{ "cells": [ { "cell_type": "markdown", "id": "761c1747-adda-4e4f-a2a0-a7556e31d75f", "metadata": {}, "source": [ "# Comparing coordinate systems\n", "\n", "In this example, we will study how the choice of coordinate system influences the behaviour of heyoka.py's adaptive integrator. We will focus on a simple (but nontrivial) dynamical system, consisting of a central Keplerian force field coupled to a force field constant in direction and magnitude. This dynamical system is known as the *Stark problem* or *accelerated Kepler problem*, and it has numerous applications of practical interest (including spaceflight mechanics, the dynamics of dust grains in the outer Solar System, atomic physics, etc.). Note that the Stark problem can be solved analytically via [elliptic functions](https://arxiv.org/abs/1306.6442), but of course here we will consider a numerical approach.\n", "\n", "Without loss of generality, we can choose to orient the constant force field towards the positive $z$ direction. The Hamiltonian of the Stark problem in Cartesian coordinates (and adimensional units) thus reads:\n", "\n", "$$\n", "\\mathcal{H}_\\mathrm{cart}\\left(v_x, v_y, v_z, x, y, z \\right) = \\frac{1}{2}\\left( v_x^2+v_y^2+v_z^2 \\right) - \\frac{1}{\\sqrt{x^2+y^2+z^2}} - \\varepsilon z,\n", "$$\n", "\n", "where $\\varepsilon$ is the magnitude of the constant acceleration field. For this study, we will pick a \"small\" value $\\varepsilon=10^{-3}$, so that the constant acceleration field act as a perturbation on the otherwise Keplerian motion of the test particle:" ] }, { "cell_type": "code", "execution_count": 1, "id": "wireless-tuner", "metadata": {}, "outputs": [], "source": [ "# Value of the constant acceleration field.\n", "eps = 1e-3" ] }, { "cell_type": "markdown", "id": "dc8e56ef-c8e8-4e94-85ca-c736f2799576", "metadata": {}, "source": [ "We will also select a set of initial conditions corresponding to a low-eccentricity, low-inclination orbit with semi-major axis $\\sim 1$:" ] }, { "cell_type": "code", "execution_count": 2, "id": "d42ee668-e1e3-4559-b1c0-6e34fd0cb20e", "metadata": {}, "outputs": [], "source": [ "# Initial Cartesian conditions.\n", "cart_ic = [0.48631041721670787, 0.6097331894913622, 0.05026407424597293,\n", " -0.917207331153677, 0.8411848961939183, 0.10100071061790256]" ] }, { "cell_type": "markdown", "id": "bd8590b0-5bdf-46b5-8e76-62fef9ab62dd", "metadata": {}, "source": [ "We will now proceed to integrate this dynamical system using several coordinate systems.\n", "\n", "## Cartesian coordinates\n", "\n", "We begin, as usual, with the creation of the symbolic Cartesian variables:" ] }, { "cell_type": "code", "execution_count": 3, "id": "f346b5ff-9cfe-426b-9a07-5ad08fe9eae5", "metadata": {}, "outputs": [], "source": [ "import heyoka as hy\n", "vx, vy, vz, x, y, z = hy.make_vars(\"vx\", \"vy\", \"vz\", \"x\", \"y\", \"z\")" ] }, { "cell_type": "markdown", "id": "5b5b4bf0-c240-4301-92b0-631bdb738941", "metadata": {}, "source": [ "Next, we build the Hamiltonian:" ] }, { "cell_type": "code", "execution_count": 4, "id": "8b14b902-dd4d-47c2-9b76-a71a97578e37", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((0.50000000000000000 * vx**2.0000000000000000) + (0.50000000000000000 * vy**2.0000000000000000) + (0.50000000000000000 * vz**2.0000000000000000) - (x**2.0000000000000000 + y**2.0000000000000000 + z**2.0000000000000000)**-0.50000000000000000 - (0.0010000000000000000 * z))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ham_cart = 0.5 * (vx**2 + vy**2 + vz**2) - (x**2+y**2+z**2)**(-0.5) - eps*z\n", "Ham_cart" ] }, { "cell_type": "markdown", "id": "2637d545-c4a6-4bcd-80c2-b2ede49e4943", "metadata": {}, "source": [ "We are now ready to construct the adaptive integrator. In order to implement the equations of motion, we will use heyoka.py's expression system to symbolically differentiate the Hamiltonian:" ] }, { "cell_type": "code", "execution_count": 5, "id": "sound-jenny", "metadata": {}, "outputs": [], "source": [ "# Construct the integrator object.