhJdu3aFlVXFlyqVSsyaNavCY9evX699hWRa+WmA0hawdxW7EsMy0jiYnedvYt+ldHwwNJRdR0QkuvefaIHzN3Lw86kUsUsxuocGmAMHDlRYuM7KyqrSQbz/DTUrV66ssFcSyURBGlDHGzC3L2MjzETKzC/G21vOY97gFqhnAc21RCR9bo62+N/wMMzfFosbdwrFLseoHhpgnnnmGfz000944403cPbs2QceW1RUhOjoaAwfPhzNmzdH06aWu0eDbOWnAU51xa7C8IzQAvPu1gto5+eOJ1o1MOh5iYhqo0fzehgQ6oOZG8+ZdVdSlQbxzp07F3/88QcmTJiAa9euoWnTpvDx8YGjoyM0Gg1yc3ORnJyMlJQUREZG4uuvv0a9evWMXTsZQ36afvdmc+PsA2QYbqHF6HM3cfhKBmcdEZEkzRkUgv6fHsDaY0lmu7RDlQfx9u3bF6dPn8bvv/+OwYMHw8nJCVlZWSgtLUWTJk3w1ltv4cqVK/juu+8YXuSswFxbYOobrAUmI78Yc349j3mDW6Kus+UsGkVE8uFsb4OPRoThwx1xSMpUi12OUVR7GnX79u25YJ05y/9nDIy5MdAsJEEQMOeX8+jYxAODwsxophYRmZ1HA70wtG1DvLX5HP7vuQ5m11rMzVqoooJ0M+1CMswg3u3nbuL4tSzMH9zS7D4MiMj8zOzfHNcyCvDzSfOblcQAQxXl3zbfLqTiXKA4v8anyC4owdytFzD3iRYWtd8IEcmXs70NFgxpiQXRsUjLLRK7HINigKGK8s20BcbBXb++Tf7tGp9iQXQc2vi6seuIiGSlV7A3ugXVw3tbL4hdikFVO8AsX778nsdu3ryJjRs3chsBuROEf9eBMTcKRa2mUh+4nI7fL9zC/CHsOiIi+Xnv8RAcScjEzvPG39jWVKodYCZPnozOnTsjPj6+/LH69etj0KBBWLp0qUGLIxMrzgNKi8yzCwmo8TgYdUkpZm+Jwcz+Qajv6mCEwoiIjMurjh3eHRSCOb9eQI7aPBaZrXaA6d+/P2xsbNC6dWssWrQIWq0WAGBvb48OHToYvEAyIXPdRqBMDVtgluyKRz1ne4zpYJ5rKRCRZRjapiGC67vggx1xYpdiENUOMH5+fti7dy8+/fRTfPTRR2jfvn35Cr1KpdLgBZIJFaQBTvXMbxuBMjVogYlJycGao4n4cFgorKzM9L4QkUVQKBT4YGhLbD+XisNXMsQup9aqHWB0Oh0A4Pnnn8eFCxfQqFEjtG/fHm+//TaKisxrhLPFMddVeMtUswVGo9Vh5qZzeLFbIJp6OxuxMCIi01C5O2JGvyC8tTkGhSVascuplWoHmIMHD5Zv7tigQQP88ssvWLt2LVauXHnfAb4kI+a6BkyZarbArDhwDaU6HV7sHmDEooiITOvpR/zgVccWUbsuiV1KrVQ7wHz22We4desW8vP/XU9j5MiRiI2NxfPPP2/Q4sjEzHUNmDLVaIG5llGAz/dcxqJhYbC15moDRGQ+lFYK/G94GNYcTcTZ5Dtil1Nj1f5k7tWrF3r27Ik6depUeNzd3Z2zkOTO7LuQ/mmBecjurIIgYNbmc4iMaITwxu4mKo6IyHSaejtjcrcAzN4Sg1KtTuxyaoS/WtK/CtLNcw2YMs4+gEatX5H3AX46mYykTDXe6BdkosKIiExvcrcAqEu0WHM0UexSaoQBhv6Vb6Y7UZexcwFsHB84DiaroASLfruIeYNboo5dtfc6JSKSDXsbJeYPbonFf8TjVo78JuEwwNC/zL0LqQqr8S7aEYcIPw/0DjHjligion90buqFXsH1MH97rNilVBsDDOmZ8zYC//WAmUgnrmchOuYm3ns8xMRFERGJ5+2Bwdh/OR37LqWJXUq1MMCQnrlvI1DG2ee+AUaj1eGdLecxpWdTqNwdRSiMiEgc9Zzt8Wa/ILz76wUUaeSzNgwDDOmZ+zYCZSppgVl16Dp0goBnO/uLUBQRkbhGd2gMd0cbfLX3itilVBkDDOmZ+zYCZe4zBib1TiE+3R2P+UNacs0XIrJISisFFg4NxbcHEnAlLf/hL5AAflqTnrkP4C1znxaYedti0a+lDzo28RSpKCIi8bVs6Iqn2vvinV9iIDxkvSwpYIAhPXPfRqDMXS0wey+m4fDVDMx+LFjEooiIpOG1Ps1wLaMAW/6+IXYpD8UAQ3rmvo1Amf+sxluk0eK9rRfwZv/m8KpjJ3ZlRESic7a3wXuPt8DC6DjkqDVil/NAogaYjIwMzJgxAy+99NI9z82bNw8KhaL8z4kTJ0So0IJYShdSHW9AWwwUZuOrvVfg7mSLp9r7il0VEZFkDGjpg1CVK/73+0WxS3kg0ZYa1Wg0OHjwIH799Vd06tSpwnNFRUU4ffo0lixZAgBwcnJCRESEGGVajoJ0wLuF2FUYn10dwM4FyUkJ+PZAOjZO7gSllZkPXCYiqgaFQoG5j7dA/8/2Y3R7X7RsKM3ZqaIFGBsbGwwZMgQ///zzPc+tWrUKr7zyCnr37i1CZRbK3LcR+A/B2Qf/t/sYItt1k+z/mEREYvLzcsLER/3x3tYL2Dj5ESgkOENV9DEwNjY2FX7W6XSIiorCkCFDMHz4cFy6dEmkyiyMpXQhAchSeKAo8wZe68vNGomIKvNKz0Ck3imU7IBe0QPM3QoLC7Fw4ULMmDEDJ06cQHh4OPbs2fPA1wQHB0OlUkGlUiEqKspElZqRsm0EnMw/wBRptDiRZYdhzZRwdbB5+AuIiCyUo601Zj8WjEW/XURekfQG9Epuu10nJyeMHDkSADBjxgwMHjwYEydOREJCApRK5X1fExcXBxcXF1OWaV7KthGwgBaY5fsT0NDWC6EuhWKXQkQkeYPC6uP/jiXiiz+vSG65Ccm1wPyXo6Mj1qxZg7S0NMTHx4tdjvkqSLeIbQRu3CnE1/uuon1oCygesCM1ERHpKRQKzH2iBVYfvi65FXolHWAAwMfHByEhISguLha7FPOVf9sithH4YEccBoT6oFHjJpXuSE1ERBU193HBU+198f62C5JaoVfyAUar1cLW1hahoaFil2K+8tOAOuY9A+nI1Uz8dSkdb/VvXumGjkREdH/TezfDhdRc/BF7W+xSyokeYLRaLXQ6XfnPu3fvxty5c1FQUIDS0lLMmjULCxYsqHT8CxlAQbp+gTczVarV4f1tFzClZyDqudjrtxPIvwX8531HRESVc3W0wZv9gjB/eyyKNFqxywEgcoDZsGED9u/fjwMHDlRYD2b58uXw8/PD0KFDMXLkSPTq1UvEKi2Ama8Bs+54EkpKdZjwqL/+gTo+gK4UUGeKWxgRkYw82a4RPJxs8c1fCWKXAkDkWUiRkZGIjIys8Fjv3r2RmpoqUkUWKv+22c5AyiooweI/4vHpqNawtf4nr9vYAw7u+k0dzbzrjIjIUKysFHj/iRYY/e0xDA9vCJW7o7j1iHp1koaCdLNdA2bxH5fQrrE7egTd9ffjOBgiompr4+uOQWH1sTA6TuxSGGAIZrsK7/kbOdh0OgVzBoXc+2SdevpxMEREVC1v9m+OA5czcCxB3G54BhgyywAjCALe33YBEx71h5+X070HOHoBBRmmL4yISObqOtvhxe4BWBAdB51OvGnVDDCWzky3Efjt/C1cz1Tj5R6B9z/AyYuDeImIaujZzv7IKijBZhH3SWKAsXTl2wiYz2DW4lItFv0Whzf6NkMdu0rGqTt6MsAQEdWQvY0Sbw1ojo9/vwh1SakoNTDAWLrybQTcxK7EYFYfvg4nW2uMCG9U+UGOnuxCIiKqhUFh9aFyd8QykaZVM8BYOjPbRiCroARf/HkF7wwMgdLqAX8ntsAQEdWKQqHAOwOD8e3+BNzMMf0GuQwwls7MthH4bHc82vt5oHNTrwcf6OQFqNkCQ0RUG2183dG3hTc+2nnJ5NdmgLF0ZrQGzJW0fPx4IhmzqrLlu6MXoM4yflFERGbuzf7NsfP8LZxJvmPS6zLAWDozmkK9aEccIiMaIbBenYcf7OgJlOQDmiLjF0ZEZMYaujnguS7+WLA91qS7VTPAWDoz2Ubg4OUMHL+ehWm9mlbtBQ7uABQcB0NEZACTuwUgKUuN6JibJrsmA4ylM4MuJK1OwILoWEzpGQjPOnZVe5HSGnBw4zgYIiIDcLKzxhv9gvDhbxdNtls1A4ylM4NBvJtOpaCgpBTjO/lV74WOXMyOiMhQRrRVwdXBBisPXTPJ9RhgLF1BGlDHW+wqaqyguBQf/3EJswYEw85aWb0XO3oCBQwwRESGYGWlwJxBIVi69yoy84uNfz2jX4GkSxD0LTAy7kL65q+raOzhiAEtfar/Yk6lJiIyqI5NPNHB3wNf/HnF6NdigLFkMt9G4FZOEb49cA3vDAqBoiYL8Tl6sAuJiMjAZg5ojvXHk5CYWWDU6zDAWDKZbyOwZFc8egXXQ+tGbjU7AXekJiIyuGbezhjSuiE+/t24i9sxwFiysu4jGW4jcPl2Hn45cwMz+gXV/CTcToCIyCim92mGPXFpOGvExe0YYCxZ/m3Zdh999PsljIpohMaeTjU/iRNnIRERGYOPqz0mPOqHRb/FGW1xOwYYSybTNWBOXs/C4SsZmFLVResqw2nURERGM7l7AC7dysO+S+lGOT8DjCWT4TYCgiBg0W8XMalrE3hVddG6yjh6cAwMEZGRuNjb4JWeTfHhbxeh1Rm+FYYBxpLJcBuBXbG3kZhZgEldmtT+ZE5eQGEWoNPV/lxERHSPsR19UVBSis2nUwx+bgYYSyazLqRSrQ7/23kR03o1hZOdde1P6OgJCDqg6E7tz0VERPews1ZiRr8gRO2KN/gWAwwwlkxm2whsPJUCrU7AqPa+hjmhrRNg7cBuJCIiI3o8rAG86tjh+0PXDXpeBhhLJqNtBApLtFiyOx5v9AuCjdKAb1tOpSYiMiorKwXeGtAcS/ddQXZBieHOa7AzkbzIbBuBlYeuwcfFHgND6xv2xE6e3E6AiMjIHg30Qhtfd3y113BbDDDAWCoZbSOQXVCCZfuuYuaA5jXbMuBB2AJDRGQSb/VvjjVHE5GSrTbI+RhgLJWMthH4au8VtG3sjk4BXoY/ObcTICIyiZAGLhjQ0gef77lskPMxwFgqmWwjkJKtxpqjiZjZv7lxLuDkBaizjHNuIiKq4NXezfDLmVQkZOTX+lwMMJZKJtsIfLb7Mvq39EFIAxfjXMDRg2NgiIhMxM/LCcPbqvDVn7UfC8MAY6lksAbM1fR8/Ho2FdN7NzPeRdiFRERkUlN7BWJffO23F2CAsVQyWANmya54DG/bEH5etdiw8WE4iJeIyKTquzogsl2jWp+HAcZSSXwNmNjUXOyKvY0pPWu5YePDcEdqIiKTe66zf63PwQBjqSS+BkzUrksY3cEXDdwcjHshtsAQEZmcR2034wUDjOWScBfS6aRsHL6aiZe6Bxr/Yo5egEYNlBhmXQIiIjINBhhLVSDdFpjFf1zCM538UNe59gn9oRzcACjYCkNEJDOiBpiMjAzMmDEDL730UoXH1Wo1Jk2ahKlTp2Ls2LFITEwUqUIzJQhAfrokx8AcvpqBcyk5eKFrgGkuaKXkVGoiIhkSLcBoNBocPHgQv/76K9Tqis3348aNQ5cuXfD5559j5syZePzxx6HRaESq1AwV5wGlhZLrQhIEAZ/8fgnPd2kCV0cb013YkQN5iYjkRrQAY2NjgyFDhiAiIqLC46dOnUJ0dDQiIyMBAKGhoVAoFFi/fr0YZZqngnTAykZy2wjsvZSGxEw1JhhgdHq1OHoCBQwwRERyIvoYGBubir9pb926FYGBgbCz+3f8Q6tWrbBt2zZTl2a+1Fn6L20JbSOg0wn45Pd4vNg9AHXsrE17ce5ITUQkO6IHmLvFxsbCy6vipn3u7u6Ij4+v9DXBwcFQqVRQqVSIiooydonyV5ilH/chIb+dv4WsghKM7djY9BfnVGoiItkx8a+6D5eTkwMPj4pfrnZ2dveMk/mvuLg4uLgYaa8cc6TOAhzcxa6iXKlWh8W7LmFKr0DY2yhNX4Cjl75bjYiIZENyLTAeHh4oLi6u8FhhYSHc3aXzhSt7hdIKML+cSUWpVsCTBlhaukbYAkNEJDuSCzABAQHIyKg4HiE9PR1BQUEiVWSG1NLpQirV6vDFn5cxtVdT2ChFejtyOwEiItmRXIAZMWIEzp07V6EVJjY2FgMHDhSxKjNTmA04SCPA/HImFQAwpHUD8Ypw9GCAISKSGdEDjFarhU6nK/+5TZs26Ny5M3bu3AkAOHPmDKysrDBy5EixSjQ/EhnEW9b6MqVnU1iL1foC/DMGhrOQiIjkRNRBvBs2bMD+/fthZWWFn3/+uTykrFu3DtOnT8ehQ4eQkZGBHTt2QKkUYXCnuZLIIN4tf9+AAiK3vgD6LqTCbECn1a/MS0REkidqgImMjCxfsO6/vLy8sGbNGhEqshCFWaJ3IZVqdfhy7xVMFbv1BdAP4oWgDzFOXg89nIiIxCd6FxKJQJ0tehdSWevLYLFbXwDAxgGwcWI3EhGRjDDAWCKRB/GWtb6IPvblvziVmohIViTy7UEmU1oMaApEbYHZLKXWlzLcToCISFYYYCyNOkv/T5E2ctRodfjyT4m1vgBsgSEikhkJfYOQSRRmAbbOgLWtKJff8vcNKK0U0mp9Af6ZSs0AQ0QkFwwwlkadBTiKM4X639aXQGm1vgBsgSEikhmJfYuQ0Yk4gHfLaX3ryxOtJNb6AnAMDBGRzDDAWBqRVuHVaHX4Yu9laba+AGyBISKSGQl+k5BRibQK75bTN2BjZSXN1heA2wkQEckMA4ylEWEV3lKtDl/tu4KXe0i09QXgjtRERDIj0W8TMhoRVuGNjrkJnSDgCanNPPqvsi4kQRC7EiIiqgIGGEtj4kG8Op2AL/+8ghe7BcJGqq0vgD7AlBYBJQViV0JERFUg4W8UMgoTD+L9I/YW8opKMTy8ocmuWSP2boBCyW4kIiKZYICxNCYcxCsIAr748wqe79oEdtZKk1yzxqys9MGOU6mJiGSBAcbSmHAQ7774dNzKKcJT7X1Ncr1ac/T8d6sFIiKSNAYYSyII+jEwJliJVxAEfLHnMp7r0gQOthJvfSnDqdRERLLBAGNJivMAXalJWmCOJGTianoBxnaUSesLwC4kIiIZYYCxJIVZ+oGq9q5Gv9SXf17BM5384GxvY/RrGQzXgiEikg0GGEuizgIc3ACFwqiXOZWYjbPJdzDhUT+jXsfg2IVERCQbDDCWxEQDeL/aewVPP+IHN0dbo1/LoDiIl4hINhhgLIkJVuE9fyMHh69m4Lku/ka9jlE4eXEMDBGRTDDAWBITrML71d4rGBXhC686dka9jlE4enAMDBGRTDDAWBIjr8J7+XYe9lxMwwvdmhjtGkbFMTBERLLBAGNJjLwK79J9VzG8bUPUd3Uw2jWMytETKLoDaEvFroSIiB6CAcaSFBovwCRnqRF97iYmdwswyvlNwtFT/89CDuQlIpI6BhhLojZeF9J3B6+hbwtvNPZ0Msr5TcLGHrCtw24kIiIZYICxJEYaxJuZX4wNJ5Ll3fpSxtGTA3mJiGSAAcaSGGkQ7+ojiWjn546WDY2/wq/RcSo1EZEsMMBYEnW2wcfAFBSXYvXh63ixuxm0vgBsgSEikgkGGEuhLQWKcwzehbT+eBL8PB3xSBNPg55XNI5eQAEDDBGR1DHAWIrCbP0/DdiFVFKqw3cHr+HF7gFQGHl/JZPhYnZERLLAAGMpCrMBawfAxnBrtPx65gYcbJXoG+JjsHOKjmNgiIhkgQHGUhh4AK9OJ+Cb/Ql4oWsTWFmZSesLwDEwREQywQBjKQy8Cu/uuNvIK9JgSJuGBjunJHAMDBGRLDDAWAoDrsIrCAK+/usqnuvcBHbWSoOcUzIcPdmFREQkAwwwlsKAq/Aev5aFq2n5eKqDr0HOJylOXvouJEEQuxIiInoASQeY/fv3Q6FQlP/5+OOPxS5JvgqzDDaF+uu/rmLcI36oY2dtkPNJiqMnoC0BivPEroSIiB5A0t9Aq1atwpIlS8p/Hj9+vIjVyFxh9r+bFdZC3M1cHE3IxCcjWxmgKAmydwWsrPWtMPYuYldDRESVkGyAiYuLg0qlwquvvip2KeZBnQV4Btb6NMv+uoqR4Y3gVcfOAEVJkELx70wkD3+xqyEiokpItgvpk08+wQcffICuXbtix44dYpcjfwbYyPHGnUL8FnMLk7o0MVBREsWp1EREkifZADNixAh88sknKC4uxsCBA7Fo0aJKjw0ODoZKpYJKpUJUVJQJq5QRAwzi/f7gNfQJ8Yavp6OBipIoR0+ggDORiIikTLJdSAMGDMCAAQMwbdo0zJkzB++++y6GDh2K5s2b33NsXFwcXFw4XuGBajmIN6dQg/XHk7D2uQ4GLEqiOJWaiEjyJNsCU0ahUGD+/Plo2bIl9u7dK3Y58lWYXasWmB+PJyGkgQva+Bp2N2tJKptKTUREkiX5AAPoQ0zPnj1RXFwsdinyVKIGSotqvJBdSakO3x+6bv5jX8rYuwGFd8SugoiIHkAWAQYAbt68if79+4tdhjwVZun/ae9Wo5dHx6TCwVaJ3sHehqtJyhzcgKI7YldBREQPIMkAk5SUhClTpiApKQkAsGHDBrRo0eK+41+oCtRZ+vVNlNUf8iQIApbvv4ZnO/ub16aND8IWGCIiyZNkgLG2tsZff/2FkJAQdOvWDaWlpXj77bfFLku+ajGA9/DVTNzOLcLwtioDFyVhbIEhIpI8Sc5CatCgAc6dOyd2GeajFgN4l+9PwNiOjeFga2abNj4IW2CIiCRPki0wZGDqmu1EfelWHo4mZGLcI42NUJSEsQWGiEjyGGAsQQ27kL49kIBhbVXmu21AZezdgKJcQKcTuxIiIqoEA4wlUFe/Cykttwhbz6biuS4WuB+QgxsAASjOEbsSIiKqBAOMJahBC8yqw9fRtakXAurWMVJREmZbB1AoOQ6GiEjCGGAsQTUH8RYUl2Lt0UTLWbjubgoFx8EQEUkcA4wlqOYg3p9PJsPfywnt/Wu3+aOscSYSEZGkMcBYgsKqBxitTsB3h67huS5NoFBYyMJ198MWGCIiSWOAsQTqrCp3Ie2KvQ2dDhjQ0sfIRUkcW2CIiCSNAcbc6XT6loQqDuJdeegaxndqDGulhb812AJDRCRpFv4tZQGKcwBBV6UWmPM3cnD+Rg4i2/maoDCJYwsMEZGkMcCYO3UWYGWtnxr8ECsPXsOIcBVcHW1MUJjEsQWGiEjSGGDMXWG2vvvoIQNy03KLsD3mJp7p5GeauqSOLTBERJLGAGPuqjiAd+3RRHQO9EITS1y47n7YAkNEJGkMMOauCqvwFmm0WHssCRMftcBtAyrDFhgiIkljgDF3VViFd+uZVHjVscWjgZ4mKkoG2AJDRCRpDDDmTp31z+aE9ycIAlYeuoYJj/pb9sJ1d2MLDBGRpDHAmLuHdCEduZqJ27lFGNqmoQmLkgEHN6AoR7+ODhERSQ4DjLl7yCDelYeuYXQHX9jbKE1YlAzYuwEQgOJcsSshIqL7YIAxdw9ogbmWUYD98Rl4uqOfaWuSAztnQKHkOBgiIoligDF3DxjEu/rwdQwI9YGPq72Ji5IBhQKwd+U4GCIiiWKAMXfq7PvuRJ1TqMHPJ5MxgVOnK8eZSEREksUAY+4q6UL6+WQymtd3QetGbqavSS44E4mISLIYYMxZaQlQkn9PF1KpVofvD13nwnUPwxYYIiLJYoAxZ4VZ+n/e1QKz52IaBEFAvxbeIhQlI2yBISKSLAYYc1aYrd+F2tq2wsOrD1/HmI6NYa3kf/4HYgsMEZFk8RvMnKmz7hnAG387D6cSs/FUe1+RipIRtsAQEUkWA4w5K7w3wPxw5Doeb9UAHk62lbyIyrEFhohIshhgzNldq/DmFmmw+fQNjH/ET7ya5IQtMEREksUAY87umkK98WQKmvs4I1TlKmJRMsIWGCIiyWKAMWf/WYVXpxPww5HrGN/JT9ya5IQtMEREksUAY87+M4h3/+V05BdrMaBlfZGLkhG2wBARSRYDjDkrzC7vQlp9+DpGd/CFrTX/k1eZvRtQlAPodGJXQkREd+G3mTn7ZxDv9YwCHLqSiTEdOHW6WhzcAEEHlOSJXQkREd2FAcac/TOId83RRPRr6QNvF+46XS22zoDCiuNgiIgkiAHGnBVmo9DaBT+dTMb4RxqLXY38WFkB9q4cB0NEJEEMMOZKEAB1FnZdL4GvhyPCG7s//DV0L85EIiKSJEkHmEWLFmHSpEkYM2YM/vzzT7HLkZeSfEQdysfqv3Mx/hE/KBQKsSuSlKioqKodaIEzkap8bywQ703leG8qx3tjHApBEASxi7ifL7/8EqdPn8bKlStRVFSE1q1bIzo6GgEBAeXH5ObmwtXVFTk5OXBxcRGxWgnKToSqsT/qvr4DR2b3gb2NUuyKJEWlUiElJeXhB/4wBGgxFAgfb/SapKLK98YC8d5Ujvemcrw39zLE97ckW2BKSkowd+5cjB+v/9Kwt7dHv379sHDhQpErk5HCLAgKKzzZvjHDS21YYAsMEZEcWItdwP0cOnQImZmZaNmyZfljrVq1wltvvVXhuLLGo9zcXJPWJweZ1xJQqgMGB7vz/tyHIAhVuy86ByDjFmBB97DK98YC8d5Ujvemcrw39yq7H7XpBJJkgImNjYWVlRXc3f8deOru7o709HRkZ2eXP56Xp1+fo1GjRqLUKQct/LnybmVcXauzJ9SHRqtDiqp3bywL703leG8qx3tzf3l5eTW+N5IMMDk5OXBzc4OV1b89XHZ2dgAAtVpdHmAaNGiA5ORkODs7c5AqERGRTAiCgLy8PDRo0KDG55BkgPHw8EBxcXGFxwoLCwGgQquMlZUVVCqVSWsjIiKi2qttq5QkB/EGBASgoKAARUVF5Y+lp6dDpVLB0dFRxMqIiIhICiQZYLp37w4vLy+cOHGi/LHY2FgMHDhQxKqIiIhIKiQZYGxsbDB9+nRs3rwZAFBQUIBdu3bdMwuJiIiILJMkAwwAzJw5E9bW1pg2bRpefvllrFixAn5+fpUeP2/ePCgUivI//229sURcxbhy+/fvr/Be+fjjj8UuSTQZGRmYMWMGXnrppQqPq9VqTJo0CVOnTsXYsWORmJgoUoXiqezeAJb7eZOYmIh+/frB2dkZbdq0wd69e8ufs/T3zIPuDWC57xlAPwRk0KBBcHZ2Rrt27XD27Nny52rzvpHsSrzVUVRUhFGjRqF79+4AACcnJ0yaNEncokRUlVWMLdnEiRMRFhZW/vP48eMrDA63FBqNBtHR0XjzzTfRqVMnrFq1qvy5ESNG4IknnsC4ceMQExODMWPG4NSpU7CxsRGvYBN60L2x1M8bQRDQr18/9OnTBz4+Pli8eDEuX76Mc+fOISAgwKLfMw+7N5b6nikzffp0DBgwADY2Nnj55ZehVCoRExMDoJafNYIZ+Prrr4Vdu3aJXYYkFBcXC56ensK+ffvKH5s6daowYcIEEauSjtjYWGHOnDlilyEpo0ePFsaPH1/+88mTJwV7e3uhqKio/LGwsDBh9erVIlQnrrvvjSBY7ufNuXPnhN27d5f/fPv2bcHJyUn49NNPLf4986B7IwiW+54RBEEoLCwUkpOTy3/+6aefBFdXV0EQav9ZI9kupKrS6XSIiorCkCFDMHz4cFy6dEnskkRV2SrG27dvF7Eq6fjkk0/wwQcfoGvXrtixY4fY5UjC3b/pbN26FYGBgeVrLwH699C2bdtMXZro7r43lvx5ExQUhF69epX/XK9ePYSEhMDOzs7i3zMPujeW/J4B9FsB/Xe5E41GgxdffBFA7T9rZB9gCgsLsXDhQsyYMQMnTpxAeHg49uzZI3ZZonnYKsaWbsSIEfjkk09QXFyMgQMHYtGiRWKXJDmxsbHw8vKq8Ji7uzvi4+NFqkg6LPnzxtbW9p7HsrOzMWjQIIt/zzzo3ljye+ZuKSkpWLt2Ld5++20Atf+skeRCdv/1+uuvVxjwc7dXX30VI0eOBADMmDEDgwcPxsSJE5GQkACl0vI2MazqKsaWasCAARgwYACmTZuGOXPm4N1338XQoUPRvHlzsUuTjJycHHh4eFR4zM7ODmq1WqSKpMPJyYmfN//Yv38/hg0bBpVKxffMXf57bwDwPQPgzJkzeOedd/Dbb7+hR48eOHjwYK3fN5IPMIsXL67ysY6OjlizZg38/f0RHx+P4OBgI1YmTVVdxdjSKRQKzJ8/H9HR0di7dy8DzH94eHggPz+/wmOFhYV8/9zFkj9vNBoN1q9fj08//RQA3zP/dfe9+S9Lfs+0bt0a27dvx5YtWzB8+HBs2rSp1u8b2Xch3c3HxwchISH3fIlbCq5iXHUKhQI9e/a02PdKZQICApCRkVHhsfT0dAQFBYlUkXRZ6ufN4sWLMXv27PLWXb5n/nX3vbmbpb5nygwdOhTdunVDampqrd83ZhdgtFotbG1tERoaKnYpouAqxtVz8+ZN9O/fX+wyJGXEiBE4d+5chQ9YvofuzxI/b1asWIH+/fujUaNGAIDi4mIMGzaM7xnc/95otdoKx1jie+Zubm5uCAsLq/VnjewDzO7duzF37lwUFBSgtLQUs2bNwoIFCyyqb/G/uIpx5ZKSkjBlyhQkJSUBADZs2IAWLVpYfPeRVquFTqcr/7lNmzbo3Lkzdu7cCUDfd21lZVXej29J7r43lv55s3TpUiQkJODWrVvYuXMnNm/ejOeee47vGVR+b/bs2WPR75nc3FysXr0aubm5AIBz586hpKQEffv2rf37xqATvkWwa9cuoX79+oKXl5cwaNAg4fjx42KXJLrS0lLhjTfeEKZOnSqMHz9eOHjwoNglScKNGzeE0NBQwcnJSejatauwdu1asUsS3Y8//ij4+voKfn5+wk8//VT+eHp6ujB27FhhxowZwoQJE4QbN26IWKU47ndvLPnz5rvvvhMA3PNnypQpgiBY9nvmQffGkt8zgiAI8fHxgp+fn1C3bl1h5MiRwltvvSXk5uaWP1+b941ZrMRLRERElkX2XUhERERkeRhgiIiISHYYYIiIiEh2GGCIiIhIdhhgiIiISHYYYIiIiEh2GGCIiIhIdhhgiIiISHYYYIiIiEh2GGCIyGi+//57XL58WewyquTs2bP4+eefxS6DiKqIAYaIjOK9995DREQEmjZtavBzq9VqJCYmGvScrVq1gpOTE7766iuDnpeIjIMBhogM7vfff0deXh5atmxplPOvWrUK165dM/h5H3vsMezbtw9nz541+LmJyLAYYIjI4N566y08/fTTRjn3+fPnMXPmTKOcGwAmTpyI9957z2jnJyLDYIAhogfavHkzPD09YWdnh5iYGBw9ehSOjo747rvv7nv88ePHkZCQgNatWwMAtFot1q1bh7Zt22LPnj147bXX4Obmhr59+0KtVuOjjz6Cu7s72rZti/T09PLznDt3Di+//DJGjBiBdu3a4fDhwyguLsaaNWuQn5+PqKgovP322wCA7OxsvP766xg/fjzCwsKwYsUKAMChQ4cwZMgQzJs3D5MmTYK3tzeSk5Oxfv16zJo1C08//TSUSiVSUlLKr9upUyds27YNN27cMNIdJSKDEIiIHmLTpk0CAOHgwYPCxo0bheXLl1d67Pz584Xw8PDyn4uLi4Vdu3YJAITJkycL58+fF/7++2/B3t5eiIyMFP744w8hJSVFaNy4sbBw4UJBEARBrVYLw4cPF7RarSAIgjBnzhyhXr16QkFBgSAIggBA2Lt3b/k1xo0bJ9y6dUsQBEHYs2ePoFAohBMnTggxMTGCr6+v0KFDB2H79u3ChAkThFu3bgmdO3cuf+3UqVOF5OTkCn+HunXrCqtXr67dTSMio7IWOT8RkQwMGzYMAwYMwGuvvYaQkBB8//33lR57/vx5+Pj4lP9sa2uLHj16AAAiIyPRokULAPpBs82bN0efPn0A6Fs+ysa1rF+/HhkZGfjoo48AAPn5+QgNDcXNmzcREBBQ4XpXr17Fvn37ymvSaDTo2bMnkpKSMGzYMDRu3BgREREYOHAgBg4ciMzMTBw7dgwbN27EiBEjMHnyZDg5OVU4Z8OGDRETE1ObW0ZERsYAQ0RV8vnnn6NFixaYNGnSA4/LzMyEu7t7hceUSuU9x9nb21f42dbWFhqNBgAQGxuLkJAQvPXWWw+tKy4uDk5OThWOnTNnTvm/W1lZwdnZufxnT09PTJw4ESNHjkTPnj2xZMmSe+p1dHSs0J1FRNLDMTBEVCXZ2dkIDg7GvHnzUFBQUOlxDg4O5UGkpjQazT0zgUpLS5Gbm3vfY69du3bPc5mZmZWef9myZdiwYQPi4+PRoUMHnDx58p5j7he6iEg6GGCI6KE0Gg2+/vprHDhwAACwYMGCSo/18fG5b9CojubNm+Pw4cPl1wOAjRs3oqSk5J5jg4KCUFRUhM8++6z8scTERBw+fPi+587KysLx48fx5JNPIiYmBkFBQVi9enWFY/Lz89GgQYNa/R2IyLjYhURED7Vo0SJMnToVzs7O+OijjzB+/Hg8/fTTCAkJuefYRx55BPv27avwmFarBQDodLryxwRBqPTnMWPG4N1338XgwYPx+uuvQxAEpKWlYdSoUQD0XTxXrlxBcXEx+vbtiz59+mDu3LlIS0tDs2bN8Mcff2Djxo3l5/1v8CkpKcHixYuxYcMGuLm5oUePHvDz86tQb1JSEsLDw2t+w4jI+MQdQ0xEUrdmzRrB1dVVOH78uCAIgvDTTz8JAIQWLVoIhw8fvuf41NRUwcHBoXzGUGlpqTB//nwBgDBmzBjh2rVrwk8//SQ4OzsLbdu2FU6cOCH88ccfQuPGjQVfX1/hwIEDgiAIwpEjR4SwsDChTp06QmRkpJCbm1t+jZkzZwru7u7C2rVrBUEQhJs3bwqPPfaY4ODgIHTs2FG4ePGiIAiCsHnzZsHFxUXw9/cXfv/99/JjAQg9e/YU3nnnHWHq1KlCSUlJ+blTUlKEOnXqCPn5+Ua4m0RkKApBEASRMxQRmZkJEyZg+PDhGDRokNilVNsPP/yAM2fOICoqSuxSiOgBGGCIyOBu376NyZMnY8uWLWKXUm1Dhw7F999/Dzc3N7FLIaIHYIAhIqM4ePAgLl68iOeee07sUqps2bJlaNeuHdq1ayd2KUT0EAwwRGQ0ly5dgo2NDZo0aSJ2KQ91/vx5ODg43LNQHhFJEwMMERERyQ7XgSEiIiLZYYAhIiIi2WGAISIiItlhgCEiIiLZYYAhIiIi2fl/fHBXSepivsYAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x=np.linspace(0,50,100)\n", "th=np.pi*74.2/180.\n", "plt.plot(x,x*np.tan(th)-(9.8*x**2)/(2.*(25.**2)*(np.cos(th)**2)))\n", "th=np.pi*87.4/180.\n", "plt.plot(x,x*np.tan(th)-(9.8*x**2)/(2.*(25.**2)*(np.cos(th)**2)))\n", "plt.xlabel('x (meters)')\n", "plt.ylabel('z (meters)')\n", "plt.xlim(-5,30)\n", "plt.ylim(0,40);" ] }, { "cell_type": "code", "execution_count": 11, "id": "0877010a-a5a0-473e-bc21-8b81f958c6bd", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(74.17274093682283, 87.39231024025517)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.optimize import brentq\n", "g = 9.81\n", "v0, x1, z1 = 25, 5, 15\n", "f = lambda theta0, x1, z1: x1 * np.tan(theta0) - g / 2\\\n", " * (x1 / v0 / np.cos(theta0))**2 - z1\n", "th1 = brentq(f, 1, 1.4, args=(x1,z1))\n", "th2 = brentq(f, 1.5, 1.6, args=(x1,z1))\n", "np.degrees(th1), np.degrees(th2)" ] }, { "cell_type": "markdown", "id": "42078faa-8439-4a99-b3d8-19562c6f5f35", "metadata": {}, "source": [ "