\n", "ta_cart = hy.taylor_adaptive(\n", " # Hamilton's equations.\n", " [(vx, -hy.diff(Ham_cart, x)),\n", " (vy, -hy.diff(Ham_cart, y)),\n", " (vz, -hy.diff(Ham_cart, z)),\n", " (x, hy.diff(Ham_cart, vx)),\n", " (y, hy.diff(Ham_cart, vy)),\n", " (z, hy.diff(Ham_cart, vz))],\n", " # Initial conditions.\n", " cart_ic\n", ")" ] }, { "cell_type": "markdown", "id": "e29f6700-bd70-4f40-a449-733c344ad1e2", "metadata": {}, "source": [ "Let us now integrate the dynamics for a few time units and plot the resulting trajectory:" ] }, { "cell_type": "code", "execution_count": 6, "id": "other-sherman", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define a time grid for the integration.\n", "import numpy as np\n", "t_grid = np.linspace(0, 250, 1000)\n", "\n", "# Integrate.\n", "_, _, _, nsteps_cart, _, out_cart = ta_cart.propagate_grid(t_grid)\n", "\n", "# Plot.\n", "%matplotlib inline\n", "from matplotlib.pylab import plt\n", "\n", "fig = plt.figure(figsize = (12, 12))\n", "\n", "ax1 = fig.add_subplot(1, 2, 1)\n", "ax1.set_aspect('equal')\n", "ax1.plot(out_cart[:, 3], out_cart[:, 4], linewidth=.2)\n", "ax1.set_title(\"Top view\")\n", "ax1.set_xlabel(\"$x$\")\n", "ax1.set_ylabel(\"$y$\")\n", "\n", "ax2 = fig.add_subplot(1, 2, 2)\n", "ax2.set_aspect('equal')\n", "ax2.plot(out_cart[:, 3], out_cart[:, 5], linewidth=.2)\n", "ax2.set_title(\"Side view\")\n", "ax2.set_xlabel(\"$x$\")\n", "ax2.set_ylabel(\"$z$\")\n", "\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "id": "03081059-a228-4ea7-83e1-3277d19028f1", "metadata": {}, "source": [ "The plot shows how the initially-Keplerian orbit is slowly being deformed by the constant acceleration field.\n", "\n", "Let us also plot the time evolution of the Cartesian coordinates:" ] }, { "cell_type": "code", "execution_count": 7, "id": "dbca3334-db50-4d38-8674-6c2455e2bd42", "metadata": {}, "outputs": [ { "data": { "image/png": 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e8oaOuPFlvZ3i3P3pEwv1yZte06+fWxxY9uyCDTr2t6/qtL+8FQjhNja06djfvqpP3vSqlm1q9CxzHEcX3vuePv371/XIrOC5+6eXl+vUW9/St/42O7Bs9uqtOuEPb+jEW95IeU0BAKA3EC71UENLhy649z1976E5gRtfx3H0u+eX6Mzb3k55E//cwo069dY39dT89YFla2qb9bV739MN/wvexLd3xnTlI3N14X3vpfyU7p43V+qM297W7BQdkg/W1un0v7ytv72zOrDMdByueXRB4BNHx3F04zMf6dy7Zqpqa/AG9X/z1uu0v7ytV5cEb7ZXbGnSV+95VzenuNlu6+jSZQ/N0bf//n7KTzL/8upynXXHjJQ32++sqNWZt72t/74fvJHcFGnT+X99V796+sPADWpXzNH1Ty7S1+59T5tTfGr479lVOvO2t/XeqmD9Ld4Y0Tl3vaPbX1sRWNbY1qFL/vZ+tx26O15foS/f+U7Kc+HljzbpzNveTnmDX7W1RefdM1O/eOrDwLnQ2RXTNY8u0EX3z0p5I/nAjNX60u0zNH9dfWDZ3Kp6fen2GSk7p3XN7bro/lm66j/zU54Lv3t+ic65652U58IzCzbo9L+8rZc+3BRYtnxzo758xzv6bYob8baOLl3+8Bx944HZgc6KFD8XvnzHO1q8MdiJnLGiRqf9+a2UN+KbIm06756Z+snjCwI3+F0xR9c9sVBfuXumNjS0Btb916wqff7Wt/TG0i2BZYvWN+jsO9/RLS8tDSyLtHXoGw/M0rf+NjvwqbXjOJr+7EfdnguvLN6kk/74ZsoO0uqaZp1529spO/fofz5cH9HNLy7V/+at162veDvasZijH/1nvt5cVqMr/zU3sO4fX16m15Zs0XVPLtKaWm9H+7mFG/XoB9V6bE61/uO7PtY2RXXdk4s0Y0Wtpj/zUeB1f/7Uh5q9pk7f+tv7gevYAzNW6/WlW3T/jNV6e3mtZ9ms1XV66L21en3plsD1saMrpiv/NU+L1kd07eMLA9u85aWlWlgd0U3PLwlcU/43b4PeXFajVxZv1mNzqj3L1tW16LbXVmjxxsaUYc6vnv5QK2ua9ePHFgRGpdw/Y7UWb2zUf95fpxkrvGUx2/toQ0T3+sKcto4u/frZxVrf0Kbr/7cosM1bX1mmTZGobn1leSDM+e8H67SwOqIP1tbrqXnea/3STU16ct56bWho0y0vLfMsc5x4m9UY7dQN//swMPrmgRmrVdPUrhc/3KSZK71lMeXY0NCmv81c41kWaevQvW+vUmtHl377fPCafNcbK9XeFdPDs6q0vt57fXxsTrU2RaJasqlRT87z3sPMW1ev99fUqbGtU7e9Gjyvb35xqRxHuun5JYFz7G8z16i9K6Z3V20NlOWFDzdqXV2r6ls69MjsKs+yzZE2PbMgHoj+6WVv/UnSba/F9+Op+RsCo4Uem1OtlvYubWho01MLvGWZtWqrVte2KOZIf3vHW3+dXTH9fWa8zbnz9ZWBc+zfiffe0k1NgfuJFz/apMa2TrV1xPQvX1nW1LZo9po6SdIdr68MlOWh9+LbfHXJlsA59uS89Yo5Um1zu55dGAyIAQDoDYRLPXTv26v0+tItenLeev3X1xl8Z2Wt/vzqcn2wtl6/e95749vRFdOP/jNPC6sjuvq/wRvf6c8s1htLt+i+t1e7NxnG/+at16NzqvXaki26503vje/qmmb98umPNGdtvX7+1IeeZY7j6CePLdTcqnr99IlFqvF9uvynl5fp9aVb9NB7a/XMAu+N72tLt+iuN1bqnZW1gRvf1vYu/fA/8zSvql4//Pf8QAf++icX6a3lNfrTK8v14XpvMPCv2VX637z1enbhRj3ou3FbvrlRNz2/RLNW1+lXT3s7QY7j6OpH5+uDtfW66r/zA2HELS8t05vLanT3m6sCgddzCzfq/hmr9cbSLYFPTrc0RvWj/8Zf94f/mRfowP/40QWauXKrfvPc4sAnp3e/uUrPLdqox+ZU69++m8W5VfX69bOL9d6qrfr1s96b+Pgog3n6YG29rv7v/MDN9k3PL9Hby2v117dWaeZK7w3qsws36qH31uqVxZt115vem9DNkTZd9+QizV5Tp6v/u0B+P/z3PM1eU6frnlwUCNnueWulXlm8WY8kjo/t7eXx83rmyq2BDl1bR5eu+s98za2q14/+Oz/QCfrV0x/pvdVbddtrK7RgnTcw/PvMNXpi7nq99NGmQOC1ckuTbnp+id5bvVU/e9zboYvFHF35yDzNW9egHz+2UA2t3nPhz68s19vLa/X3mWv1oi/wenbhBj3wzhrNWFEb6NxH2jr048cWaEF1g67+7/zAufCzJxbp3VVbdctLywIh0T1vrtJLH23W84s2uR0BY0F1g+58faXeW7VVv3za+x7t7IrpR/9ZoI82RHTVf+cHRjf84aWl+mBtve6fsVovfxQMctG/vLcq2Xn2X6fWbm1xz+Wqra2BTuR7q5PrvrbEG36+b7UZr/uC0Q/W1rv//+byGs+jNW0dXZ7w9oO13rbHboteXux9L82x/vbNZd4RHss2Jd8fq2qaA6OB5lijW97yjQ7xvm73ZZmxotZzvYm0dWi9tZ15Vd7rjV22N5d7X3e+dW16y1cWe4TUmtoWTyjtOI4WWB+EvOMLrexlbyzzbzNZlndX1Xo+FKlpalezFVLP810751nr+oOyheuTfzvTv8x6nTW1LZ57gljM0VJrRM27q7ovi7+cH1p1NGv1Vk9ZNvjamkXrvWWx133P9wGZvT/+bS6y7i1W17Z4Pmzp6IppTW3y/eMPrewPr2av9p7zizcmtzlr9VZPO7DKdw+weIN3BNISa13/h32LPXXk3eYSq5yrapo9bVp7Z0wbrTp8f033++tfBgBAbyFc6iG74z3D90nuc9anRm8tr/HcYL25bIsibfGOY1O0Uwurkzcare1dem1psqPxpq9z8OicZIjlvxF/4cPkNueva/CMbFq8sdFz42bfhDqOo+cXJTsL/s6B3Sn33xS/sniz2jriN/U1TVEt25y8uYm0dXhuAv3r2p9Ev+W7wbfrb9bqrZ4RIB+srXdvFjtjjuexkc6umOeRDv+okxetOnrDV87XlmyWuXdcU9uiqq3JjsOWxqi3Y7bM/7p2HXlf196ft5fXeDpBH6ypd28eG6OdnscI2jq69PJH3de9PSrBX077U8sPN0Q8czCsqW3WMisQsc8jx3E8n0T7X9c+x15fusVzs/3aks1qTIxA29rc7rnRbYp2ekY7vL7U25m2w5I3lnrr7zmr/mav2eoJExdvbHRvtrtijud864o5enZhMij1159dR6/7OugvLNqkzsR7dn1Dm6cjUdMU9XRO/XVkPy7jP0/sc2HGilpPsDxz5Va3g9fR5Xg6B9HOLk8dtaeZzwT9w0rrnFpV0+yZ18UfWNqP5MRijtbXJ//W/wGEve7MlbWewN8OQ9o7Y57O/eraZtkZqj+MsEMh/+NO9vwwSzY1ejr3q30jq2asSJalKdrpuTb5HwG062jGilrP9Wat9bot7V2e682qLd5t+sMIuyxzrOu6JK2qSZblo40Rz6NSmyLeD2XmWfVQ29yuxrZkIOwvi71N/wcFdvjR2NappZu9AYPNDkccx9Faa7SXPxC062FBdYNnvqIqX2A516qHTY1tbrsuKTDyxv5AYr4v7FprlaWupcNzbvhHDfnXtUdI+cORjVbdL6hu8HwQ4w9f51qBW3Vdq+c94D8u1dY2/ee1fe7WNrd7jsU632guOyDs7Ip5Xtf/Ht1snfMfbYh47gmq67yva+/TFt+Hgv5R3fZ7aW4V4RIAoG8gXOqBTZE2z42vf84H+xOwpmin50bjXd+Nmh36vL+mznNTZ3+K1dkV89xwfbQh4gmt3lvlvZlYan1i7L+5sfe3amur59Mw/6NHdud5S2PU8wmn/1PARVZQ9s6KWreDLnk/yWtt7/LcWC7yjWqyA5rOmOO5QfV/Cmhvc/HGRm21OjYfWdt0HMcTnK2qafbcbKc7Lv7w60PrU8q65nZPffpHaNkBQ2tHl9ZYnQH/PA52Pcyrqvd8Ym1/2hmLOfrAOqZLNzV6RiHYHTjJe0z94aG9v+sb2jyhmv+42J/k17V0eDpb/k9g7U+331tV6wlEPrLqr62jy3NeL1rf4OlEejrWjve8DhwXq7O8YkuTaprarWXestidqer6Vk8ncpbvXFi43hvM2p1w+9g3tHZ4OuwL/fVnBWztnTFPZ2WOr2No1/3C6oiaop3Kzwlr8S9O1Mn7jxb6h/bOmE7/y9s68IYXPMGo/1Ej+3z0jyy1z4WtLe2ezrL/vKmzzuPGtk5P+ODv3NvBygbfiKL51vvXcRxPG7GoOuIJRtOt6+8s2+/DDf468HXu7eX1Ld7RSNVp1t3qe2Tcfk/GYo6nfuevq/fUpz1SxHG87YB/Ymd71JW/bhdUe9/79vKaJm87Gqg/a6SV/5FdO0SLtHWqxWoj5q/zXjvtYxa/dibXra73Bz3JstT75h760Dcqxw4x1m71jhSKtPnXterPF87Z9wDRzi7PvY+/7bHrryvmeEJUf/3Zo7L8x2XpxuR6juN46ndVTbNn//37a9ef//1rl8UOGf3rSd76i3bGPB/2+Otvsaf+fOX0nWMR69xdsaU55SP6AADsaoRLPWAe6ynKzZIU/xTQ3KA2RzvdznxpfrYk76ePZt3ivPgye54JcxOcar2lm5rU1hFTQU6WQqH4TYn5JMtxHPdTS7PuSiuQMR2XksQ27U8X318b70iXFeTEt7kl+e0nDS0dWpfoHJjl9hwfJkAw9bDGUxZvHdhh3IcbIuqKOe569S0d7k294zj6yLeuHS7NX9f9Nk3HpSRFHWxoaFNtc7uywqGUdW/qz60He38Tr2uWrd2aXGY+JTXL1je0ujd1HV0x92bWPabWp8nmkYYhhYnXrfXWkbcOrJEOtc1qjHYqLzusnKyQOrq8N8mLAvXQ/evanU/zSag5T9ZsTZ7XLe2dWpXYP1PWldan/P517U99TZiU6ngu2dio9q6YSvOzFQpJze1dbijkOE7adf3n2DqrI+s/F+z1tjRGVV3fqlBIKkycR3Y9mDpyy2KdC+ZmP9V5sqi6QTEneTy3NEbd+cRiMUdLEx1Ds