That is, $\\theta_0 = 74.2^\\circ$ or $\\theta_0 = 87.4^\\circ$.

" ] }, { "cell_type": "markdown", "id": "7e678173-3941-43b3-8f48-6f75adde3178", "metadata": {}, "source": [ "\n", "---\n", "\n", "

A spherical projectile of mass $m$ launched with some initial velocity moves under the influence of two forces: gravity, $\\boldsymbol{F}_g = -mg\\boldsymbol{\\hat{z}}$, and air resistance (drag), $\\boldsymbol{F}_D = -\\frac{1}{2}c\\rho A v^2 \\boldsymbol{v}/|\\boldsymbol{v}| = -\\frac{1}{2}c\\rho A v\\boldsymbol{v}$, acting in the opposite direction to the projectile's velocity and proportional to the square of that velocity (under most realistic conditions). Here, $c$ is the drag coefficient, $\\rho$ the air density, and $A$ the projectile's cross-sectional area.

\n", "

The relevant equations of motion are therefore:\n", "$$\n", "\\begin{align*}\n", "m\\ddot{x} = -k\\sqrt{\\dot{x}^2 + \\dot{z}^2}\\dot{x},\\\\\n", "m\\ddot{z} = -k\\sqrt{\\dot{x}^2 + \\dot{z}^2}\\dot{z} - mg,\n", "\\end{align*}\n", "$$\n", "where $v = |\\boldsymbol{v}| = \\sqrt{\\dot{x}^2 + \\dot{z}^2}$ and $k=\\frac{1}{2}c\\rho A$. These can be decomposed into the following four first-order ODEs with $u_1 \\equiv x, u_2 \\equiv \\dot{x}, u_3 \\equiv z, u_4 \\equiv \\dot{z}$:\n", "$$\n", "\\begin{align*}\n", "\\dot{u}_1 = u_2,\\\\\n", "\\dot{u}_2 = -\\frac{k}{m}\\sqrt{u_2^2 + u_4^2}u_2,\\\\\n", "\\dot{u}_3 = u_4, \\\\\n", "\\dot{u}_4 = -\\frac{k}{m}\\sqrt{u_2^2 + u_4^2}u_4 - g.\n", "\\end{align*}\n", "$$\n", "The following code integrates this system and identifies two events: hitting the target (the projectile returning to the ground at $z=0$) and reaching its maximum height (at which the z-component of its velocity is zero). We set the additional attribute hit_target.direction = -1 to ensure that hit_target only triggers the event when its return value (the projectile's elevation) goes from positive to negative; otherwise the event would be triggered at launch since $z_0 = 0$. Other possibilities are direction = 1: trigger the event when the return value changes from negative to positive or direction = 0 (the default): the event is triggered when the return value is zero from either direction.

\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "id": "b741e99c-1b13-4460-a7ce-381203a20252", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Time to target = 6.34 s\n", "Time to highest point = 2.79 s\n", "Range to target, xmax = 64.12 m\n", "Maximum height, zmax = 49.42 m\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy.integrate import solve_ivp\n", "import matplotlib.pyplot as plt\n", "\n", "# Drag coefficient, projectile radius (m), area (m2) and mass (kg).\n", "c = 0.47\n", "r = 0.05\n", "A = np.pi * r**2\n", "m = 0.2\n", "# Air density (kg.m-3), acceleration due to gravity (m.s-2).\n", "rho_air = 1.28\n", "g = 9.81\n", "# For convenience, define this constant.\n", "k = 0.5 * c * rho_air * A\n", "\n", "# Initial speed and launch angle (from the horizontal).\n", "v0 = 50\n", "phi0 = np.radians(65)\n", "\n", "def deriv(t, u):\n", " x, xdot, z, zdot = u\n", " speed = np.hypot(xdot, zdot)\n", " xdotdot = -k/m * speed * xdot\n", " zdotdot = -k/m * speed * zdot - g\n", " return xdot, xdotdot, zdot, zdotdot\n", "\n", "# Initial conditions: x0, v0_x, z0, v0_z.\n", "u0 = 0, v0 * np.cos(phi0), 0., v0 * np.sin(phi0)\n", "# Integrate up to tf unless we hit the target sooner.\n", "t0, tf = 0, 50\n", "\n", "def hit_target(t, u):\n", " # We've hit the target if the z-coordinate is 0.\n", " return u[2]\n", "# Stop the integration when we hit the target.\n", "hit_target.terminal = True\n", "# We must be moving downwards (don't stop before we begin moving upwards!)\n", "hit_target.direction = -1\n", "\n", "def max_height(t, u):\n", " # The maximum height is obtained when the z-velocity is zero.\n", " return u[3]\n", "\n", "soln = solve_ivp(deriv, (t0, tf), u0, dense_output=True,\n", " events=(hit_target, max_height))\n", "#print(soln)\n", "print('Time to target = {:.2f} s'.format(soln.t_events[0][0]))\n", "print('Time to highest point = {:.2f} s'.format(soln.t_events[1][0]))\n", "\n", "# A fine grid of time points from 0 until impact time.\n", "t = np.linspace(0, soln.t_events[0][0], 100)\n", "\n", "# Retrieve the solution for the time grid and plot the trajectory.\n", "sol = soln.sol(t)\n", "x, z = sol[0], sol[2]\n", "print('Range to target, xmax = {:.2f} m'.format(x[-1]))\n", "print('Maximum height, zmax = {:.2f} m'.format(max(z)))\n", "plt.plot(x, z)\n", "plt.xlabel('x /m')\n", "plt.ylabel('z /m')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d4c0700c-c8be-462b-a804-ecf408c52424", "metadata": {}, "source": [ "\n", "---\n", "\n", "The equation for governing the motion of a pendulum consisting of a mass at the end of a light, rigid rod of length $l$ may be written as\n", "\n", "$$ {d^2\\theta \\over dt^2} = - {g \\over l} sin \\theta $$\n", "\n", "where $\\theta$ is the angle the pendulum makes with the vertical.\n", "\n", "Taking $l=1$ m and $g$ = 9.81 m/s$^2$, determine the subsequent motion of the pendulum if it is stated at rest with an initial angle $\\theta_o = 45^\\circ$. Compare the motion with the harmonic approximation reached by assuming $\\theta$ is small, which has the analytical solution $\\theta = \\theta_o cos(\\omega t)$ with $\\omega = \\sqrt{g/l}$.\n", "\n", "

The provided second-order differential equation can, in fact, be wrangled into a single first-order differential equation but we choose here to reduce it to two such equations in variables $\\theta$ and $\\dot{\\theta}$:\n", "\\begin{align*}\n", "\\frac{\\mathrm{d}\\dot{\\theta}}{\\mathrm{d}t} = -\\frac{g}{l}\\sin\\theta,\\\\\n", "\\frac{\\mathrm{d}\\theta}{\\mathrm{d}t} = \\dot{\\theta}.\n", "\\end{align*}