+6KzcH3ktkf+9N4cz05fFK58nOyhP4jNzusdXWtamjt8JwrJpg1567dAQ12MJPLTIc3FIr/e11dq2dkZ8T3aOgSK1g228wKx1e2R5qajqt5vyy1QozGaDLEyA6H1O571MiMyjFlsScpNiGKeS/ZH5iY/bHbJTPPm+M47nXAXK/tspgOulnXfn/768DuvNe1tLsfemSFQ2rriHkCsIgvGLDryAQVpv6WW0G3WWbapVU1Te6HP3Y4l1jV82GLWdeUc4V1XfXXgX1ctiTCroKcLIVD8Q+y7FExpo7MPtnrmonX3W1abYQ/HFm+qdG9J3Acx73vMGXx1r13Xft1TTiXneL8829za3O7Z/S1qSNz3tvvF1NmUxb7fVabCL7MdXXp5mRZmqKdbqBVnOJab8qZlx0OlKXO97r2/Y3//buhoc3zmLM5LqEe1J9dFlNOU+/LrfUcxwls136PAgDQWwiXesDMZfDZfUcqKxzv3JsbhuWbmxRzpOEleTp4/FBJyZtve16Gk/cfJckbcJhO7fF7j5Dk/YTLbPPAyjKNHVLgWbemqV1bm9sVCkmf3mekJO/QaxNanZTYpj2k24wE+ey+8fWa27vcx5tMp3bskALtNapEUvITz86umDtq46TESApPhzix7Li94mWpscuSqIPDJ5erojjXs+66ulY1RjuVmxXWMXtUdFsPpxwwutv6M2WpaWp3OyumUzO5okiTKorcbUnx0QXmRuyExLp2WGM+Lf7knsMleT/RNB2Mo3cvV2Fulhwn+anmqppmtXfFVJyXrWkTh8XXtcpiPn39bOKY2QGHqdvk8Wxzb4pN/e03plQTyosS9RDfZkNrMhD8rFuW5CeeplPziURZ7E92TVjz2X1HKhyK14vpHC7d1CTHkSqK87Tv6FJJyePiOI4b5phRNeu2BuvPnNd2HZiO335jyjSmrMBTD1sao9ra3K5wKHke2Z/emnPXlMUupzkXTtg3fs43tnW6QY85rydVFGn3EcWSkp/yd3TF3HPlpBTvUdOpMefCJms0g+kkTJsw1A2YzOMnVXUtau3oUm52WEdOLo+v203dS9IGa2SBORf2Hl0i9D+Th8ffoys9Hfh4R/DQxHXBHpFnOtqHJZZ9tDHivvdNB32vkSUaWhgMec3rHjJ+iCTvSBfzvjPnn91ZNiHGUbvFl61vaHNfa5MVHu07pjRRluQ26xNhzuGJ17U7/qaDfvTu8Wu5PWrRvP5eo0pUmJulzpjjXocjrZ3uaMejdy8PlMXU0UGJcqYKR6ZOiLe/q2uTozhMHZQX5Wr34fH3fqr6O3BcWaAsJgw7YnL8uNgd/7rmxHqVQ5STFQ+t1ifakEhrMsQw1yrvCKTEMUvsr32emBDIHJcVW5rcUaomCKsoyVXlsELPuvFwLnG8d6tIlCV4jh2QKKcnHEkcz/3GlCo7HFJze5c7aqy+pUMdXfFz0Zy7qYKVvRP3CytTPBZ3eKL+Vte0uOe12WZJfrZGleZ7XtdxHHfdY/cYHiiLWffgxLmw0vcYsyQdNmmYQqH4/ptz3dRBTlZI+ySurf5HoOP7W54oS/AcM/Vnh1Jm2cjSPA0ryvW8ruMk7xXN+9v7WGTiPTGyJFAWc+6aerc/vGjriLnHZY9Em+Z/pBIAgN5AuNQD5kbngHFDNLQwfvNQ2xxv+M2IjUnlRRpdFr9JMjeZZl6GUEg6InHDUmsNKTcdf3MDVdfS4YYjZsTQ7iOKNTJx82VufkxIUTm00A2eaqxRTaazbm7wN1mdcLPulDGl7iectYmbL3MDvM/oEo1JlMU8qlBd36poZ0x52WH3Jt5+JG2xW5ZkQGRuJE0d7TGyWBXFeSm3uduIYo0qjZdlizsXTcwNTkxZ7McLTP0dObnc/XTP7JNZtteoEve4mEBhdW2zumKOivOSnafapu7Lkiog2n1EiVsWs83F1jZHlua59SDFb8JNGJIsi3UuJG6ezTbbOmLuY3yra1oS2yx2y2I6nWZ/Rpfla7dE58k+F8yn15/Yw4RLybKYcGTfMaUaVuQ9Lma9va2ymJCtobXDDSQPnTTMs017XbPNrc3tbgfJfHq9x8hijfDVkelATCwv0vhE58ks67IelzSvaz8GYurh4PFD3E+XzbqrEzfzkyuK3PeSWXd9favaE+e1CYc979FN/nAueV6bDu5uw4s1siTxHm30nn97jCjWKPeYxfcn2tnlXiOOSZwL9iNAZlJk0+FA/zI5EWavTNEBNYGCHWLYwUkoFP+3uTaYc2ZEafL9bc67WMxx34fmmmw/PmSC2SN3C3aWzbVl7JBCt3Nvgl9zjRhZmp+yLE2mLONNWZLbNNfCw6zrgtmWKWdJfrZVlvi6dYlRK0W5WdpvTLwDvypF5/7AcUMSZQk+WjSpokhDCnPkOMmymvobXpLnfshg14MZOTJ1wrBg/SXWPWJSvP7Wbk2OtDJlGlqYq4mJwN8cFxNAlxXkaJ9EMG+PADb1d1AiqLBHsph62G9MmQpy4gGceSTQrFecl2Mdl/i60c6Yoolr7KETh3qW2ft7QKL+Vtc0uyOtGqPx+htWlKuJidc19WDqYGhhjvYcGQxkAkGPPXIpcR5NnTDMHWllzmsTlJXm5wTC2EZrhJEJRu36M+fC/mMTQdmWJveabEK/0WUFGje0wLO/pg6K87Ldc8EuixlNfYgbWlnhXNS7zdrmdve8M3VQmp8TOMfs0NSERKtShHMHVpYFlm1JvH93H1HsBssmmDL7mh0OufcwhEsAgL6AcKkHpp95gOb97AR9ceo4DSuKN/LmJsZ0/CdWFKo8MSrHDKE2Ic/o0nz3Bt6er8B0cPcfW+YOvTc35+YmYsKwIvfGwsyvYW5Gdxte5G7ThAJbmqJqae9SOCRNSdwI1VnDzVckbhr3GFmiYYl1t/qCssnDizU08Qmc2abpoE8oLwyEKvaElocnbsTbu2LujbsZCVI5NFlHW311NLmiSMNLvGHDhvo2dcUc5WWH3ZFU9hwj7rrDi91wxKxrOia7jyh2P02sT2zT3DjvNiIZdplwpNmadPaoRMe/obXD/STchCP265obZlPOieVFGp54XRMCmZvNESV5mlBe6KkDSapOjHjZc2SJ++iH2Q9zYz2xosgNN826pt4rhxW62zRlqWlqV2M0Hm6aDuaWpqj76Jt5XHL8sEJ3RJlZ1w1NK4o0InHumpDVdD6HFOa4IaQJZOxw85AJQ91HIszrrrSOS3mR9zwy600oL3TPBdO52dAQD4Fys8KaNjE5QtB0KsyjLuOGFgSO6ZrETfeE8iL3fWgCV7Pe2KEFgfrr6Eo+QnN4orPc3hlzb+yT78Ni97w261Yl1ptYUeSGaOZcWFfXKseJP2Kxf6KDaY+cM4GqOU/QvyQ7y8HOqRn5sKY2OIqjvCjXGs0XP2fNNWB4cV4ykElcv5rbO935wMy13h51Z65LdtBjzl03qMjPds8zs259a3y9oUW5mmxG+yTet51dMbUmroWmLPY2zeuOGZLvXh/N9cvUQXF+jnYbbgKZeFmSwVOOuz/2yE4TDBxYOURS/LpnrsmNVlAxIRFKmxGENVa45B6XFCOX9h9XmihL8n1o2up9x5S6QY95b5r1ivOyA8fFHM+hhcn9scsSafMGPfbjgW7oUpCtymHekZ12OOc/LvZjZibQso+L2d99RpcoOxxSa0eXe/9h2mlP/SXWNSOpyouT4VyqUTsHJY7LSuvxQNNWjyrN15jEh2CmXbFHLiUDGW/95WaH3VE5qc6F/ceWKRSK15nZVlPUBD3ZqhzqLYupg5L8HDdEW22NMDLnrjnHVlpTBphyjipLti9mXRMQlRYEwyXzIWRxXrb2TNzD2EGZqXtzLmxpjLr7WW9dF8yIZXNdSLVN/7fa9mcLFgS/9RYA0D9kHC7deeedO3I/+ryywhyVFeS4N8z+kUsTyos0pCC+LPm10olQZVihFdbEb1jbOrrciTRHlSZvxE1nwtxMjS8vDAQKZtmkimA4YgKD0WUFGpHooEc7Y2pt75LjJG+Oxw8rdDv3phNid9DNNhtaTdiVLKdbB4n1NjXGA4ucrJDGDS1w5+LY0tTmLcuwYFnsOkoGHN5yVg4rTAZEiQlu7dEfdjhiQo519clAa4jZZqLuzSN5E8uTYZe7XqIOTHBi5l8wx8U88lg5tMDdpj/oGTu0QMNLvaNVTDAzZkiBW+/mHGrrSM47NG5ogSp8IZuZ+2iiVfd1vrKMG1KgihJvwGH2Z2RJ/OY+HIqPAHLPFescS9ZD1FMPlcOS59GmxP6YkGRkSb7K3ZFoUbceWzu6FArFH6+sKPaGRGY0xeiyApW755EJZJLH2x802iMQTEeltaPLvTk3jyaOG1oQWNcEoxMritxRRKZjZR4ZHTskWe811rGOOVJuVlhjhxS4dW/CNfe9VF7o1oOpW/u4mFFN5pN8+/0wOhEm1Ld0qLW9S51dya+fHje0/4dLl112mWpqarb9hwPI5Apvxz/a2eWO3Nt7VKlCofi5a645EStY6S5QKCvI0W4jvIGMWS83K6w9RpR41pOSHe1Rpfnu6EPTgTcd9JK8bHeUoLkWm052SV6w498cTc73ZEKM2uZ293Gd5OiQHPd1TZvUlGLkkgn6zeiZ4vxs95GvtSnCkQnlhSoriI9OMiM1kqFBcl23LFF7hEwwKDNfomBGS21oaA2MTiotSIYRph6SQVl24LiYZUVW3drzHprjsufIEje0Wuur+2J7XbcsiXLmZbtBWapROWYkVVVda3J0UltypJV5XbOuO/KmwKq/xPWr0a2/bE3ybVNKhhz7ji5TdmJOK3P9arKOqX+kkB2O+I+L59z0BZ/xssTXrSjJc8NY861/jSnqz5QlYodzvv2JdsbcubkOSAS1Da0dbmjlnmN52ZpU4a+/ZB0lj4v3fVaan61J5WaZHTTGX3ecdT9hPrC0A+CJiXpY7T5GmgzR3LqtHTjh0sEHH6wf/vCHnt89//zzvbQ3AIDtkXG49M477+iyyy5TLJaY42bJEp1//vk7bMe6c9ttt2nSpEnKz8/X1KlT9eabb+70bdrczn2iY2CP8DAT95pPnOyRIcOskUCxWPI5/LzssEoLsoMhkR3IWMGKlAwqRpXlBUZMrLFGGBXnZbsjR+pb21Xf0uEO0R5Rmud27gPhyJCC5Ggp/wit8sLgeolO9pghBQqHQ55RJ/ZIlniglTooGz+sMNC5TxVKxZz4jVW1NfqjojjX3aZZ13wCPW5ogTvazIR5pu5HlORZj+mZ9Vrc9UKhkPsY1aZIm2dy0xFWIGjWdUfBDMl3A5lU4YgZMdbWEVNLe/LbBYtys1RWkOOOoNni2yf7PPLXvWfETqMveBpaoKxwKBn0RKJqsCZVj4dz3a1b6KkDs368DpLnX11LhzqtxxhHleYrNzucHLWTWNeu+2G+YM8e4eYGRIk62GLVX35OljsR8ZbEaAzTCRozpCAwCsuUpXKoFZRFvCOXxg1Nhl01Te1ynOTjKGOG5CscDrnrbkycCybQGlNWEAg37df1j1yyj2dpfrZyskKJOmzXhob4aL3crLB7HvRnxx13nD73uc/pl7/8pVpbW7e9wg7WG+2F3Qm3R0RI8fbDjJ4z50HECkcmDIuva67jzW5okKVJidDKLGtsS4YCphNe19KhSFv8vWhPXuyObqgNBjLBECPZqfWHGGZf87LDGlaU67YTbhhhdYj9r2t30M3+mrna7ODJrLcx0qa2jviHIm7gYHWm19R6O/fpylKUl+WGAqt9gYwUb7/zc8KKWXPo2UGFP4xItb/m2ucJiMqTy7pijjqs41JakGJdt5w5gaDMHrlkgoo1KY7n6CH5ygqH1G59CYhnXV9ZGlNs039civLscKTZGnUXXz6sONcN/c110wSRJVbglQwEg6OlzAdCdqhiHm2LtHW63/BpnwsTE8fUfU9Yy5L1FzwuJixc43sPhkLxAM60P/5zoSQ/WRZ3vjBrRJQZLbU+MYeeXX8TEvtqPypqh2xu3fuCveK8HI33HW97veQ8jMnQqr/bf//9lZ+fr4svvtj93TXXXLPTt9vb/QsAGAgyDpfuv/9+TZo0SSeffLLOOeccfeUrX9Epp5yyI/ct4JFHHtEVV1yha6+9VnPmzNGxxx6rk046SWvXrt2p27X5O/er3UduClVW6A0xzI3LhPJCd8LfrpijxrZOt3M7sjRfoVDIM2qnobXDfY3xw5Lr1gXCkfxkOGIep7O2GQqF3FE7dc0d7o3mkMIc5WVnWY/UeUe6jB1aoLLEeuYRiY2RZIBk1mvt6FJre5d7M2Tmf0oGZe3a0hRVW0dM4VB8XROUmVFEydFJBYFQxQ6XcrLCbqCwtaXdfeyocmhhov6S4VxXLNnxrxxmjVxq9s1jUpLvBgomHHFHzyRuEu3jXWdNblpRnJsctRMI5woDYaEdqhTlZik3MSKqtqnd82hWKBTyjLzp6Iq5rz+qLD9Zf6lGS5UkR0TZo9TGJm7QzXkUaetwb+TLi3JVmJudHMXmH7k0NBkImpt7M6fIiJJ8DS3Mdb8FZ2tLuyeck2Q9atbuCeeGlwTDzXVWIDPcCsLs+jNlNEFuQyJoNMeqMDfbCqbaPcdgREm+ey6YT37dOhqSrL/2rpgibZ1WQOQ9F+pb4hPqmzlORpblWeGct/7GphhJZebeGjMkfrztstjrhc1EYv3YF7/4Rb377rsqKyvTEUccoXvuucfz9ek7U2+1F/FrUvz6uLW5PRlw5GYpKxxyry3+0UmlBTluGLHWHy7lZ7vXV3NtS4YqOSrOy3bfT1VbWzwjjIryst1z2HR67RDIP1LIDlXMsrqWDrW0d3o69pKS6/oCrxLrcbs1/tAqLxkaVKcIcuLXpPiXJZi5/sx1tzgv272eVbtlSXa0uw3K8nLcOtjUGFWn9dh2YW6WcrLCgePijrxJsb92WcYOKUy5rCQ/W6PLCpSTFf/GvY2RNk/QWJSXrTFDEvM0+uZV8gRltb7jkp/tBjkbEo8G28FJTlbYnZvPXw8lnnXNeWQ/ShZfZtrB5narLEPy3W+u3drcrraOLvfDqvjr+soStc+xRP3V+bZZkNwf99y06rYwN/nB21o3CEouNyOXzDU1GUzluMcsGM7luNusN+e19ZrhcCgQlDVZ6ybfS62e/bHLEjhP8rNVmp/jXuuT9ZAM2brbZlFeljW6MNV6yQ9/OhPHo78LhUL6xS9+of32209nnXWWOjo6dnq70VvthRldaGtt79Ks1Vs9X25jOI6j+evqPd/Saava2qL3Vm1VtLMrsKyhtUMzlte49/y2zq6Y3l1Zq482RFLW9UcbInpnRa07stO2KdKmVxdvdj9A85fl1SWb3S9W8Zdl1uqtemPplpT7u3JLk55dsMHzxS5GfUu7nlmwwf1GbltHV0yvLN6klz/a5D4+bZtXVa/H51R7vmTFWF/fqn/PrtL8xLc7+8vyxNxqPbdwQ+B1HcfRa0s265FZa1PWw5KNjXpgxmr3m6pttU1R/W3mGj09f0Ogfju7Ynp8TrUemLHafXLCNmNFje54fYXmVgX3d01ts257bbken1Ptjp42Gts6dN/bq3TXGysC9eA4jv43b71ufmGJ3l+zNfC6c9bW6TfPLdZ/318XeN1NkTb94cWl+surywPHLdrZpfveXqVfPvVhytd98cNN+unjC/Wv2VXu9B3G4o0RXffEQv3hxaWB90VDa4duen6xfvL4As3x1W8s5uhvM9foykfm6l+zgq87Y3mNrnh4jm56frFn2hop3vZe8+h8/b9/z9M8X/22dXTp9y8s0f89OFv/nl0VeM/8e3aVLrp/ln797GK372TMrarXt/42W997aI775UjGlsaorvrPfJ3/13f13/fXeV63K+bojy8t01l3zND0Zz5y732M5xZu0JfveEff/vv7nm+oleLf6vv1+97Tl26foSfmVmtny850xQ8++EBvv/22Nm3apKVLl+rVV1/VhAkTduS+Bdx88826+OKL9Y1vfEOSdMstt+j555/X7bffrunTp+/UbRvDrEesWtu73MCnclihezNgbpzsx7rysrNUnJetpmintra0W5Omxm+czMicequDXlGcp6K8bHebdYFwJM/q8CbCETeQKUq8bo5qmqKqb2mXeU+ZERjuJM6JxxpMoDV2SIH75g2O9slXcV62crPCau+KqbY5ao3Yid8clSZuoBrbOtybodFlBcrNDicDhUTHf6PV0TaPoPkfKzQ3VsOKctXY1qm65nZ3zhzzmJMdAm2KtKkz5ig7HB95NMyqW7ssw0vyNKQwV+FQfETU1pZ294bRlMXu+Jv13HDO2qbjOJ6QKJa4IDS49ZcMZEKhkMqLcrWhoU1bm9s9I8bM65ttxl87/nXEQwtzrXPBH44kRzV1dDmecMQ9LvmJcKnVHsEWrz/3kbrG+OTb5hwbMyRfGxJtt/m01B65lBUOaVhhrmqb44GL6bCMccuS65bF/uah8uLcwKN4poEbbYWQrR1dauvo8pzz5risq2tVpLXDfV+YcrqPHSaCRhNeVZTkWp8Yx/9bnQjZxg4tUH5O8j1a2xRNjkxK3Ly79dfW6XZmKorzPOeCCQLtehhq1YE9atEOykyo7I5KTByXgSA7O1tnnnmmysrKdOWVV+oPf/iDbrrpJp188sk7dbu91V7kZsdHnW1ujGp9fZsbvhYnAplxwwr03moF5u9JNfLGfsTKnN+1zfG2xw1VrKCntjnefpjrVm52WLnZYXdd/wiZ4rxslSTOa3OtbvZ1iEvystUY7dT6+lbPemab89c1aO3WFu8IoxSPhNmjSkwgszHRIbbDj1AopPHDCrV4Y6PW1ra477tQSCrKTdaD20F3R8Fku38bfMwsSxXFecoOh9QZc7S5MZoc/ZFYZ/ywQi3b3KS1W1sCI79Gu19w4Q3nSvKtsKuuVY7jWKPNspUVDmnc0EKtqmnW2toWN/DIzwkrJytsBSvecyHVY3HJAC7Hbfda2rvU0NrheeTLlGVdXauqtrZo2oShnhFRgTDH81hm90FjXna8DrckzuuRZXnucSnODQYr9rqBQMuqe3M8TWBlBz1S/IOnmqaoqupatOeoYrczU5Kfo9GBbSbrz4wYTY6qS75fvOd1m3vMzLkwdki+5lUFj4sJ2aTklzDYE3qbsmyMxEeg+t8vo8vy1dDaofUNrdpjRLFnn8ZagaHkDQTzs7MS2/TVX0G2KorylJMV/xbjTY1R93X6s+Li+CjNK6+8Uvfff78+//nP7/SRr73RXjS2deicu2bqm8dO1ukHj5UUH7l2zl0zta6uVVnhkC44cqJ+dOJeys/JkuM4uuTv7+v5RZskxb/J8jdfPMAdvfaPd9foJ48vlOPE+xY3fGGKTpwS/xbcJRsbde7dM7W1uV25WWFdfOwkff8zeyo3O6y2ji6d/9d3NWt1vGN+9O7l+u2XDnTPpVteWqpbXlomKX4O//qLB7jfoPvOilp9/f731NYRnxPzW5+crCs+s6eywiE1tHTozNvfdr/s4Li9huu3XzpAI0ry5TiOrvrvfP1r9jpJ8fu3m846QEclvu3yqfnrdfnDc92R3N/79O76znG7KxwOqWpri754+wz3vvDTe4/Q7798oIYU5ioWc3TR/bP05rL44/jjhxXqD2cf6H5pwz1vrtQvn/5IUnwE7g8/t5cuPmaSQqGQFlY36Mt3vqOWxOPSJ+43Sr896wCV5ueovTOmM2+f4X6b78TyQv35K4e48x3+4qmPdO/bqyTFr+8/PXVfnXd4vE/81rIaXXDfe26wcfpBY/TrLx6g/Jws1TRFdeqf3nIfJ95teJHuPH+a+83Glz88V08v2CBJ+s1zi3XjGfu758o/312rHz+WnJ/snEMr9fPTpig3O6w1tc06+Y9vuo9+3/XGSt15/lRVDitUe2dM593zruYngrlbX16um88+yP324j+8uFR/emW5JOlPryzXxcdM0rUn76NwOKQZK2r01XvedfuTf5u5Rnd/bZqGl+SpOdqpM/7ytnttvPvNlbrtvEN01G4VchxHP/jXPD01P16We95apSs+s4cu//QeCoVCemJutS5/eK5blkc/WKe7vzZNJfk5Wlvboi/eNsMtyz/eXat7L5ymA8YNkePEj/f7a+rcOvnpqfvq60dPip+7Ly/Tn16On7uPzqnWCx9u0p+/crDyc7I0r6peX/1rsiyPz1mvBy8+TLsNj1+bz717ptu2PD6nWjeddYDOOHicJOlnTyx0z90XPtykGStq9fuzDlQ4HNLjc6r1w//MlyS9snizXvhwo/75jSM0qixfWxqjOu/umW5Znl+0UXd8daqO33uEumKOvvW32fpgbb0k6c1lNfpwQ0Q/OWUfhUIh3frKMvd9OGt1nd5eUaN/XHyEygpz9MHaOn37Hx+483C+taxG9190mKZOGKrmaKcuvG+WW5bZa+q0vr5N3z5uN+0sGY9c+s53vqOLL75Yc+bM0cMPP6zTTjtNb7/99o7cN4/29na9//77OuGEEzy/P+GEEzRjxoyU60SjUUUiEc/Px+XOndTc4abT+TlhleRlJ0cuJW427Hlg4uvGl5sAREp27s1NYaPVcTWdWnf0USIc2eyum+feDEnxmxGzT6PKvKFVXUtyf0ck5oAZaoUYZl9L8+OdDTN/lD9cGl6Sp1Ao5JalrrnDPWHNJ3qmLJHWzkBYY4+8sT8JH1GS54ZS7Z0xtXV0WR10s7/JdZNlyUvsd7Ljbz+ClhVO7qsZLWUHFVnhkNu5ilgBkrkxtYMe/zbt+Y/qWzrciW5Hl+VriAnYop3q7IoFAgU7DKv2jTBK7k9ycvHy4kSQY835ZQda44YWKC87S/k58bd0Y1uHdS7E6890OCNtHZ6RVJLc4x1p63DDnuxwSEMLc63jGXysULKOaVO7O3eUGXk0xH1PtAdGztnfUOc4jjuHV0Vxrkrzs91J7u1gzz9yKdLW4Xl8TbLDzU7VNkcVS4Rz5UV5Ki3Idl9T8o42s1+3oTU50s+8X8y6Eev9YrZpH8/OrpgbOg8vznNfM+ZITe2d3ZYl/rXZ8WXmEdH+7qSTTtLEiRN19tlna+7cubr11lv14IMP6j//+Y++//3v77Tt9nZ7YXe0G32dZX/oYndO/YGCHVSUFmS7r1Fd3+p5HMd+