" ] }, { "cell_type": "code", "execution_count": 14, "id": "bd3a9235-6dbd-40c8-a698-03e0b3384d9d", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.integrate import solve_ivp\n", "\n", "# Acceleration due to gravity (m.s-2), pendulum length (m).\n", "g, l = 9.81, 1\n", "omega = np.sqrt(g / l)\n", "omega2 = omega**2\n", "\n", "# Initial conditions.\n", "theta0, theta_dot0 = np.radians(45), 0\n", "y0 = (theta0, theta_dot0)\n", "\n", "def deriv(t, y, omega2):\n", " \"\"\"Return the derivatives dtheta/dt, d2theta/dt2.\"\"\"\n", " theta, theta_dot = y\n", " return theta_dot, -omega2 * np.sin(theta)\n", "\n", "# Integrate the differential equation from ti to tf secs.\n", "ti, tf = 0, 10\n", "soln = solve_ivp(deriv, (ti, tf), y0, args=(omega2,), dense_output=True)\n", "\n", "# A suitable grid of time points.\n", "t = np.linspace(ti, tf, 1000)\n", "theta = soln.sol(t)[0]\n", "\n", "# Small angle approximation - harmonic motion.\n", "theta_harmonic = theta0 * np.cos(omega * t)\n", "\n", "plt.plot(t, theta, c='k', label='Numerical solution')\n", "plt.plot(t, theta_harmonic, c='gray',ls='--',label='Harmonic approximation')\n", "plt.xlabel(r'$t\\;/\\mathrm{s}$')\n", "plt.ylabel(r'$\\theta\\;/\\mathrm{rad}$')\n", "plt.legend()\n", "plt.show()" ] }, { "attachments": { "3ece9595-d19e-4c16-8f05-b4839ae206ec.jpg": { "image/jpeg": 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FniubSMqyyB2+cOCmfUA1O5RYm026MMZW+WS2jlMg3kIyr6Ajk9fXtXO6ldWN5qBtrraZT8qPAA28noO5zTXkJ+Zq2fheGK4axtTNlF3M8jKRu7gccAdK5Y2V1H4llSW2MVyHLRHkjOePw96adxNEutXccl9JEbUW98i7HyuBL6g+tVNL0yw1UGL5oZscYbofpVapC3Zcl0qOEiOd8uqGJmwFOQeD+XFc9fadPYP+8XMZJCuOhoTE0U6KoQUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAV6F4C8MtKv8Aad1ZecZCEtY2XO71fH9frUzdkVFXZ6bFp8Nov2nUY42nVcIqHCxr6DpzXLXrXL3dyg09JkPKOZhx9R7VijRme13c2ryQeU0l0+HSMMuCvoorR1mW5Tw9ayajo4SKR93z7S/HPQHIqhGRJbJZwpqNrp8BeRMqkp++D1xzXNQXtl/bMd59h+zXELbtka4UHsce1UiWddpOrQm4aZJVDNnIJ61c3CadZScmM5z7VJRzPiG3trm7eWYlT94PjpXGwwzJeoYJAp3ZWUNwOeua0jsQ9zqzdLe6k0zIHSUhWC4boMZwK2dThuH09YbO2ibPH74VBRxGsaaLKEGVQlyH2uq8D8qxiMAe9aIhiUUxBRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAU9I2kdURSzMcAAZJNAHpvgXwBHNeQ3mqqkiJ8zRdQnoD2JP5CvWy1vpiqkcX72UkIVT1/hXsPpXPOV2bRVkc9rtncSapHHc72g4ISMnJz64qhfaPDpZmu5LhUTr5UYzk+mT6mhMbM+00ue7aK5aMW0LZClvvHjtRLLJbaqkUrNcInyoXbOF/GmSa9/Na3tk0NwpaPAxtXOAOvI6GvHrxooLyQshkjDkJKAf5/wBKqApFq8kjOjR3Fsh893ywI6L6/Wlgm1VdNN3HDLDsBLOM7SuOciq9SShca/Lc27204VomTAZRyD681iY5wOapKwm7mlZ2l9ZXsMpgdH5ZNx2Z9eTXTLqhuNVt0vtJkZ2XajGfHy9SRjANJ6jRzF5MsmrzrIHS3eY/K5yUGePyrOddkjLnODjNNCG0UxBRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQBd0vS7vWNQisbGEyzyHAA6AdyT2A9a9X0PwpZ6IpQiCaZ0w87KWPvjsBWc5dC4LqdlpMBtY1gjKlC5YkccV0FxdRBUBC4Q5BI5FYPc2RzuvwXV5YtdW9wEn8wIpxgFeeKp3UEUuiW8eoEmVn3sTweOB/OqRIonkgsbOK1U3TQZ6AA4/Hiq17eJcXcPmQx286AEHhuDzg0wNLVY7K7j8xFRLsKN0itgsB2PrXnWs+FII4ReW/nIJXwuW704OxMkQ3Pge8fRUuY9Q2PJIE2SfKG96tr4V1fw94dn82RLgT5wquSpFXzJk2Zzk2kWN7p6XWn25huYQBNAzZyfUZqQ+GYZJobnyitsygyBScKfX2p8wrE2u6IsMUc8N1IoVioATfj34rN0iSS9k+yz3KRyBgIt6YBxnp79fzoWqDZl3xRot86iULHIsCgu0ZwefUVlWvh0XWiHUYrnmPPmR7Og6UJ6A1qZrabItrJMGDhGAwvp60y7sJ7Py/MAIkUMCpz17fWquTYrYI7HikpgFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUoFAHq3hvQJ/Dvh9L7zB9s1ADcY+scRGdueuSeuPTHaugg2bTbtK8ceVG7b0H49awk7u5slbQuxaiLO7RQo8oxEh93f3FJqXiP8AslImu1YiVSynHAH19am1yrlx7yLXtJtfLma3hlHmKSuCcCqEDLeFrL7SGwMfvDkg+uKBEmm2zyztbPOoAO0lGywx/SsS4tY7nxFJ5U7sLd9rkHqBTW4mWZbdrjUlf98qMP3bRLkYHrVi7trm+tFh8xHTdjb/APX7GgC3rVo0Xh21tpyqRhgsciNnYwHGamtn+36ClrPIMopXcB3A4NHQDlbjQr2O5DWckMsb8sjEqfw60lg7lZ5Z4/LiUkOqnPAqr3EXY7LS9X00w2giMvl749knORXD6/CEtYrK5H2e/glYo7jbv+v6c047iZoyxXL2BaSRpIpkzKe6seSM9xxWJoF9NZx3EKsJrZ859V+op9BD9LCrezNAytkbxGT3rav7Jf3N6IxhkPmIy5GR0IHY4oe4LYwpPDgu7Br3TpX3nJMXbB7e1Yk2l3EREcibJtpbaRjd9PeqTJaKBUqSGBBHY0lUIKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACut8AaKmp68s91AZbO1G9+OC/8IPrzzj2qZOyHFXZ6zqCfbpGWKYlwc7CwGMD36VzdxcN5m8OhMT4MO7g47k+lYo1ZZ04Nr9whnlPlIcKi/Kufr3Ndtqej2ErWsf2aOZEUACVchSO+aTdmNakEunWd1CzTAxyRv8u09PUYrOvdOtYL63ujcO3JUKFAAHbkUJg0H9n6XJfvdTLcLdMhUlXYKR68d6i0dYLEziK5LkEq+8An6ZouwNOC/H2eQgjCg7cVy11ft/pVvZSIJtwkhV+Ax64+lCQMs61qct54eW3kSJQdpfa+4qR79O9c3Z6tNbLLCGZ+4+aqS0JbNTS9a+1pHIrRASZCkPnBHY+lJE1hDPiG5lcys3mxN0U/lRYdy3BoEdvfpe6Y6wKAd8LElc9yPTNY3i3RLrxFa+fHGEurc7VDHG4dx/WmnrcTWljkPD2sT2cz6Rervtrj93hzzG3Yg/WobO0udE8SxI8bNEX2k44ZDWhBPfaOJNaf7KJEVm+QqcEemK6KO6uLGW3i1GOTyccyMnQj1+tS9RrQ0NNu5LJb+1njLBpDLDIoyrI3I+mOar66Dd2pYDBVgv6f/XpdR9Dk7nTEvo2dhsnVeG9cetcy6FHZT1Bwa0TIY2imIKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAfGjSOqIpZmOAoGST6V9AaF4Xbwx4XtLeR2ju5f3sqq2DvI5B+nT8KzqPoaQXUkaxkuifMKIrZAAH3eOuRUkeh6LZW+0QrIzEZZ+dwzWVy7Gfq18un6h9nsrZnkiwUjRcZq+PFcJWG3uz5Nwx4TqSx7Ci1wuX5yXBkCJIijLKByayb68wqWvk5T76hBnB9/ehAyZpIbxWALeaqbevHFcnBe3Y1SeI2jrLIw3MOh96aEzRu4FiSVTHJuGM/OR1HOPQ1U23Ja2lEMjhVHlOT/d6cimITTree/S4sp7PaAhL7TgsM9ahi0f7MrRNZvIQAVCg5YHuD7U7gQ2FiNKvpBEh8snpInIz2NYGqXDC/N/agkMxG1c5BB5yKa1YmdppeoXN5o6zAxwOy9XyRn3xWVqfiC+0+3F2TE21iJEGcMTxwe3FJLUbehytrcQXTh2VWO7cPVT7V0lyqvYCUjI6Z96pkohskDXUDdcMBmuquSs+nMrIG3EAZHapZSOfvHEUu9MoSPLwOmOv9KffPi2DH+M/rTEY5iw3Tg1lt4duRNflYElWZP3J3cq2QfwPWqTFYyNcsTYXMcbxGKVowzjHB9xWXVIhhRTAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKAClFAHefC/RHvddOqMv7qxI2kjI8xvu/lyfyr22ZQEMdxLkA8v3Y+g9BXPUfvG0FoYGp3sEMD28zMqseNo2njv71LaaXfPYxTx258kj7zNwo9frUlEVxLJPawOISjglGA6n8aIrOyinF68OLggj5ucZ9PSmIWy865vpIbcgqeck4Aqk9pfjXRmGTarbSqjOD2oQFyWwg+wzX1hMryRy+XcwY+YH1qSzS5S7iZbMvG3JyvAz9aANV9FtZb50uo9yyAcBjwagTSl00tbbg0LfNGMfdpXAsWWnxtcK7KN+Nu7uV9KrarobCSO709gvlL88bk4K5ovqO2hTWKOaKaSeJS7KQxFZNt4LjEommZWikG6MqevPp2NUnYlouJoDaV5cNpICmSSXGSM8j8K57xFpl1eu8EkcRLRkPtPBPUGmnqDWh5VNBeadc+U6tHIOnvXU2Wtb9Ba2uUZLgyALlcBgO9avUzRp6UwaRRj3rp5H/wBERMdGzWbLRzt06PdGN87S2eOvFGpf8ekbEnggCmIDZuYkmjUuuMFR1zU9tcRSZWP70Z2upGCD7ikBS8YxWlz4fa5kgzcQsFRweRn+leaVpDYmW4UVRIUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFKKAPoz4caV/Y/guzjyvn3n+kMemNwGAfoMVsahBDG6oW89t27c3G0+wrlbvI6EtCGS0hu42mk2tOoOFbovf8eKuJqclvppinjaKMHaplG0sB3A9PeluMzLy6h1bSmSKRd8L5U5x+Ga5tLy4jf7JLC7q+QGPO38apEsgspdSi8ShIECWKKRIxPB966WK6u11sXltbFg6hXKnhwOmfcU2JGzPGQRfx26o8n+vQY+b3q/p11EyY2KR6GpGJcsPMyODj5TVfU8iNGA5XigZBZ3RV0YEj1Ge9X5ZQ1tKnU44pAYCII5DuAKHI+tTqiBFRCwWPlMNnHt9KoRMYxcM2Thgwx+Vc7qRO1Zv4hwaEDOC8QWcc7b9orl9SDwxRSAkoCc89DWyMmdB4ZukuWB3gFR82T0ro768RbmGxjkAuHUuqHqwHp+RqXuUtjmr69WQSyW+WmjAKqByQcZ4+lak1xaX3h95I3BcuNgYEEdQQR/npQBHY/avsh8iN/l+7GxJxx2JrMuLm6TUPPh2pcthZYJRjcB3oQCeIL6S50p7NEAkYhnAOenOBXC1cdiJBRVCCigAooAKKACigAooAKKACigAooAKKACigAooAKKACigBRTlUsQo6ngUAfR8l1qFtaxQfZfmCpEHHqAB26VeB3ypFlS2Ad2eh759q5ToK6rewapvbBiJJwB2q7rOmLqNqtyrgSL1VvSjqHQw5bNbPS2jiybgycrjA/D2qbTdL1WOxWS7gKp94qOcknjjrwKdxGwdNEandEFjkGAcd+4qW1tvsjGNIlweQR60gJXcvC0bYBzis+B5bO5xIrBH5Ukd/SmBfuH8yHevVCCcelNupPPthyPu9PSkMy4CQ684+bFa24kE5/GhgY8j5lf3pySHdgelMQ7zjGxYHkVnz4nhkGMhufpQBxupwhYjvBAZTsbtuz0P1rmlSF1lt7tG2Mv+SK1RDH6TpcemSTT+asynAxjouec1q6rFZ4trrfjaCoZTkpn0NDeoktCmlo32SI4SWVHK78clT60lxIEsJ9oVt3y8Hp60AdJp7fZLeIKclVHfrWL4vcPdWWoRLmaHIk7EqegNStynsc288d5E7OjC6BbC5xnI5I/CubdCjlT2rVGbG0UxBRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAtaWgWn2/xBp1qV3CW5jVh7bhn9M0nsNbn0RdyzbStqGwJCue3/66sW9lFHF5rOGBBDA9sd8965ToM959QuL+CK1UXESEtNID8qD0z3Jq5PdzLC6shj5wd1MRUkH2V47idgWOcAdq39GvzJKhk3Agcbv50MDrZraG+sjEQMtyD71xd47Wk219yhTtz6GhCY2eQvAlwP721ves24unXIDZHoaYFm1vRhWB6jBp13dHyQ+AFJ25A70hmVcXS2ts0z8LuAY+gzWpDco0IdnGzBOc9fSmIzGcFyc9s0lpOs980KsNyjlTwaAILy/8q1MgGVHJz3FM8O363m10IeM9R1p20DqYXiyCO21cxRW7iEpvGM7Tjqvsa5C4LEB9jKmON4xn2+tXHYhlVtVl0qGEvCGZznkdQD616BoOrab4gsJ444lZCCrxSL8yEj/ODRJaXCL1sYGqo1jaNdxFcW/yuucbscA/WqPhy1j1OB5GJKFycf0o6XDrY6VtPtYgscLMs2OFJ4NcHrcksCTyh5UaSYqY39R1IoiEjMjv45JrbzGxt4Y+meKbrNsiahKI8ZXlh/WtOpBlUUxEkkRQBs7kPRh0NRng4oAKKACigAooAKKACigAooAKKACigAooAKKACigAooAK7j4U2vneM0nKbvs0LSj2PCg/rUz+FlR3Pbb6zaUqwmBwCwC8DdWdpi3myRJYt0KZwX7muY3JHvms0iMQSNDlHjQY5qbUXzBHPbxy7/L3bj0ODg0xGY5a5053YMzw/Nx2qPT9eENypuGJHQtTsI9K07UYprOFo3DZGcis7VkSW5MhAZZF2shHDVIzEntlgjEduSE7ITWJfyCJwsisjn14yKpCMyXVY9NnLTsRbyAYfHCmtuC6hv8ASblI5FcFNykHIBHINNoEVElhlT7PcsMbdrqCCDTp4bSGzMcHyoOeKQGfY3iTliZ1CqcNVjUIhAv263+/HySQcjjnBHb60wIIryK70uSH7khA4YVmeH7RdH1S7kS7C29wQyxnojH/AOuafkIlnmv57O8s7kNI/wA4R+vuP8PwrD06a3v9Il0zUI8OW7HpjuD2NNeQmZfirTPKsIBGzOkZ+Vm/h9iak8G+RYWpl88pczE4x2A6A/zqr+6T1Lmp7r7RL+3Q75cbvdiDmq/w/uYWjltXcLOrZCnqVpfZH1NHWNS1DSPEsIuYfMsZSAkij7ue/wCFYfifUbO71b7AgV4ch93+0R0FOK7A2ZV9o0Flf2gKfJKBkBuDg8kfUViXW9LyQ5YhWIBPpVp3IZCAplAHKk1ZmsGAeSIhoxzjPNAh2mxmZ5In/wBUVywPY9jVIgBiAcjNMBKKACigAooAKKACigAooAKKACigAooAKKACigAooAK9V+DGlPdXeqXTB1iMS26yKcYYncefYAfnUVPhKhueryWgtWhgSQzdgT1z/wDXqpeIkEgi88pIcYXOQf8A69c6NzOnlQmFUVpAx4wvOc1YutZjjxbyMIvmA2vxz9KdhXL0N3bxOsaBNzDLkfxGmzaDp17ukQCNj95R0+oo2Afp2ktp42LdlQh3Iyn+Yq5d3BktGyfnXv70AZYuhdWzqThkPFQ3cY1fTjaSFftCAmJyeVPpn0NMRxkwuLXT5kv41dASR36Vh6B4iMN6beEFYnJC47VaV0Tex0NzaTmSGaGVGhkyXDHmnabNNaTLDdoJY5Aw55wQeKXQZl3WuW1vqlxp0dtsaV8DC988V19nNJ/Y852hpBGR6jNJoEzK0nVbe9lZSo2qdrBk6VNpmo2l7ql9aJGirFIUK7eR6H8aLBcy5LpNRnMtpIY5wwEigfxA4PFc7qG5NZlLcfNgsoxzVITNWISyQuI5ElBTG1xkGo9OsFt9SimtlVYyhWSB1yM+ooEWLTSLp7vy7Yx/aIss0eeSOwrmy8F3qC6nERbXMc/JUY5HXI96aBnYPcNqCKswVgF4GOM+teVaxDLBrdxGy7X8zj+lOApGnquoSXsVuyribOCpHQ//AKxWVFdLJJJHcptR87m/umqSJZRaNk2kglT0PrVm5mcMjwyEK6jIB6HvmmIvrAzgSKAGaMbyvRjVKbTpQC8Q3LjJHcUJjsUaKYgooAKKACigAooAKKACigAooAKKACigAooAKKAFFfQPgFTa+CNMjtYwkk8Tytgfebc3J/ACs6uxdPc2l8+Jpbq7k3OihREvROvPuaX7dY2sCXt4qyjBKSP0HODxWJsY974gSDU7SO2gdmlfEcYGCoI/pS6v4Yu/EOqK93OVihVSzqfvce1Naak7ly6s4LJ4kTLKmAHyQalivtnAYnHQ0DJXviyhgTzT/taSROGPUc0gMS5juSHMbABuPMXqMdCaoSw6tp8rXFxOGcjIVegGOKokfY6lHqMbieLKnhg4qLTNIsorueVbeIAjA460bBuX7xo7i0eAxoCikrtAGD2xWLbTNDOWuV/dxAfMaEDNGe006+xfJEq3g5EvXNS2qXH2KVIoy8mfu4o9Rg8EbWrJFB9nl27myuN3tUejtauJLowqt0flZ+hIFAGRa2I0zWbh2BCSDevpzWD4gka31JnkXMb8kjpVrch7DdKvMI3kvvBONvpXQ2BVgs4IIPBIpMaK+r3FzpGo/wBrWMji4MWHjxlZEHf6isO2a11WzmIZdxBZWHUN15pra4nvY2dL3XGnPNGczImAM9xWHqF/Yava3n2lY1uogXgY8NleooW4M55bhFhtr9SW2ylZ4mGcdOR9aieaynjuhyv7wMmBglT2qyC7cWsF1Yy3Awkucpt45HHSucJ5OaaBmvp16DAbdRiQDKluRx2pNVvo7iKF7dQhwVkx60rahfQpXF0ksKIseCAMk9c1VqhBRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAXNL0+bVdUttPtgDNcSLGmTgZJr6atbOLTNNs7JIliSBBGgB5wPX61jVeyNaaGult50jSjcj/ACsu7gGqbtawXqwSos0KruiwMBTWRoZ9yFttWijiMLXDbjE6jkJjnNWbibVLR4zHHlNoXcO/1qiR0hd0L3DFS3UYrPniMLrJBJ5iMMgNwaEBUub+aBQVUqCclSOKhWe6K/vOHZgVBOOKYjQtr1oJ2tpFB3dVPTFR6xLJIBJHhlxjr0pdRktvYRhYblWRwRhx6cfrXO3+pm11tLXayLPIEYoDgD1FNaiZu3iJB/ofmbWwNsjc5+tV5dGJs3iuHEsE6EeZH1Uj1ouBz+h282nXVwjyTvbxrkIe3PUV0Z1qJbcXaDARx5hHYZpvVgtDohex33h68bcGDQlo3HY9RiuVsw8kTIT5cgbcGPANShsW6hmiKNIA6iMrwc98g/hz+dcndl41nN0qy2pBKHdzirRLIrPTlt9Mj1K1kzEuPMUnp/k1vaVPbLGfIy0bNnDc/Wm9RI2fs1tdugmTIVCnXsetcrqXgD+zoJLvTNRKleTHIP6ikpWG1cg8OaZq2ZljkTzFPy/Nw2apXbtcSXFhqFpGlyIyNrphlYck8deO4quuhPQ5+z8m7sp0LbZUXJB/iQdwfUcVTsLe3k1NIZ5VEJJBbOAeOP6VZJ0Vroc1vBKtynmWx+ZJEYHFczeWn2aQlTujLEA9/wAaSY2h2nhmaRYwDKVygPfHWo7gx4AETRyA/OD0pkkMmzefLzt7Z602mAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFAoA7L4YQLL44tJHj3rCkkmPQ7SB+pFe5XMTPbCWabMrEkhP4R2H5VhU+I2p7HPXUrxMJll3QRv8AvXJGCPX8OOK3IIrWRBJOFlhVgAmcADvUFFZNNgbVibb513bhITxsHI5qG61UxzPEwZSDjFG4FePUFlfD4YHjB71DfsxI8pCOMhQOlMRg6pfXEFm0hj8zsAOoNS+EL64vGuWv1+UKAiuvJ/OqtoK+pr3tnBdO9xA7RzhSQueDWT5U4tPIvMguGwydqSAm8Lte2sUsN46bB8sJzkn6iuhv4LUR+fNbxyptADgYZHHah7jWxg61pseo75IryS2A2lTnoeh/WpdJS80uGKCec3MYBbzQc8Y496L6WF1IrhVFxG+91R0OGC/KcH7p96y9b064tbcnT5PNVs5RhyR6e9NAybwje3EOjmzu0MOWIUN0I/wqp4tmvNLvLW7sj5luyYKgZAbPI9qf2hdDfnuiulWwaPErnOO4BFYV7BFcNeWDwhV8nenGCD6ikhs5nXbn+z9ItrSLIV2y/vimaDrdukqwyyBCxwN3AzWlroi+p6FaSgbSTyTgVV1i6xYzHdwGAJrPqX0HaEgjtFkHLSfNxVLx9pEtxZWus2scguYCVdlHOOoP86E9RPY8rlaPYXTckjDBweCO9V4pGilWRDhlORW5kdnoerR3dhIlx5cJiIGRwrZ6fjxQ+lR6lE21RuOWUHue1Z7MvdHIRPJY3qsyESRNhlP6itPU5Le4iN5bOD5g8uRWHt1+tWSYlOwuM578imIJEEcjKGDAHqOhptABRQAUUAFFABRQAUUAFFABRQAUUAFFABSigD1T4UaYIoLnVXOHmf7PEPYcsf5flXpcsEEqrFG7AkEjLdDjv7VzzfvG8VocfeacrXElobgsiyefOi9Cey/T5a1bC7h1PTZRK/kyRSFSkfO4Y7+lAFWxW4uri6tY7r7HFtjWPbztVc5H1rRvIoJZCdx3Due9IDHnjdDkH8RVO61abT7QgMxIyQW7e1UtRGN4d1c32pva3AZmuGLRt1CMBn8uK6a1uZbaRpo9pIb95H0JHtQ0JMks7pprqWcROkCOFDMOvrWjaSZkuGeNQsi5Qkc5qWUjDuJGa7yrLGynJ3cCrcWuwXzS20ZEm9cOV6H3+tOwrjLmVTaCWNgNgKSQuMhs96hiMrW4+UBWyPlOCo9KAJb+D5oIllBYkbkPoe/1qrcXCpc29tJlhkqGPTPbNCAsSyW+nxBJVjMzEfdOQKy7LVxFPNay7ZFUkgNyCKdgubFldi8lVyQQO1SeIrPzoReW6gXHlmNlB6p3/lS2YdDitX06PVdI24KXseXiJbiQDqPrXn5UjrW0TOR3nhnWJLmzMEzZePBDHqPQj3rpoVjmsJba4QlmIAb+8OuazkrMtbFYwXNpZSRadOWliIZEY8EDqPyrprO+N5YIvlELJhij9uKTGjzTx34a/svF3bxhbaSUkheik9fwzXEbG3BcHJ6VrF3RlJWZfkXyitmzeXEwDMf9oe/1qXT9butNlCb/ADYQeVzn8jTtcL2NrV2ttQ0U3yxqWPzbiBurIit1l0xXUgwq3z8YKn39aS2GzIkj2YYHKN0NWNNMP2sCdVMbDB3dBVEleYqZn2ABdxwB6UygAooAKKACigAooAKKACigAooAKKACigBakhheeZIYlLSSMFVR3JOAKAPpHw9pcGh6BaWWwM8KFWP+3jLH8yapXuofYXmnYEgqAq475rl3Z0bIrx2xaCaZAvnyYEijlgT6/lVjw7o0Gl2xW7VmuLuVm64xngD/AD6076CsXYYIYzMLdQkiNyXGc+1U7mykZzIjKUPPBoQFG6051XfHcF1J/EVnvaxTxvbzSOGYfKf6U7isXre0so1VbS3WKVQFDAcnsRUd5py2w3y8Nyc5ouFjlb/xDcxSGC2+djwSMn8K7GyV7rTY5Z3aCU8qMZ7DrTasJM47UNVu5L2W1igYtGSHIGc+v4VreFrF7KzkuSjebKpAXhSPoab0QLck1SWW8kTzCyqgG7byWA4/E0+9dNJle3WVC7MuwueoI5pDJ7tt1t9rePypl4DnjAqtaQ3EtpJLGiTYcAODu3L1z+FAGN4g1m2AazlZ92c7scg1yl1ebzH5ZYMi4Mmfmb3NXFENnU+ENXRi9vI3zkgoc8+9dhrEk8Vvp7RruVpGDgdcY61ElqUnoY0KebeTxRbTGwby1YdD6/nXlCI8V8sbrh1kCsp+uCKuBMjVjnXSNbmhXcU3lM+grvIb4xw5GZIyAAVIyPU0SQ4kFheqbuRC3G4/N6iuvslXapP3SM1DKRVuIU1nSbi2kjVhICArD7pHT9RXlPiDT/7P1aUGCQeXGucnoegqoPoTIltNPtNU0F0gLCWIkqzjoeuK5cggkEcjrWiIZtaUVewltppG2SNlQD90+oqi8z2TS2ed8W7kdKACa3iW0t5UlDRlsSAdUJ9fwqWS2t000zENzLhSpzkUAUJo1jcBH3qQGB/xqOmIKKACigAooAKKACigAooAKKACigAooAWu7+FWkrqPi4XDxCRLKIzAHpv6L/U/hUydoscdz2WW5ktA0jqM54OO/fFYVzi71BBHGGjZd7Kf4T1A/OudG5bsG+xRyTTFDNcFWlIHcDgCmXMkl1cRXDqQsThl+b7xFMCzJerPbHcVSVmO3t+dZaTtKGjDgP2JOAaEJkTwX2wgbTnn5TmsuaSRdpk2gjkZ4poRJDeTW8Rlc9eQfWon8W2M6LaPukErBWx25xnJp2uFypJLo+h3D25jYyMSRKefxqLRpdUS6mu5cJacsqS85OMAj+dP1EVnkvru/SKIFGRiZnjGdwzx9a09alnm0yA6dKI3jJ8xXODj1oAw9JuL0Xq3AbdP/wAs9zdT3GK6G60r+3bi21GdfJuYyPMUDg+lD0YLU17rTk1XTJrSKcxTscBc5Dj19qwfDlrPo0c0buWALZB6enFJPSw+tzP1Kxju9YhgjUMHi8wnqce1Qa1plrFdMlvtPyhenOcDNUmTYz9L09LJjPJK0TD7rY6V195qEOoadHD5+Xhy29eOSMUS1YIp6fPHuSNl/ex5y3f61n+KdEtblvtkEP748sVOM+9JOzG9Ucglu5muWnUlowCrN1NXk1SbTWtvMgdoZBkHPDDPatNyNi/Pc2sReWF2KHjZ9etdjoepC506D95v2AKW7sahrQtPU3xJyHIAHb61i61YXX2w6haG3njeEwz204wGB4yD2qENnAXWdKivrdbK4S3wfKcNyhI6n1FZfhyxe8vZHKqY1Qhi3cnt9a26XM+pTa5uLB5LfCMgyuGUHv1HoaoMxdizHJJyTTRIBmClQTtPUetGTgjJwe1MBKKACigAooAKKACigAooAKKACigAooAKWgBRXtnwa09bfQr3UWGJJ5wq57og5/Vj+VZ1H7pcNz0O/WCa1Mj8ADCDH61xrIUjgiiVi1xfIrsT0wQf5CsUas3mt/Pujbsq7ACOnJI7Crn2KGe2RQiQ4XHOcg0AZcunfZJvNl2yKOhXpWdLYPPJuhTAPQ9KaYhRDcW6kPIuQMjv+tZFwUuWZZVyVHBzTQii/wBqlUwra5iUZEmcD6U1NMsrSyeeG3XzC2GbOcd6oRx92Lm/1cxLukcttUdTXodxYfYNOtLYttMcQEhIzzTfQSMW0vmMOoo8qqsAUoUHzdas3llBaW9xf3V1JIs6gHA+4PSkMr6HdafqOpwqsLboVcoAOG9M12moafA9sY4z5ZwHALYw3+FJ6Ma2M52axigeFS537WOckCq15NLFrDSWoE1uy8rn7pxSA5o695ckbmyDXMMv7tl+U7e+cVraktrc2325Skcm3lW4yaq1hbnM2U8txPLbOm6JuWIPGRnGPzqJI54buN0ZtokHC87hVEltL64s9Uinhcm1jdt6O2CN3XrWmmqQ3V9O6lPs7HCjPAak0NMmu9It7ywkGcKR8xxnbkYyKwIdGmtNPjtp/JuI4pi4xnoeOD+tCYNGQ9j54PkzMrxn5l9Peug8PWlwumrKHZAzb4yPb0pt6CSOkTUbmRo48qdh3SAHseKbqWrCEJFuAMjYANRYq5Q1JY7iwmjkx80ZJrJ0O2WxslhwN5YsWqugupjeItGghtpryKTbJHKEdCPv55yK5WtIvQhk9zD9n2RlTvKht2eCCMjFQUxBRQAUUAFFABRQAUUAFFABRQAUUAFFABS0ASQxPPNHDGMu7BVHqScCvqbQdCg8Oadb6ZH8yw22w4Xl5CQWP4nNZVX0NKa6jDv8tY7hgShz9Mk/yqlb2qPfRqchGlLqD/Dxj+VYmptQQxqxuUbEykhM/wA6rX9xuYl1w/fAxmgDLGpKJDDIMqe/oabLfDyuMBT6d6YjJubpip54qhpcsN7ptxPwWW5ZM47ADFUSZl1rMejyJ+5EiFsHmtK0ezu9OE0JKw3Gcg/wNTt1C/QSz0XS9IlW7jfzZzk7296brWpC4gaSL/XIMFM9fSjdhsZOjae3lXN0zwtcSR7ghb7rZ6e9T2Ilv7KWGVQyTAhjn7vpgU2IpaPoc1ll0LCZX4P0rp5tQWexe2vJVil3ZBPViOwpPUFoVpYpDZKqAlc8HHQ1UUtEuAP3id/WhDM6ayEtz5yjG8gEVTlWdg8TMxXJ2iqJICwt2L/xdMD1rBu55proRhyqn7uD3qkSyXUJZJrS2UsSyjDN61QVJSQqOQd2QfWmgOntdbnstJlSdvMkIKBR1/GlXU2bShKsZ3bx8vqKmxVypFOr3PmlPLZxtbPGQe1b0UbQWltbJvEMWQo9RSYIXRN26ZZTkpIy7s9qzNYla80m6d5MNbfc39cA+tC3DoMg1DfoiJdkb2UMr5yGGcVp2Vm0tsDG6ndyCaHoCMTWYLmLdbXSOinOM9CK464ha3naNgQRVxJkJJM8qoHOdi7R9KjqiQooAKKACigAooAKKACigAooAKKACigApaANzwdbi68Z6LCRkNexZH0YH+lfSus3dxpwMsuFKtuxmsKu6NaexOIEEk4wPMI3Yz39P1rMn86G+SUgGNH2rjp0zmszQ0Vjiu4hLEdsinDKe30pssUTxBZWVmAxQBh6hbRsCAoUjv6is9bHyLfyw+Sx3DuBVJiZCbKEI3nMx4xt6VDLZWmn2wktceRMNzYPR+/FMRzeuadBe2qypIFZux7Gsu2lazsp7KC63Mh3sNh9gcGqWxPUjubq9i08eZP16A9axTezO+XdicYzmqSJbOw0BZhoaTxQMcykGTHT3qLTLLULXUS8khWJj19ako7LT/JtzL9plSNHOA8ndz0Aqve6KRNCHbc8eXQ/3gf8Km4yb5IggbJVDyB3qneW6l2eAlg4IwRyBQgM8xxxCNbjcMqT0xmmzWz2to17LGGWXOwdwcfzqhGJqUSrpPmmImfcoyD+efwrAmgDXMghJMSDIJ61aJYgxNF5efmH61lSM8l15YXaEOOOtNEsuare7re1K8TLnc3qKdNfi50uMQSn7SG+dduOKLDuCCaa1tZNxYxzfMp9PWuvi1Np9QtbMRkRqpZ2XkZqWhotNFb2d062jF43y7qTnaxPQGi4sLe/tnUJskIwTj+YqSjl9X0t4NGaPyyjwnIUHj3xVXwv4hksrlLO5ctbOcKSeUP+FXuiNmdxqU1te6FcrMocRpvUjqMc15rKkWpwXN0pdZIEB2kdRmlEcjIorQgKKACigAooAKKACigAooAKKACigAooAKWgDovArTp450ZrcAyC6Xg9MfxfpmvoTUkbWLlbeQkwk5c+3WsKu5rT2NF5DHpwDlty5UEjBIHQ1RsNQivVmhDbpIjzu9SM8/57VmaGikcEGZFLbnGcE8Vm3ksTP8xIHqKEBgXV8z6itim5g8bEv2XFJFDJFaooZpGycs3qT2+lUSZ1y8uWUkjPXFVrWApbXEgiaVXbbtZyQO+QPxpiM2aLN6u9VMeduwHAB9qvpZReRiJAZf4vl5NMDm9f0hmla6lkKoo+6BWTo9g+q6iEWPMYOXP91atPQhrU7pyNHmSaGXbaiPYY8ZU59R9ea07XULC/WC1K+ZNEN0jemen9azfctDtQ0xZYoiSCIJPMAPf/APVVPUb12vrR2ufLXKhRuxuINCA1wDMrSyhR3Y+lIyw3FuRDyJFKbl6jNIZmz2ks0SsY98drktkdc8YrVWGCZbd1CSWvlFZYG6g+opiOYvdLkNsVgiZ1x90joaybnQ5bC3MYQ7pjsBIzjPrVJktHPNp+dNguoiyTmZlaJuuB3FQRrBfTzsR5UyLnLd+x/GrJM7UFEMn2eZTnggitPTLO2WzaUh0cDIzyGpvYFuUZbqKC7ZckKD0rptDuhZxPOr5aX5kzyPf/AD7UnsC3LUNrJFYg28vmEncD3PPNdDApKD5McVDLRX1mKNorYPhTJIIl3cBiegrj9T8JxFvtVpOI1z80bDoQecEU4uwmrk2y9SSKBZVaJkPmj19Kw7+FtJguIkjKmb5SDyAPUH6cY96pEsxpYgttA3G593Htnimxx9GcZB4A96skSaIwvtJz3qOgAooAKKACigAooAKKACigAooAKKACloA6z4bQtL4/0oKu4K7M3soU5NfU8kNrDJkRKqZ5OPyrnq7m1PYxdVy+7PIrz7Q5ZrHW76WSQBd7KUPfGCD+WalbFM7Wa4jktY5oWUxOgZcHNYV7K23I6n1oQMw9Bac3l+t3uEIkDRtg8k9h7DFdCiYZfN4w/I5NNiQkunPNK64AjPRielUpNMe0t5ADncct7UXCxnnTreQxu2Cc5JPStldGB2yQ3CM7kE44/ChsLGPPYpeC4t3Taynhj39qjtf7N8O6dJcxIkoz+9UcGn5CLN1BHfafb3NuMRTRCQRscleadp9nDHeq5j2l0zuA6+1AzqHtofICMFd2Zcqf7pPNcj4t0FIr5PLVtsRDJzzg9KSeoM1dPuo/sDGWMkMu0g9eeK53xQ02lQo+nOwU8BSCGDDrx3prcT2NYS3K+HLeRmHmTlfMB7+o+tZhvpY8uRsRcgjuKLATQ6ukybg3PStGRV1O3iTeFdGBz7UbAcp4s0xzK7qmyQtlcdGHrXKXVvI9ozSRjzihDFeCTVxehLQy+sV1GRGjfY5QDDdM9xW3BYutisO1TMEIVMj5sDpTbEjh7pFkvXIDgKB5isMFT0I/A1LFdzCEwRnJA/Annn8jVknUaTfSpFASpcjIZR3rrrLUI5ccfhWUkaJmd4uvkOmwR4USBw4z/eB4x71iWN1JLEIJ0O8sCffnJppaCe5NpG43k6zgFlcjg56dv1FVr2W0udN/tebYWjmykR/iAJAU++eafURgvpPlW8t3NG+zy2ZMDIUnp/M1R02ISiRW59Ae1VcmxUugVuHU/wAJxUNUIKKACigAooAKKACigAooAKKACigBaWgDp/h5evY+PdIkXPzz+U30cFf619R3IkhRkblT/KuerubU9jlpdSY3Vxa8gwYyT0IIzx61z9wti118p2TxjdID/GrcZ/X+VSimbWkabLY6HFbMS4WRypPZScgfrVlNNSRh5iM+7jg9KAK4TypFiI+Td0C06b/R7osjYDH1oAqXeogMxz83r0qjpOtHVru7iRw8NuuG3J39M07CuS4jwzMo64OaxLeS7ufFsFva7zbxcuwztB6/nTA6O/RJnuvKKq3Oe2cVxF/pk80huJCJIVyNjfdLe+KIsTNHw1c3V5KdyeVDCojWIfdwPSt3wzeyXZP2mPADnCkdBmhoEatnC0c0s0w5ZvlLHoPQVneII1ubxdRBLqAI/LI7jvSQyk0rPbNCMKT0JHQ08SLqduIbgKZY+OecHGM0AJqFs8sf2ZWO1cECM4I9xWDrrTFWjn8xTGMRuwwXFNCZ5+97dWty0qSNtJx7V2vg3WpLycwzNll6GtJLQiL1NDxmbmHVrdm2vbzKAjKemPWsHXrV4orV8qpkjIO0dKldCmZVrL5MkYnBIJwMCteRA7hYJBu6ru4/WmxIx9T0zzzJOYSkxGZePvD1rn9LjS4vmiyVLZ2t6VSehLWps2ySHT5Z1IElq5Dn0I71qaLf+bdxzKww4xLGe3oRSY0VPEV0LqS8t5kYKsitH/u+1Z0V55FyGEh38Y5/hOKaWgPc1ZJYrCSGSSXDXMgAYHBx61V8U6alpHaYul8q5nJ6cLgAZP50luDLN7/a2ii4lhMdzbyoFkjYE7Rtxke2KyWgiW5a6tItkEkakr2Vsc4poTOeuJDLcSOe5qKrJCigAooAKKACigAooAKKACigAooAWigDU8NFx4o0nZnd9sixj/fFfWmqXIZSEGSKwq7o2p7HH3UTebNKVO5znjpnGK5DxDBMl7ZTxE/vEaFyPfj+eKmI2dp4L1KXWNDCzEhg7gE+owT/ADNaF1LLpzFkfbnjI70uthmbLqDM2TkeuKoXlyHKhHyG5IbtQBFdRLcRsR9/Hr1NVNE0kaT9vm8/d9oI3x/3cdD/ADp30FYY16JL2O3UMVkbaxHb3resUtLIORJtIyvpzQwRTuIooVd3lYxyggMKh0uGG/0qa3SUeYH3DPfFADbcQ2EkMef3sxYKi8cj/wCvUdpe6gku2S0jgIyZNo4BFAGwt5cXVmzmMlcZ34/WlLfa4dkLA45GfX2pDM292PMuwCN2B35GC2OlZsVssEVxP5zrK7AD0U/5NUhEJfUbbVEwVdByCxxke1X9XvY7/QCZI8TI2QDyV7EUCOS1vwi0kVvPbOvlMm6QcDafX6VLomlzaddksGUvhkPYr7VXNdE21LeuxXWq3ELrKUVAVJXpwR+XU/lVTV7iJr+3szCTAse4N/fbocH260IbDw1p5u4JGuCr+W5CjHIUd6geFpryLZGGgDMGHcjpTvqLoLq1xBaTokrn7oRQDyq56mqcfhiCQfarCVvtBGQhHBP9KL2C1yheRPpdybe5tp0a6kAkVeCQe9XtIsUtfEM9i7b1cB4pAOCPQ+9PoLqGspHHbz6hkrJAdnkydJVzjg+tZH9liR0vIY3aNlwY88oPahA0RX2XtR5ttJNBH/y0Tqmf/wBVVtbuvt1jayRMzQRkoN3YnHX8qpCZuSavavpMcV1KYnlhEeMdMDFYy6g+jh7R5TKu3fHIjcEEccUkgbOfJyST3pKskKKACigAooAKKACigAooAKKACigApaANjwnKkHi7R5ZASi3kWQP94V9XukYhQsSO2fSuerubU9jAvhiTy0xjNcTrvnRTyqW3xvEVCHorcYbPapiUzoPCUT2Gl7TKrOJSSEOR83Jx+ddBcJblW85/NA5HOKT3Doc951pqIaSyc+WsjRtkfdYdRVa8a0sYZZZN8jIpb5eufaqEKsE3lxSMhjDoCFbqCexqa0iZ1mXA4HegDB1K5fSR9qjALRHcV9R3FR3c0HifSXu7RniBOyRCcFW9van5i8jV0SCWPRo7O5cPhcbsZxjOP0pkNt/ZjSuykMhO0k4BpDG2ca313FLvUYztJPc1eWMxXHkzy4k3EEM2Q4PpQBUtrnWbO8ubOWBXtFOY8cEqf50/RpC+oXFqAwYDdGPX25oYFnUZYzbMxX50baTjnHtWfeutlZi4ZDtkIzn2oQFy5w8Nk6ohVumB3rO1C3cTJcKVIAJaMHBK+3vQgZWs7oxoY7vDqy7SGHGKdaXEUDRRSQlowdsfOdo9PWqEWtd05Rpa/wBnHyZZGJ2MflPcnnpVAojWCvcWnmqpHJHK+pBpJgUb6FLCzEmmySKkpIfJyV9qracJIpI2kVjtPUVQjivE13NJ4hu2bIBbCgjHy44rf8H3kzRtG7MNuPLOent71bXukLc2LfVn1DxDOL2PbLAFRUI7DPI/OqN1eWkHxCkIfy4/KRcdtxxnH51KRVzofEvhz+0dJaaKceXbZldGGCAO4Pf6Vx9rM1vfQpv/AHVwuFPbIoi7oGtR+mfadGvrxJV8yCZjwwypU55rAjsJjDLLCha2JLYHI4qkSzMvbsXGxVGEUdPeoJp3ncO5HChQB0AAwBVEkdFMAooAKKACigAooAKKACigAooAKKACloAs6deNp+pWt6ihmt5klAPfaQf6V9YR3I1CwhuYWHkXUSyR57AjOP1FYVd0bU9jCvHe3+dmJx+lYWvW32uxd0UhmU4Ge9Qima3hG08vR4pNpDShSWbkFh1/Hk1c1SEl2jgfLtwR3o6h0Kem6RFo+nG2Q5klkMjEnJJNRyWReTL8KOTTuIgnmczly3fgGqc811C5UykAdRQBTvFtNQiaGR9m5cE9aq3RHhjR2g06MStKQ5yM57VS7C8zT0vURcNHd26MoeACZCpAU9yPxqlJqWZJ4b1iYCRywwR7g0rDuX7KG3ubKGONxheRIrYz6GoP+Eev7jWIb+ScyRxtwE6Y7UXsFjr9SuJ9PsldojhTt8xcH8/SnWy2Wq2ZuTH5c8S8Tr8pyfX1FSMzIEsrlmimjZTu+Yhjng9apX8SJd+Sjo8YYH5vusD3+vT8qYhsbTWd95E4IjBDHZzhD3HtVW+vIr2S5ljZRsyFYelMDlr/AFUWcMe9TJExILDsaitdUlmvII443kgPPmAHiqsTc7izjW7fEjny8cMe1VrAiaK7tH3LIjlAc5DAHrUFFbRpLS91+407UYxErKwEbjAYA/eB9e9clrOpnR9Taxdz5EUrBH67wDwfyxVpa2JexcuNLtdfNtKxXdsDLJjG9e4ptzobaRKZEINsF3MUPKfUU79BW6kBnklu21W2KS4jEeAOcZ5rJ8TW1nNqenTqGAn+Wd19sfrimtxPY6U61ImiPZC5EiviMlhy6en/ANesK/R7OG0dYwyo5LAj9aSGxNW1U/2TM8S7Qw2hvrWV4f15LWI2k6jbg7GPf2NUloJvU565XZcyqBgBjxUVWQFFABRQAUUAFFABRQAUUAFFABRQAUUAFLQADrX078PrxtQ+H+kyOMbYPLBPTKEr/ICsa2yNae5bvzm3K+VvBOOnNNu9ODRlkA2Kuc+9ZI0ZRAn0fT9OSCQSReYsMyEHkMev1GauTQCK5kbO3A3DnnNADVuonlhLxHe5wD1qa5haCIJImM87vWgRhNJF9tVGGcHJHWqs0kTO/nIVB6N6VQjNlsVy0mckfc56+9SaKWmtp4NRj4hbMMg6lT2piJbvX7HT2FkoAdvl+UZJ9KydY1y2sv8ARp7SWTdxyBgeuD/SmkwbMm21D/ibQeU00KRLtWNV+8vXGOx5rvrPU5JY8wKzJj5sdqJIES6Zqt/JeXFjcxK1v5ZLEnrxxVVdZxB9liJ2enpU2GSf2mnmLK0altvzcdKa0cF3IJ428tEBJzyD2oAp3OpLHehjjaV2Bj6elZum3FtexXunyW5hjJIDqME+4P1p2EZWtaOiadFaw7mijPL56k+tO8I6TeQSfbp8pGchRnhQPWqvoK2p0MGrQGFnd8BWxtHHerK2MdsTeQTHOCWR+2fSp2KKl1FJdpbPc7sx5xOONo9PxrjPFmjTX5hmtW81lDbh/ez0IqovUlo0xn/hHLO2iPl3UGNm7jjGCD9aGuftti8ZZ4ruVfKkzypFAilpdm0FzClpL8kbkSK1M1mKEanBGJPLkuMs0ZHC+9PqHQdJo8khUM6K3IBHANWUt5/Ic3SnaFwM9GwP50XAwNT0+W20x7ZsiKTEisRyvGdp+lceyMMkg4BxmriQxCSTk9aSqEFFABRQAUUAFFABRQAUUAFFABRQAUUAFLQAle2/BjWRcaHf6G0rebBL9oiU/wBxsBsf8CA/Os6q90um9Tv47szWwMqeUyZH1HY09JA1uUD53JkjPAI/+tXObmepihIaYlhH85I9ulTu/nWyynJcgtyOGGaYinJdxR7HzsK/dGOlLHrtncwmEzKWPzKh7j1U96dhEM9vCG+0xAl1+YelZhzdzmOSHacZVlPDeox2poRMbXbblWbbn7ozWRqM6uxESszbQMD2700JnCpFex6uZURjMjb9p5x9a6jzJtVskWazjMucBtvyrVslGXpWmapPrMczHCRTfe6ZGeePeu61SOXTrnZY/KsmHZfTPapluUjOa/nNyI97JAfvtuwFxUc1/pSapHAY5BOxIBxxz0+tKwGZq2ow2Es0E00iSMuPlHAqPRdWuRhoHE1sFw2/5WB/rVW0FfUq3qX19YzRRqZJWlzGqDotZ2lPeQ3SBmkVV+8rE09LC6nVCMQyLuLCCTG4kZ5rbuUI09ls7iMqckoRgt7VBRjaZaWmqi4trhDBIh+7jvWTqN3q2nxtHbHz4CwAc+npTW9mI7LTpobnS3WV9iNHjnsaw5YIJrWcbzG8IPPYikhnN3Iu7dVtrvBM8REbj1+tSWs1vYWkEFyxW5mJRGYZGRVkkli/2WMOzAmR85Hc1JrmlGa+TUkRi8cXzL/eHqKXUfQ56y8R+Q72Ny4eMTZilI+6p6j6dK7NpbW5sfIkAdCBjB6EdCKclYSdzP1kI2nSb2yzsAB1wP8A9VcQYLYaRLHO227T5o0zjI5/Pg04ikYVFaEBRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAV0Hg7xLL4U8R2+popkiGUniBxvjPUfXuPcClJXVhp2dz6V8+xubCO5t1LQXUSywt6q3NZ8CbInVTt4bAbpnqP8ACuQ6RsUHnQlzkB4t209hU4jLxIImYLjbz6UxGXNZoUKv/Cc/WqN5o1veW37yEAAbU2/w1SYh+nQXOnywRTSNNA/yMTyQK0737PZr9xRMei+lIDERGvLkBiyKMnntiqtzCscmFVuehx1qiSGRILNWmeLLldvA5P8A9aoNG12CWaaBrKUqQoJjAwpz70WuBuQ3Wm6YQJ5Y0Xdw5bqT0GKp+IJL2WSJ7ZkYTD5XTnK//qpLcZnvbRRagu93k3R5I/hJxQ89vHFDd3a+Xcbyiuq5+mBVCM7W5LeWeK48hJ3c4YNxxjBNYkV+1reixtbfKM+WDdTz0GKpbEs6HWJ5LS8sHs/LV4yp8vPJOc8etaWqrb7DdraH9585PTnNSUXt63WlW0iKMK2JVA7etWNTtIbY+dbyIqBAzLnp7fpUjOVi8R2MmtXMezZJMxUN2Xj+dSQzfY5XhUiS3kJHz8jmqsTcvzTGOzNx5e8LICVXpycE4qW4EEGpRSxvlLi1aOSEj5SM9QfX2pDMPUrZvsxs3cO7cwNjkVnXVqbzT1gcfvrd/mB6+nFWiWYmnald/wDCSxWcoUwibBjYdAAa9Ujkh1K3S2mUKVB8tx/Cfr6UpocWeG6xaNY6vdW7D7khA+ma3NCup/7KYNk7GIQk9RWj1RC3Ld1qUMlotxMWDRdU9TXPa4LeUWt7b3HmG4Q74z1jIOMGlFAzIoqyQooAKKACigAooAKKACigAooAKKACigAooAKUUAe4fB7xDJqumyaDdNvewXzIM9TETyv/AAEkY+td1cWzRSs2xiF4ZCO1cslaTR0Rd0Rws895FGhYW5iZWVv4TkEH/PrU4dkXcqMAGAHPapGQBYprhmPIAJC+tP32v2Uk4Dg8imIz7pVljDxyK4GOFPSqst3DPeJHIgWTPy5OQTTAfsgknCi4jSUgloScN+HrVZ2gwQJA2DnFMRhanfWsEkUVwXPmSbSwAwpPc+1FrBLpd1ceWgeSTCkHoB6iq6CLOraRbahbxiUMi7QzgetOWWO3sbbT7LcJIgyxtJ1BP9KQCwo8xSO4kUyKm58Ljn8ap3sAj8mRiCjDdGw6Ef40IGcnPZ3jXG+2mMqAkqc8e9Vk0++hDNE7G5DhwVyCB3wa0uiTproRzvpt/K6/aEi3zf7JHqKh0vxlgm0mtS1k8hO9+cZ9PSptdDvY6ZpLIxI+ny5DA7l3ZApt1am50l4ukmMg5qSjgrfQXtL4yS7g6NnDf1rrkMcz2qIVXz3wxI4Vh/jVNkouXNujWxSNgsmei/WpBEEgBuOVXHzelSM4PxB9r0vxrHdODLBK4+ztnjbjGB7itzVjHLDFqEXEzOocjox9TV9ie5zgtFuNVF9GQk4J3qejdifrXW211LBb4wDIF459elDBHmHiO5kutdupJU2OG2lfcV1+g2Md94XhXOH8tiGHY5NU9EiVucjrc5E4RWUkx7JFHqDWNVITCimIKKACigAooAKKACigAooAKKACigAooAKKAClFAG94Q8TXHhPxFb6pb5ZV+SaMf8tIz95f89xX01fSrrFjBe2xKrLEJMHg4I6VhVWtzam9LGfbRra3DWx+cMh5z39qZZ6glzPcwZPmIoDRt1BHQ/iM/iKyLKjRSG9hkDsoVvmUdGHcGr1xbLHuUjI7iqEOa2tjCyRN+8K7iMdqwZY4/tCOV5jYHOKEDMnWtPOrXsb4Mex9yyj7wxTJ45jPI6kheaokqvYLqY2TABogDj19627YHCDJ8zG3zCMk4GeaGNEdxHI1rG5kyNxJb/Gsy/vLSyiE11KrhGwgU5JIoQiwl+JbaG9TEgkQq/y4Jz0FZ+o332ZbWFlLRxtyG5PPWmkBoXiIdOFxpcaBv4ty5HYfrWdBZXIIlmlZ29AAF+mKEBZtLGGVpoPKGG7d81EukxxvzGNgbB4ouItSx2+mNC6kIzSeWV9emCPbmta/il/stpLYZkAyCy5AApFFe6ih1TS5IZWRbrYCrdGB9D7EVglXV7e0Q7XBOfw700JmjGn2cKpbDDhSauo63ljLZ3ClGZSMjsexpDMLVNNleKKC4AkCnKEdRjuD61kSXTWyxWTqGEjfNntVLUli6pYC0tftkGSEGWHfnvVGW4e8ktZ7eUhYjyvTP/1xzVIRzniFJbvWrq4jiJTKgso4zgDNb9rqx0XRGKgriLbFkdSab1ViVozhZHaR2djlmOSTTaskKKACigAooAKKACigAooAKKACigAooAKKACigAooAcK96+EniY6j4Wl0qc/6TpzYRyclomzgH6EEfTFZ1VoaU3qddeWLSae0yP+9OQCP4T2rA0G01CHUrS8uZRI80TRzAjk4OV/Ln8DWC2Nep0cke2QsgwV657Gq0jytEQxJbPGTzigBlszm5V+chSAvaqTRguUkIAPJpiIZr7TrWZI3nRS/CbzjJrG1LV7GK5S2WcCZztUY9aaTEydZYbKQySKucbWzUR1AXtzm3GPLkAIHT6igDQktnNv5TSHLyjArPvNEiF2kHlq/lseduRmmmDRcSCKPZbMoBzn6elczd34fWoYls2likfazdxz2poTOmitI7ZVuY2P2d2KhCOeO2KbNcW0UaAK4EjEEkcqcDke1SMpPGbWN9zNlDuDA/eFZcusS2cN5PtMokAZUB5B6VS1FsVrS0udTW31C+QI0ZzGq5wR7+9dlY3cisYySyAcClIET/AGCCW4a4xtDoAxz0IrnWhKaikk0TITu24oQ2XdRiLQxzLjYv3s9KltohJIhZGWIjIkBoEOltbp2MhXzIk4DKMgj1rldUgW4u3mVOVO0nsRTQMiu7zymhjdj5TKfw+o71jXNs2mw3ZjI8rAdOfbJqkSzlodXu4ldFKtv65HNdf4imt5fC6RnAYBXQf1BqmtUSnoefmkqyQooAKKACigAooAKKACigAooAKKACigAooAKKACigBRXS+BvEreFvE9vevk2jnyrpP70ZPJ+o6j6VMldWHF2dz6OaaCSya4sZEuLS4AdJEbKn3BqK3jRZ7aUj5Tncvo3/ANcfyrlOku3CwLbgFtsh5I7E5rLTYLgCUHOcDFMRDdSmJiqKAehNZtzGxJOTk9aaEzHuNIgvFK3MQdc5APUGo4fDdmGVjACwYEMT82Rz1qrk2LGr2/2mcopBYnkAVVeO5tYI1tljM6t95xxj3xQBq6EupSPIb+aJlPMaIvCH1yaBcuGYI43biS7e9IY2J2DJJITKwz+PoP51mXUENpi6XDIG456GmhMsJqM00ts3ytA2SQo6E9/rV24jC2kUTrvYZO89T3pDKSCO8sp8dRwoFZstgLaFrmUYGMHiqQmaemxLeWrwwSKGA3Kp7mo28xSMgrIjDPqKQGrE6zX1vE52M8ZKk9GIPSmT3KNdSWckHzJyGI4zSGZWpX9pJprRBtokQrIM/dXua0NMEGr6ULOOZljGApU5wB2NN6IXU6hIlsNg+VkYYGKyZbS2uL+QvaqIc4yV5J9fpUplM4nxfoYtLj7RACbcgFR/dx1rA11C2iBSw2hOX9iMitYu9jNo4+0t3ivVEyFSAHCsOoPQ1c1e62WMdgDu2sGB7qMdP8+ladSDDpKYgooAKKACigAooAKKACigAooAKKACigAooAKKACigBaUUAes/BnX9tzfeH7mfEU0ZmtlY8K4+8B9Rz+FetSysLZCihzE6u2Djp2rmqK0jog9CW5WGVNwb6D2qhNbK0rRoRx3qEMhuIgDHE5+Y9aieHdJgc+gpiI5IQZMIuSTzjpT5Y1gjLcbh0pgY8EG+6EkhIGck1PFbo8pkbhScKDTEXRNb2aHLcsMKwHArCkhZJmVlx3HvQgZDeGYIFEhQdFKHmo7uEXWmpGy7dgJ46MfWmIfocKrFIZVysSlh7gc1DY+I7y+me3u9NRIhuWORD0HvRYCSQpBOkWPLGMFUP+frWkzrq1tPbXK7RJgo4HKkdD/jQMy7IHTNQXzflZDhh6j2q3qStcQzXEQIkZtx/OjqIFnZ7ZPMQF4vmQ9wazLnUZ7bSZ9SEhZ/Q9yTQkB521xf3Vw5ZiQ4KkA8c16R4Lg/su3MT8k/Nu7n2q57Ex3O3a9Sd49wChRgGtGMwyRgsiOcY6c4rE0OQ1mKUXbXE2TbEFML/wAs/qO+a4jxIFF/pdvtDafIczjbyMHOD+VaRIkV7z7LrV1dTC2DwYW3gnQYMeAckj0z0rhtYt1t9VuIY3aRUbG5uvQVpHsRIoUlWSFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUALS0AW9Mv5dL1O1voSfMt5VkAzjOD0/HpX0fpepQahZwalYy+ZaTJmSI/3T1H+8prGquprTfQ07hC1qIoSN6jKsOdy9jVGykuls5HvY0WRSVbHIIHQg/TFYmhUaZ7rMkMocZG3Bzg+1aDLcMqyzBQx4O0cGmBDbu0dxkL1PNS3Fv5krFWyQThfpTEUjtw6bRgrwR1BqLaZLXb1KHIHemAkSDytrHILDA9KR5Els2mJXdGccenpQIqSfZpI4lUAyscsR0C/41HqVv5Eaxx/dkGQaYEVoNillJII249aWKKG33EjjOAB3PpQBUldTdb2X7xG0VqxqwQypgAchf5ihginfx+dMswXcoHX+lLbO5WJQSU3dMdR6UAW4kikSKRD8smcxseUI/pzWB4qsJLLw8sYUhZJ1BI6Y5/8ArULcT2OU0y0W5mkRGwy/dBH3sdq6jSrghApJOOhq5Eo6G3uWIwTWraXTKR1x3xWbLRmeJ9Yj+2afpscYZZ9zyy4ztA6fnz+Vcd4na1k1Wy06IEeau+V+2M9Pyz+dVEUipqtodMmWTTl/cNCS0YPRh/TFcFZ3zpqq3ExVxI+Jg/RlPXNaR1RnLRlS5EYuphCcxh2CfTPFRVZIUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUtAC13nwz8VNo+uQ6bdy/wDEtu32EN/yzc8Bh6ZOAamavEqDsz3Pb9iuSgwhjJCk9CM5IqHU5BcBo1HlsV5UdCK5Tco6FprWEJt0ClCxcFuoJrblhYWYB6kjGTTApraHBPG7sTTVVUbeeoP5mgCo0OFyec1VYMBhTjntTEVpXaOPAJBPWqZ8x/kAGCckY60xFyOMSXEfAG3g49KNRZpLljwERdqj2oAhhjMB+fAUjK+lQSRskIJADht5460wI/IFxGHxh06+/vVqzQSRbC2CjZU+tADlm2308Mi4i8soVx1yOT9agSHZaKofBHQikBBpNwDeyfaY28wEjIbpXQajYrqOkTWTnckozGx6hhyKHowWx5XoZNlP+/Uho3IOR154rasRtOQe9aMhG9AcgYNatlKiyEPwTxg8VDKR59d3csniC/dn8t/mKE9Ao+7+GKvWsdv4i0FZEYC8tywRWIzkeje4qthGO+rIZQMMdoVGB7A9T+n61yus6fZ29uk9m55kZWUnnHbj881cdCXqYdJVkBRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABS0ALSqSCCCQR0IoA+iPBPiU+KvDKXE+Gv7VxDcKD9/A4bHuP1Bro721WN0kGU8wfKR0HqK5GrOx0p3Vy/bRkIpTAcqMk0l9K0trCu3Dofm46+9IYy72hYwzBSSDx61Ve3zIRkbwc7e4FAhjqrARKwM2CdvoKqSRBVORjHWqQjMnHzBsA+gp4RIw0iDlgMA9jTES2ibbhTjPaqUqPKz7ifvc0AR3Y2COP0Gc1ZkVvs6SOuQeDx1FAFORDFKQmRH2P8AeFX7RIgYoWBG8HB7CgCq8Tpfyxv94Hmm3csdpEEIyZMBcdM0APGmeWyykDJUcjqDVrUL02GlCYglgOFHc0bhscpdw2F9LbzD5DKN0uexB61LPo8thcKImDxjHG7kg9Kq/QmxaUSwiNyDjOGBH61Nqt2tzpgjgOLgPtbscHr+lAHEajO9rcwytniPyh7jnj9aXRlbSoJZIX3REl0Hdc9AavoLqZ0lqSjyxEgyMW2nkg56e9YmpQsA5K4JOcdug5polmLRVkhRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAtLQB1HgXxM3hrX0kkb/Q7jEVwP7q54b6jr+dfTL2Rm06G4DhgUDfLyGPrXPVVnc2pvSxW2stuyBj8gzgdcVAskt1FhGMnl/gfxrI0I3W3LjzQwJXIbH6YqeN4mma4JPCemM4piKNnE5vXf727IDVLf2xWYIehGaYGLcgFsL0zgVKkJCDPWqJHMfs6ZH3+1JaIkpZZMBmfKe1AGRdN9vmmaLgRjKg/xD1q9ZXBuPJhdyIkXLDH3qGCJGiE5kUJsiDEoO4FLENzIu0Zj/maAIr6N/wC0UkyTuHzfyrO1m3IurdeSo+fPbFNAzobTYtsftBARQPmPpWTqoW5tEkMgjSNsMHHXPA/nSW4dDFj0i4EoYxjqVIByOvatjSHS60tYr2MfaAuQ+MFSDyv07U2JFXVIn06ykzkptylZFhjdiY58wbmPoaa2AyNS08ahqM8MbcW4yPc1kNqcljYwQFAwnkAYn+HBq1qQzYuba3udMiubQmOa3Kloz/EAeo+lZOqaeblnjiA84R+YF7MM9B78UJgziJ08uVl6YqOtCAooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKWgBRXu/wAKPiDby6APDmpXKreRfLatM2BInZQfUdMemKzqq6LpuzO8Z1QSOQ2QuAVPUelZUscy3keoaZLIrp9+Jz8si9x/9eudGxPeQz6gxBU26BTsmjbv1xjsaq6dHqVmLiG6dZ8EESYwXQ+o6Z+nWn0At2ur2CXAtfMYTxtuAKnkelXrpzqKSTBGEmNqqBwAP/rUbAc7Jlp1UDoa1oY0eF5GwAOvsabEjImljlvgm7APAqaaJrFC7HAzw1MRhNNhmhhAWNuC3fHpWnpSmCWIYBWTIbI6U2JHSyWaSRo6Lgr1x3FZ8dsFuCQc5OCKhMoo3LRXepSDeY1jbAPZuO9Z1r9oTULgyZZQ3yDORiqEX7yNrs27RHbHH8xQdCapXikz+W3KABsf5/zxTQMmRSVxnjsKj8so5YdTyaBFSe5l2iNm3R9CrciqDxbpi8a9s4ApgYs8rWupyXMfORuxWbfWEV7YLHEQkokDRk9N3p+NUiWRaddvHJ9nmUpIvDqf8+4qaa523kJiGWiKiUEZymTz+HH507COP19opdauprdf9Hd8oR0Prj8c1l1a2IYUUwCigAooAKKACigAooAKKACigAooAKKACigAooAKKACloAWnKxRgykqwOQQeQaAPovwJ4oj8R+HE+cHUIl8u4U9d2PvY9GHP1zWyPOtELAB8DJGOh9q5GrOx0p3VzL1DVbya2820H2a4Q7Wjf7rjsQR/kVJpOsz6i3+mOA6KQZITkDH8LDse/oadtBXNh5dPMJlJAYjIKgEZqu/iFkiYRQbh/Fs7ilYZDam2vZw0KuCeueqH0xWlc2rw2DsFxvTcBQIzNOsQgMoHzH+KrOux/wDEsBYc5wPyp9RHMW1vhwWXIJrctQrO0ZQAg8GmwRtIzCMckGq1yp3+avDHr9akoyLyIb/MVQC3Jx61VHEgPpVkFu3wCRUV7EMhh1HFACLwikDqKa6DeSvTtTEZd4mJPrWdeO9tNayoxV0Y5x6H/wDV+tAFHX44/Ot54wB5+d6joD/9es2KPPyN06iqWwmV/Ii1rUZ5bGdPMgXEhY4Dfj+Fcfqd7dJfyfOUJA+6eoxVR7EszCzEbckj0zTaskKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigBaWgDoPB3iabwrr8V/GN8LDy7iL++h6/iOor6Mt7rT/Emnx32mXSyIwz+7b27jqPoeRWFVWdzam9LGLqEN1ZWUiKgcbsAOcF/wAfWsmPyzJDdwF7a4PyOCmA47o46H+fpUIplu90Ce2DXVjM7W8h3PCG4yf7p7H9DWRPoOqjUVC3Upt25BQ4PsfrTTQrM0I9D1KN0c3EyyqwZypwHA7kdj616BaKl7ZrHJLuJQqCT0PpUspDodPMMXlkYOcVh60xu75bZD8kfHHrTQij9l2EjH3Tg/WrVpHiXce9DEbTx4QEdCM1BImYs0ijPv4QsSAjBIyKy9mJMe1UiCxABvFSXCAqVPagCBV/dle45FRvzGD6HFUIpXwA2MR1rH1wLFp6SMdrFhz+n+FCAzIgby1+c5ZWyo9Kx9flms5tPWIkBy5k98ADB/OqW4nsYukXyW1zqLCQIwQyf72Oorm7iZrq6eVh8ztnA/lWiWpDFuIBbERswaXqwU8L7fWoKYgooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKAFooAWrum6rfaReJd6fdS286HIaNsZ+vqKTV9GNO2p9I6B4m0/xzock1pHsmiwLiKUDKNjOf90kHBpsmmidDsOfNGHVuVyO4NcuzsdG+pQfTby2aJ95dVcLKuSCV7fiK27hFs9MeSJt27lOeR6/SgDzi9vvE8+tgWLT7CNuxjlGHuDXovh+6vJYRLc2ghuV4ljU9x3HsaqSVtCY3Ore4S7t0KMVaMZZcckY/lXIzo0F/Cu07i3mMeuKlDZJdMG1FkyPKYb+PWm2ys0gZgQc9PSmB0MwC20TgZXG1vrVJP3kRx9KQzO1YlGtXb7vlFT+dZMEgnkYjscVS2Je5ftYt8vPpmnXGNzhgcp1oEQPGBHcj+KPJB9uDj8jVVHDK+7ke3v0poCLVkWNVb+BsED+Y/DmuV8QSGTToFzlhJg+47f0qkJmbDMkMe0sNzKdo9cc1jX2qef4buLy6Qi5kJjjOOAc/p3qkiWzmtJltg0kM7spuQYy6rkouM8fU4FVZ4nsJDGSPNI5x/CDVklSimIKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigApaACloA6bwL4n/4RXxPBfSb2tHBiukTq0Z68dyDg/hX0fbWsd1Yw39lcGS1mAkjx0ZSMiueqtbm1N6WEdhcLceYDGyrwxHX06VkNcQRN50piRGOyRycA+mfQ+9Zosmis42uwI9m5RnAYEkdjx2rfW3/AHUUkZ2sOCaGCJrWMSkxsds6g9utZwhj8maAsqzDcOnOaBnPZk85VXJGec1s2q732kBWHI9xTYka029dPlULltpZc+uKyrC5UKGfILHk9iaSApa9KXvoYkJ8sN09cgfpUNlZbA3ABJJ/nVrYllmycG6lUD/VEZ/Ec0Nh7u4QEHsfT/PJoAzku/LuZFYHD4Iz6gf4ZqC3QKJEJwCSCf5UxGJ4s8QJpdlH5iBy8wCq2fnQn5v071DqejyS6DJqETsI0/fLGfmOMDjP5VWwtzza61dZrN7dZkUsx+fpt5yf8Ky9TuYLi4Y2xcK4XcuOCwGK0SM2yvbu0blY4d8g5J9AOf6VXkkaWRpHJZmOST3qhDR1pTjJwcigBKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAWigBa7/wH8R7rw3JHYX8kk2ldFA5MGTnI9R14/KonHmRUZWZ7paanp98guYbmGe3lAO+JgwAPeq1+lnBOsKR/aA/XYAygVzHQR6bpNva34nt1A252N2VT1HsPatmDWLZ7meyG0SKdxGcY9+aHqBJc3cRvoNgZCRgk9PbmmakrQzLLEUyTukJ5xSAzltY7ib7REflK7gCO+egp9+HsbcXaqMqcDPrTEMkupLyFPMkmEgOcIMD9O1VJp1hjIlViN+FA4GfemBaWB7jRzcyRr9pgTeB2OKr6THJfQebcsEnU8KOAB2FF9BDbmZdNnkbYCSuV5xub0NVYYylwXSbeHOQD19/1pgRTlPMlkdNioN30Pr9MVgahfSeVDcW3zQu+1j6YPSqRLOZ8Q2lzLpdvDgzp9paV5M52gkkZ/lW5HrGzwVPKCHjRCm/PCn6/WqeqEeLTMrzOyLtUngelXrGzkRvtU6BIYxli688+grUzKiJMiNcxhki3bNwPr2/KmW8PnXEUZO0OwGfSmItautpHemKz/wBXGApPqe9UKEAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUtABS0AX9J1e90TUIr6wmMU8ZyD1B9QR3Br6N8C+J9I8YWKLCscWpqMy22fmT1I9V9PToaxqx6mtN9DbuJ1WGQIkkcm7lQM8j+hribnxRPY6mvnaNLNHyGdPvEfyrJK5o3Y29OvbKSQTadIz2shAe3fIMZ7/Kehrql0+GULICoXByfUf/WpMENs3WKNVljxycY6YrHnvLW8S5tmu0aRXL7GYdB7dqEMWC6imsY5oEEnYnOMY9ah1RTd2UcsSbiQGG3gZ6fy5piGXctyNHkt7TD3aqGQMeCO9LpMCywbpyVnXlmUYAP09KOgdSe4jiu1ZLjDOOy9SR6VTFsIZxNv2BU+bdxQgMDU55nuHSdC9u+5QwGOOtcyTcRL5ETlo15TI6H1rREMddamt1P/AGRHGJJWixLxhUz6n1IrF1/U7Gw0VfDlq+WZgX+b5UXr857n2qkiWzEh0yDRIF1W5dZkPFuMAhz/AHh+RqIM3iC+aaTENuzZ8vdgE9cZ/rVeZPkYt0sjM0pVViLkKI/uA+g9qiaUsiIAAEzg9+feqJIqQ0wCigAooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigApaAFqzY391pl7FeWVxJb3MTbo5Y2wymhq4HtnhD4nR+IHW01m5W01IqFEvCxT/0Vv59vSuvudMZV80l2C9CvAx9O9cslyux0J3VzEktrxbw/ZGgiVjllkBL/UEdDXWabfyvaPb3aFJMfI4OQ31pMaNFrqIxhGBV8ABQM5PY5qnBokEdxLOYE8yZtzNtGc1Iyz/ZCeUyBMI3XA/Wsuxma9meBtnlwMRlR3HemBj6xFOLwvGjRDGVw3P1q3ZxyHJkdt7gKFz1+tUSRNJDZ6q1uHkWYgEMR8ufSrOoXUM9lJFKymYrjcP60gOUtxNcJIskrJbxkkO/APFZFqv9qXczWVwjhWwFQ8Y/rVokrReems3EFxbiNoz80i4II69RXJ3Whx6rqM1zavJ5LysXXGTkeh9OtWnYlof4jiM66XYeWEbiKGKM/LGvGT7k5zmubu5VhLW9vIdisy5B6rk4/OriSyjk4xk49KKokKQ0AJRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUALRQAtd54G+I154duI7HUZ5rjRn+Voydxi919vVamceZFRdmewxavourW0c2mX1tdNI3yhXAYY7FeGH5VeAuZFjAKjB5OK5WjdF6eeT7DiOFHuVI2lm2gj61zuo+I9YglHkJJFOvLKSGX6c00rg3Yo3PxMnRktNQtpbfeuGaNNwP5HNLp96bi2lbTp4zE5wrLn5j6MCKfLYV7l6xgvLi/8AtM85li2hCwXG1q0r5Lm2uFCqG4DKvQn1xSGYmrSStetdsiK+0CIF/vEdsVjSTNfzPqk6PHNbttYAYTOOn5VSJKV5qMWrpBEEKxu+Hidch/Y+1LaxNpNvJFDE6tLn5z1APfP8qryJ8yjdxy29pHvmdBIpGVPIP+TSaaIbDTjEhRYlTcwPBPvT6AcXrWpXkd0u6BSjuXRsct2H0x6VnXb2x0aBxCguHYxnHRQOSfqcitEiGZNFUSJQaAEooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigBaWgB8UrwyrLE7JIpyrqcEH1Br0Hwr8V9T0i4ZNXDalaOOckLIh9Qe/wBDUThzIqMrHsXh3xp4d8TRbLC7H2jbk28vySAd+O/4Zq7rOmFbN5w4AC8SFd2K57NOzN7po5mz0W0eKS5klE7MocOeh+lY1tPd2uoqlmU2F/mgGBn6+lVuLY62TWI44HVwqylMr8wJBHfA64rK1i9g12CBhevm3U74Ypdm78MgikgZlS6zp+rW0FvbxT28kLBlllGAAPQ5/nVK6vzqMjg3UKgAZQuqmQj/AD1FVaxNy9EsM15AqwJAUT5nU5Umrt+A0ixfu3jAyWXrSA5q4ubdbmWBLhZGkO0LLyUHfA/rWXJAY7UI8pDvJwpHLLnpn0q0SVdRurfRYQLu5WW5k5MCrkqp9Ow/GuIvXtjtjtmkdV/icbQM9gP6mriSypRVkiUhoAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKWgAooAkhmlt5kmhkaOVCGV0OCp9Qa7uD4w+L4rRbWS6tp4gu1hLACXHuRiplBS3KjJo07L4sxyW4h1HTSnPLWzZH5HkfnWtH4n8K6oXX+0Cm8fLFcKYwD9Tx+tZODWxoppm9oGly5823W38jrG0b+Zx/vdKXW9MHmC9vY4bhB8rNGAh+nqTU31HbQ5e6t9Pido5C6QM+UQvgfhjk/lTJl0+xIintbh1flH2b8+h5qtRaGpFPbJCrSNGo4whI3frU8mr2c6BBcwxIDyHcAg0rBcwdTv9Ihumuo54EdP9bM2Dv9AADkmuCuvE15IfLgKpCjloyy5bk5ySe9aRXciT7GTcXE11M01xK8sjdWc5NRVoQFFACUGgBKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKADNGaAFzRmgAzRmgC1Z6nfae26zvLi3PrDKU/lV1fFevKhT+1roqTkhpM8/jUuKY+ZorXGtaldOXmvZ3YjBO/HH4VWkuriY5lnlf/ecmnZBdkRZm6kn6mkpiAU6gAooAKSgApDQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFABRQAUUAFFAAOtOoAMUUAFFABRQAUlABQaAEooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigAooAKKAClzQAZozQAZozQAZozQAZpM0AGaKACigAooAKKACigAooAKKACigAooAKKACigAooAKKACigA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" } }, "cell_type": "markdown", "id": "10d2f431-115d-42ee-a2b7-e9dae79f2733", "metadata": {}, "source": [ "![Hyperion_true.jpg](attachment:3ece9595-d19e-4c16-8f05-b4839ae206ec.jpg)\n", "\n", "https://www.youtube.com/watch?v=tk8r85lM3SY\n", "\n", "Hyperion is an irregularly shaped moon of Saturn notable for its chaotic rotation. Its motion may be modeled as follows:\n", "\n", "The orbit of Hyperion (H) about Saturn (S) is an ellipse with a semi-major axis $a$ and eccentricity $e$. Let its point of closest approach (periapsis) be P. Its distance from the planet, SH, as a function of its true anomaly (orbital angle, $\\phi$, measured from the line SP) is therefore:\n", "\n", "$$ r = {a(1-e^2) \\over 1+e\\, cos\\, \\phi} $$\n", "\n", "![unnamed.jpg](attachment:e7e8802b-2be5-43e7-8787-6fe50ae72a36.jpg)\n", "\n", "Define the angle $\\theta$ to be that between the axis of the smallest principal moment of inertia (loosely, the longest axis of the moon) and SP, the quantity $\\Omega$ to be a scaled rate of change of $\\theta$ with $\\phi$ (i.e., the rate at which Hyperion spins as it orbits Saturn) as follows:\n", "\n", "$$ \\Omega = {a^2 \\over r^2} {d\\theta \\over d\\phi} $$\n", "\n", "This means that:\n", "\n", "$$ {d\\Omega \\over d\\phi} = -{B-A \\over C} {3 \\over 2(1-e^2)} {a \\over r} sin[2(\\theta-\\phi)] $$\n", "\n", "where A,B,C are the principal moments of inertia.\n", "\n", "You can plot the spin rate $\\Omega$ as a function of $\\phi$ for the initial conditions a) $\\theta = \\Omega = 0$ at $\\phi = 0$, and b) $\\theta = 0$, $\\Omega = 2$ at $\\phi = 0$ where $e = 0.1$ and $(B-A)/C = 0.265$\n" ] }, { "cell_type": "code", "execution_count": 15, "id": "87173264-7573-4110-a49c-7d85b60c0b29", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.integrate import solve_ivp\n", "\n", "# The orbital eccentricity, e, and (B-A)/C for Hyperion\n", "e, BmAoC = 0.1, 0.265\n", "\n", "# Anonymous function for calculating a/r as a function of true anomaly, phi\n", "a_over_r = lambda phi: (1+e*np.cos(phi))/(1-e**2)\n", "\n", "def deriv(phi, z):\n", " \"\"\"\n", " Given z = Omega, theta, calculate and return the derivatives,\n", " dOmega/dphi and dtheta/dphi.\n", "\n", " \"\"\"\n", "\n", " Omega, theta = z\n", " aor = a_over_r(phi)\n", " theta_d = aor**-2 * Omega\n", " Omega_d = -BmAoC * 3/2/(1-e**2) * aor * np.sin(2*(theta-phi))\n", " return Omega_d, theta_d\n", "\n", "fig = plt.figure()\n", "ax = [fig.add_subplot(rcp) for rcp in (211, 212)]\n", "\n", "z0 = [(0,0), (2,0)]\n", "phimax = [100, 400]\n", "\n", "for i in range(2):\n", " soln = solve_ivp(deriv, (0, phimax[i]), z0[i], dense_output=True) \n", " phi = np.linspace(0, phimax[i], 1000)\n", " Omega, theta = soln.sol(phi)\n", " ax[i].plot(phi, Omega)\n", " ax[i].set_xlabel(r'$\\phi$')\n", " ax[i].set_ylabel(r'$\\Omega$')\n", "\n", "fig.tight_layout()\n", "plt.show()" ] }, { "attachments": { "97f5e004-5471-4a14-b9b4-3e1bfdfdbce6.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "2646b6bc-4425-4fe5-9b73-9920828fbda4", "metadata": {}, "source": [ "What is the radius of the orange circle, which is tangent to the $y$-axis, the unit circle and curve $y = \\sqrt{x}$?

\n", "\n", "\n", "![circle-fig1.png](attachment:97f5e004-5471-4a14-b9b4-3e1bfdfdbce6.png)\n" ] }, { "cell_type": "markdown", "id": "ba30f7eb-2481-4538-b940-1d74523a0ff6", "metadata": {}, "source": [ "You can solve this problem using SymPy, Python's symbolic computation library.

\n", "\n", "

Let the centre of the small circle be $(r, b)$ (the $x$-coordinate of its centre must be $r$ because it is tangent to the $y$-axis. The equation of this circle is therefore

\n", "

$$\n", "(x-r)^2 + (y-b)^2 = r^2\n", "$$

\n", "

At the point $Q$ the small circle is tangent to the unit circle: let $Q=(d, \\sqrt{1-d^2})$, where:

\n", "

$$\n", "(d-r)^2 + \\left[\\sqrt{1-d^2} - b\\right]^2 = r^2\n", "$$

\n", "

The gradients of the purple and orange curves are:

\n", "

\\begin{align}\n", "y' = \\frac{-x}{\\sqrt{1-x^2}}\\\\\n", "2(x-r) + 2(y-b)y' = 0 \\Rightarrow y' = \\frac{r-x}{y-b}.\n", "\\end{align}

\n", "

and these are equal at $x=d$, so

\n", "

$$\n", "d\\left[\\sqrt{1-d^2}-b\\right] = (d-r)\\sqrt{1-d^2}.\n", "$$

\n", "

SymPy can solve this pair of equations for $d$ and $r$ in terms of (the still unknown) $b$ straight away:

" ] }, { "cell_type": "code", "execution_count": 2, "id": "88f7a0a1-5016-4c0a-839b-5126441ee4bc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[{d: sqrt(b**4 - 2*b**2 + 1)/(b**2 + 1), r: sqrt(b**4 - 2*b**2 + 1)/2}]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy as sp\n", "r, b, c, d = sp.symbols(\"r b c d\", positive=True, real=True)\n", "E1 = (d - r)**2 + (sp.sqrt(1 - d**2) - b)**2 - r**2\n", "E2 = d * (sp.sqrt(1 - d**2) - b) - (d - r) * sp.sqrt(1 - d**2)\n", "soln1 = sp.solve([E1, E2], [r, d], dict=True)\n", "soln1" ] }, { "cell_type": "markdown", "id": "451b4f61-4bde-41fa-a72a-bbc802ba3317", "metadata": {}, "source": [ "That is,

\n", "

$$\n", "d = \\frac{\\sqrt{b^4-2b^2+1}}{b^2+1}, \\; r = \\frac{1}{2}\\sqrt{b^4-2b^2+1}.\n", "$$

\n", "

At the point $P$ the small circle is tangent to the curve $y=\\sqrt{x}$. Let $P=(c,\\sqrt{c})$, so

\n", "

$$\n", "(c-r)^2+\\left(\\sqrt{c}-b\\right)^2 = r^2\n", "$$

\n", "

and from the gradient of the red line,

\n", "

$$\n", "y' = \\frac{1}{2\\sqrt{x}}\n", "$$

\n", "

at $x=c$ we have

\n", "

$$\n", "\\frac{1}{2\\sqrt{c}} = \\frac{r-c}{\\sqrt{c}-b} \\Rightarrow \\sqrt{c} - b = 2\\sqrt{c}(r-c).\n", "$$

\n", "

This pair of equations can also be solved (for $b$ and $c$)

" ] }, { "cell_type": "code", "execution_count": 3, "id": "12796197-d26f-4b5b-9d86-b168744737df", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[{b: (3/16 - sqrt(16*r + 1)/16)*sqrt(16*r - 2*sqrt(16*r + 1) - 2),\n", " c: r - sqrt(16*r + 1)/8 - 1/8},\n", " {b: (sqrt(16*r + 1)/16 + 3/16)*sqrt(16*r + 2*sqrt(16*r + 1) - 2),\n", " c: r + sqrt(16*r + 1)/8 - 1/8}]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E3 = (c - r)**2 + (sp.sqrt(c) - b)**2 - r**2\n", "E4 = sp.sqrt(c) - b - 2 * sp.sqrt(c) * (r - c)\n", "soln2 = sp.solve([E3, E4], [b, c], dict=True)\n", "soln2" ] }, { "cell_type": "markdown", "id": "088e1246-4a36-436c-a7ef-6852d348b1c1", "metadata": {}, "source": [ "

This time there are two solutions (equations for $b$ in terms of $r$), and solving each of these gives a total of four equations for $r$:

" ] }, { "cell_type": "code", "execution_count": 4, "id": "cab1bc44-3cdf-4e83-ac4e-ba1d70f39aa9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1/2,\n", " 11/8 + sqrt(227/(96*(251*sqrt(3765)/9216 + 2159/1024)**(1/3)) + 2*(251*sqrt(3765)/9216 + 2159/1024)**(1/3) + 145/16)/2 + sqrt(-2*(251*sqrt(3765)/9216 + 2159/1024)**(1/3) - 227/(96*(251*sqrt(3765)/9216 + 2159/1024)**(1/3)) + 1631/(32*sqrt(227/(96*(251*sqrt(3765)/9216 + 2159/1024)**(1/3)) + 2*(251*sqrt(3765)/9216 + 2159/1024)**(1/3) + 145/16)) + 145/8)/2]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b1 = soln2[0][b]\n", "r1 = sp.solve(soln1[0][r].subs(b, b1) - r, r)\n", "r1" ] }, { "cell_type": "code", "execution_count": 5, "id": "ed065fab-50dd-4665-97e5-6cb89b0bc5c7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[-1 - 25/(12*(75/16 + 175*sqrt(21)/144)**(1/3)) + (75/16 + 175*sqrt(21)/144)**(1/3),\n", " -sqrt(-2*(251*sqrt(3765)/9216 + 2159/1024)**(1/3) - 227/(96*(251*sqrt(3765)/9216 + 2159/1024)**(1/3)) + 1631/(32*sqrt(227/(96*(251*sqrt(3765)/9216 + 2159/1024)**(1/3)) + 2*(251*sqrt(3765)/9216 + 2159/1024)**(1/3) + 145/16)) + 145/8)/2 + 11/8 + sqrt(227/(96*(251*sqrt(3765)/9216 + 2159/1024)**(1/3)) + 2*(251*sqrt(3765)/9216 + 2159/1024)**(1/3) + 145/16)/2]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b2 = soln2[1][b]\n", "r2 = sp.solve(soln1[0][r].subs(b, b2) - r, r)\n", "r2" ] }, { "cell_type": "markdown", "id": "efade4ca-3dcf-4216-b169-216cc90dc34e", "metadata": {}, "source": [ "The four solutions can be plot together for comparison:\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "c209f5ba-c266-4410-9d90-27ac5af24e98", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "def make_plot(ax, r, b):\n", " th = np.linspace(0, 2 * np.pi, 100)\n", " x1, y1 = np.cos(th), np.sin(th)\n", " x2 = np.linspace(0, 10, 1000)\n", " y2 = np.sqrt(x2)\n", " ax.plot(x1, y1, c='tab:purple')\n", " ax.plot(x2, y2, c='tab:red')\n", "\n", " x3, y3 = r * np.cos(th) + r, r * np.sin(th) + b\n", " ax.plot(x3, y3, c='tab:orange')\n", " ax.axis(\"square\")\n", "\n", "fig, axes = plt.subplots(nrows=2, ncols=2)\n", "make_plot(axes[0][0], r1[0].evalf(), b1.subs(r, r1[0]).evalf())\n", "make_plot(axes[0][1], r1[1].evalf(), b1.subs(r, r1[1]).evalf())\n", "make_plot(axes[1][0], r2[0].evalf(), b2.subs(r, r2[0]).evalf())\n", "make_plot(axes[1][1], r2[1].evalf(), b2.subs(r, r2[1]).evalf())" ] }, { "cell_type": "markdown", "id": "e13e7214-aa42-4c9b-adc4-851c151fefb1", "metadata": {}, "source": [ "These all satisfy the condition that the orange circle should be tangent to the $y$ axis, the unit circle and the curve $y=\\sqrt{x}$, but from the figure provided in the statement of the problem, it is clear that the required solution (with the orange circle within the unit circle and above the parabola) is

\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "5f44c95e-30a1-409f-bee1-67388f718bb8", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle -1 - \\frac{25}{12 \\sqrt[3]{\\frac{75}{16} + \\frac{175 \\sqrt{21}}{144}}} + \\sqrt[3]{\\frac{75}{16} + \\frac{175 \\sqrt{21}}{144}}$" ], "text/plain": [ "-1 - 25/(12*(75/16 + 175*sqrt(21)/144)**(1/3)) + (75/16 + 175*sqrt(21)/144)**(1/3)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r2[0]" ] }, { "cell_type": "markdown", "id": "55b4cf18-9d3a-4e09-8749-59dbb1cb8911", "metadata": {}, "source": [ "and the centre of the circle is at coordinates:" ] }, { "cell_type": "code", "execution_count": 8, "id": "8ed6407c-ac1c-438e-bdfe-58d862a76c90", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.213841779235356, 0.756515988944906)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r2[0].evalf(), b2.subs(r, r2[0]).evalf()" ] } ], "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": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 5 }