3TW1LZ6QR1Jg1JPdcTXrrW9oVbSzK7BusixtnhEcUnKE57q6VrV2dLk3afaIqHWBR+ZyNKIk3iHuisU7xMlH5hKva9WDGxjkxkeVuOFSvT808D7WFYs5nqAsKxxyr4UbGlo9jyP6t+kf+eUPR+xvbjPBU2tH/MMme4SRlGz/q+paPEGOXbeBUTv5KebCiib3Nz8nyx3tXG2Hfr5zYe3WFrW0d7mdmlQjjOygwtRBfUuHGts6rMcKvefC+obW5Mi5PO9xSZ5jyaDHzC1nyumOvCnIUWlBtvvNtXaAaQdlpiz2yK/4qLHUo6XsCb03Rto857U5LqOtdf0h0Jgyb1nsMNG/zH5EbXhJPMDsijna3NgWKIt7HtW3qbm9032/lBYkz6PAyK+8ZIi2oT4+Us2+ZoTDIbd+zbf79jerVq3y/PuNN95w///CCy/Ut771LW3evHmnbX9724sd1VY8MGO1Fq2P6IpH5uqnjy9Ue2dMv3zqI62ra3XnyLz37VX68p3vaENDq55esMENlrLCIc1cuVUn//FNPbdwgzY0tOqG/30oJzFP5KZIVJf8/X39+tnF6oo5+vlTi7S1uT3+yGxXTLe/tkJn3/WONkfa9Ne3VmnW6jqFQ/F1315eqy/c+pZmrd6qlVuadGsiaMjPCWtDQ5suuPc93fryMnV0xXTNo/PV1hFTUW6W2rtiuvWV5br4gVlqjnbq9tdXaMWWZmWHQ8rJCum1JVt06p/e0qL1DXpreY3bOS8ryFF1fau+9tf39MistWrr6NLP//ehumKOhhbmqL0rpt+9sFRX/muuOrpiuvGZj7S5Maqyghxlh0N6efFmnXnbDFVtbdGzCzfqzWU1iXu+XK3d2qKv3P2uXvpwkzY2tOm3zy2RFL9Pj3bG9MunP0rUm6NrH1uglvYujUi8j59btFHn3jVTDa0d+tfsKn20IaLcrLAqinO1urZF5941U++vqdPC6gY3WJpYXqi2jpiufWyhbn9thRzH0Y3PfKSumKPKYfEpKh6fu17ffHB2YvTLUm2MtKm8KFflRblasaVZX77zHa2uadYHa+vcYGmPEcVqae/SFYkROJG2Dv3q6Q8lSfuOLlU4JD08q0o/+Pc8xWKObn1luZrbuzSmLF9DC3P04YaIzr17pjZF2vTIrLWav65BRblZ2md0qRqjnfr239/Xq0s2a2tzu+5+M14W8y2gf31rlX7+VLyObnjyQ8Wc+BcqlOZna25Vvb5273tqinbqoffWan1Dm4YU5mjvUSWqb+nQxffP1tyqes1aXaen5m9QVjjkBpO3vLRM97y5SrGYoz8mAqBDJw5VUW6WZq7cqm/97X11dMX0uxeWqLm9S3uMKNaeI4tV0xTV1++bpaqtLZqxolbvr6lTTlZIx+81XDFHuuF/H+qJudWqaYrq9tfi5+4pB4xWbnZYL320ST9+dIEcx9Edr69QzIl/OcnE8kJV17fq6/fNUn1Lux58Z42q61s1qjRfn9p7hDpjjn747/l6d2WtNja06dEP4qN/zjh4rLLDIT02p1q/e2GJumKObno+fo6duN8ojS7L18otzfrW399XtLNL/3h3jZrbuzShvFDH7lGhaGdM3/3nB1q2qVGvLN6sD9bWqyg3S187coJCoXjdPzyrSi3tnboncVy+esR4lRflamF1RD/8zzw5jqNbXlomx4l/A/VhE4epMdqp7/zjfdU2RfXE3PWqrm/V6LJ8fe3IeOD5m+cW65XFmzK6bvVEj0curVq1SpMmTXL/PXPmTPf/DzvsMD399NM666yzur1x/7hqamrU1dWlkSNHen4/cuRIbdy4MeU606dP1w033LBD98OEGI3RTs/jVaFQyApk2hWzJk4eXpzs3FcpflO7yZoUWUp2iCNtHdZ6JiBKdj7bOrrcTymHF8fntcnPCautI6bGNqvjWmyCKfNIXfLxDNOpdbfZ2pmc2DhxQ2avJ6V+LGlTJN4psB/N8tRRW4e2NIYD65lymhEwBYkRI44T/xTUcbxfx13hDypaOqyv6DZlyU7WX2JZhVt/iePSHAzKzLoNrR1qaA1uM9XIpeH+QKs1WQcVxfE5gcxcV/F96gyMvBmSItgzN552WUzA4a+D+P4mAy3TaSrJz1FbR1SR1k4rrAkebzNyya4DUxYz71J5ca7C4ZBbzubEhNP2I53xejD72+nWfbm//lpSBVrJ+rP3qaI4z31cbGtzPLjrru7Np8Ce+su3z4V4WYYV5SornHwELdIaH2ZvRhCOtgK4eMe90xN2mbqV4udmMHhKvq4ZKRUOxYPhrHDIfY822Oeuey4kH9Uz558ZCdXf+NuJG2+8UQcccICysrI8f3fvvfdq77331h/+8Iedsh+93V6MHVKguVX1Wl8f7yRIKQKZ+hbFrNENpfnZ7vuwpin+6JYJR4py4yN6xg4p0JJNjZ7QyqxjQoz19a2eUEWS9ShZMBypKM51z8+NDW2ex5LMuks2NWp9fasKEyGAPapEigcg5jXDofg13XTCzRxlTVaYYzrEa7e2qLqu1ROqmPqT4iGGv4M+1hfI2I8HjirLVzgUf7S1pjnqGfklxa8R6+paVV3fptyscKL+cjz1t66u1Z1gPC8x8ssO2CTvKKz8nCwNL4mP6Kmua/WEAv7jYuYXShX6+Ud+mX1ujHYq0tbhCThMWWqa2rW+vs0zssZ+XXt/ssKh+HGx6jZef8lgrzgvW0MKc1TfEm/Tmv1BY1lyRI//PsIOyvwjv7IT88qZET0Ra8ROKBR/DG3Z5iattwLM4rxgWUwdmEdM7bBG8s7XVFGcq7zssKKdMW1qiKasv6WbmrShodVtF/wh0Pr6tvh7tN1+JNGMYosfM/t1TYC5rq5V6+vt/TWva4eb8WW5WWHlWeeY+dTfDqXtANMeqWbqfnRZfvy9VN+qaep/9tlnH11yySX6yU9+ooqKisDyM844Q2ecccZO2/72thc7qq349nG7q70zpj+9slx/m7lGL3y4UZsiUYVD0nNXfELVda36/r/mav66Bp36p7fcc+KKz+yhLx4yTj/41zy9t3qrLvn7B+5rHjZxmB68+DD94cWluvONlbrj9RV6bM46bYpElZsV1ss/+KQWrY/oqv/O15y19fr07193r2e/O+tATZswTN/+x/tatD6i8+55V3nZYXXFHH1q7xG67bxD9MunP9TfZ67V719cqj+8tFQxJ36/8vqPjtfLH23SVf+dr9eWbNEJf3jDbW/u+OpUTawo1Hf+8YGWbmrS2XfOdK9LXz96on70ub11zaPz9fjc9brqvwv0x5eWaXNiFN4r/++TenxOta59bKEen7te86sbtHJLs0Ih6V/fOlIxx9E3HpitlTXNOvvOd9wP9r736T30jWMn64qH5+iljzbr2/94X5VDC9XeFdNhE4fpkW8dob++tUq/euYj3T9jtWasqNHSTU3Kyw7rmcuP1fpE0LBofURfveddd76zH5+8t844ZJy++eBsvbdqqy689z33WviFA8foj+ccpD+9vFx/eGmpfvPcYs1evVUfboioKDdLT156jJZsanRHVp1790z3sb7bvzpVk4cX6cL73tPC6oguuO8993p01tRx+vUXD9AvnvpQ989YrWseW6BH56xTc3uX9hxZrKcuO0avLtmsb/3tff1v3nqFQ3JHCN321akaWZqnc++aqdW1Lfr6fbPcft0PP7eXzjtigv7fv+fpibnrddk/5+iY3SvU2tGlKWNL9ei3j9Ljc6t15b/m6f4Zq7Up0qYlmxpVmJulv3/jcNU2RfXlO9/RRxsiuvyhOVq4Pl6Wq07cW2ceMlbfeGC23lxWo2/9bbY7us6U5a43VujGZxZr+rMfaV1di1ZuaVZpfrbuvfBQra5p0Tl3vaMZK2r1g3/N07ML42X5w9kHaWJFkc656x0trI7oO//4wG0nvnLYeN1w2hT96ukPdfebq3TVf+frc/uNUkeXowMrh+gvXzlEby7bogvvm6VH51RrZFm+nlu00T3vhxXl6ozb3tbarS268l/z3MfK/t/n9tIXDxmryx+eqyfnxUfTHZ8Imw6bNEx/OPsgfWLPCn3/kXm67bUVamnvUnV9vE255ZyDtDkS1ef//JbmVdXrN88u0ZPz4qHU/zthL504ZZS+9tf39M7KWl320Bz3PDrviAn68cn7aHRZgX7z3GLd8L9F8XusaKcmlBfq51+YorOnjdeZt7+tFz7cpD+9vFxvLtsiSbrxjP1VUZKrL/z5bS3f3KSfPrHQHbF+0dGT9M1PTFY4FNL9M1br1leW6/i9RigUSvZXd5Qej1zaZ599dMUVV3T7zT9jx47VK6+8ssN2rDv+SnAcp9uKueaaa9TQ0OD+VFVVfeztm5vfprYOq5Pt7fjHnPi8NObmyjxyZN4ETW2d2uJ7LM4eubTFF46UWKNyzLLcxETgkrej7YYjiW2mCnNMp7bE6oSbx8zMTYwpi5lfwQzhCwQr1uuaspRaZXFHYhR766DRDlxK42FCOBxyl9shm78eGqOdVlm8jyyl2mapNYqoNfEYQap1U23TDpfsMNF+3Xh45B0xlp0VdstS39Lu7m+q+gsEFVY4V+MLVUrsICdxrEsTHRy77u2ymKDCXuYPeuyRX8F6T2bQjSmCMjuwqWn2BjKpRn6lmjfJ1EFJXrIsQ9wRPe2exwo967Z0uCFQqtf1l8WUszPxeJp5xKLcPVeyA+uWFwePmT94KvOEwybQynNHX9kjAbsdudTa7s6FMLyfjlzytxMHH3xwIFgynnnmmZ2+P73VXoxJMSqixDdiwj96oSQ/RxVF8U9MY0587jl/6GK/rh0KxJclA5Bgp9YbYtija0znPr5uq2femu7K4g+BqutbPaFUKBRyg/+2jlh80v02b1Bhj0Dyd/ztAMk/Eij4+FVy5E1OVth9pLS6rjUQVIyxRof4Axk7BOpuxElNU1TRzuQjif7RSdX1LZ55k+Lb3Pbrrm9oVUt7lzukvSQ/R0WJoKfbde3X9detFSbaj4rZx3pjQzw4aQwEFcnApslX96OtOY66H4XVGhj5NaIkPsl4V+K6a4+8keSOzFlfnyJoTHFc/PsTHGGU4ynr+gZ7BGH375dU51hze6d7XErzc9xtNrfHP+jzl8UOpvwhrz2Cyz5vTXBsl8U/Us2Mjl1f3+aZJ0tS4JG6/ubNN9/UokWLtNtuu+lXv/qVWlp6Z3LynrYXO6qtyAqHdOUJe+mvF0xTcV62+2HXl6aO054jS3T83iP0v+8eoz1HFqu2uV3tXTENL8nTN4+drMphhfrnNw/XxcdM8rzmVSfFH6G75uR99MdzDlJudth93fOOGK/KYYU6ccooPXHp0dpteJH7fttzZLFOO2isxpcX6j+XHKXP7jtS7Z3xD61DoXhnOD8nS788fX/94vQpykq0U5L07eN2U3Fetk47aKwe/r8jNbQwx70+H1Q5RJ/eZ4R2H1Gi/3z7KB0xeZj7Ps7LDuvbx+2mgtws/eHsg/StT0yWlAxYv/up3ZWXnaWzDx2vO8+fqpyskPutkidPGa29RpVon9Gl+u+3j9KkiiKtb2hTa0eXSvKz9fWjJ6k4L1t3fHWqTtl/tDq6HK1MzJH7vcSjWN84drJ+88UDJElLN8W/4fGcQytVUZynA8YN0YMXH6aS/GwtqG5QpK1TY4cU6NzDx6usIEf3f/1Qd4SIed1LPrmbQqGQLv/MHm5ZXl4cH3F30TGTNLQoV0dMLte9Fx6q3Oyw5qytV2fM0UGVQ3ToxKGqKM7TfRcepsphBVpT26KF1RFlhUP67qd2V1Y4pOs+v6++eMg4dcUczVwZn7PoG8dMVjgc0qf3GanpZ+4vSXpi7np1xRx9Ys/hOqhyiEaXFejBiw5XeVGuPtwQ0YaGNpXmZ+tL0yqVkxXW7846UIdPih8XE7h89/jdFQqFdMbB4/Sjz+0tSXp24Ub3/CxLfNPnXV+bppys+OixTZGoRpbm6cxDxiovO0u3nXeIdh9RrE2RqN5bFd/frx05UZL0zWMn68vTxinmSA+8s0aSdP6RE1SSn6P9x5Xp918+SJL05Lz16uhydMj4IZoytkzFedm66/xpGlKYowXVDXpnZa3CIekbx8br++qT9tGxe1SorSOmJ+auj7/uEfHROsfuMVz/74S9JCkxqkz65J7DtefIElUU5+n286YqNzusVxZvVnV9q4YU5uiU/UcrFArp11/cX5OHF2ljpE0Pvbc2Uffx994ZB49zt3H/jNVuHeXnZGl8eaF++6X4OXbv26tU09Su0WX5OnHKKOVkhfXHcw9SeVGuFm9sdB/lPPvQSknStz4xWUfvXq62jphue21F4vwcr3A4pP3Hlen7n91TkvSHl5bKcaSjdivX+PJCFeZm60/nHKzscEjPLNio+esalJMV0pmHxB+nvObkvXXZp3bXgxcdtlOCJWk7wqWeXPzz83fePCEVFRXKysoKfIqwefPmwKcNRl5enkpLSz0/H5e5eWtKEXDk52S5n4au2By/2BTlZqkwcYNvbmoa2zqTkyKX+jquVqfWHyg0Rb2PZpmTwiyvS0w0LCVHPRXboZXvde1t1vpCgfgn5fEym69fLsjJcoev26NgzGNUgREyaQIi+xG+EVZH2uzTpoY297nnCl892I98BYKyFIGCHY6Yb6tJFc7Zj8X1ZOSSJ1RxR5wky2KW11mPO5njnWrd5AiZ5GOFW3xBmam/9s6Y+4iG2VfJO4ImGTT6Ry4F68+7njdUyc4Ku8fdnhfIHblkH29Tfyke+UqOqvNus7m9y31N+3Ew+zHTQN1boZUJZCqKgmXxr1eYmxxVZuYBKLTeo6neh/7gKWJts9wXLnkDreToI9NJrG2Oamtz6vPIE2j105FL29NJmDx58k7bj95uL+xObXehgN1Bz8mKj24Lh5PfULmhoc3zWJwkz/w+3QUyGxpSdcKTc/RsaYy6owT9o0PW17cFHxFKETz5Axnvsvj5bHeINzS0BfZpjDUiJRAC2WGD73VNHWxtbldjW4f7wUeqR83MhNT+191Qnxw54g8FquuSI3bM6KGhhTnunIAbrbL4g7J1dSkesUoblCWDRjOax4x0lJLnSnVdcn/NfURy7p9Wz0gqe3+q64PnyciSPIVD8bn5apqsuacKfAGc9brJkV/BcDMZcOQnt+kb+ZUVDmmk+QY2a9SO2aa9bpOvnHZZ/I+Cmv1pjMa/Ta7Jd7xHW49B+sPEMe48WsFHV1PVX05WSHnZYRXkZrmjydfb51GBd389gaCv/jZYjxW6AVtif7Y0RtXS3ukZ+WUv3xhplf0onuR9xK8/OvTQQ/Xiiy/q3//+tx5//HHtvvvuuuuuu9xvo97Ztre92NF9i0/vM1KPXxoPdM48eKyuPXlfd1nlsEL959tH6WtHTtAn9xyuO8+f6r4fs7Pic/v86dyDdejEofrZqfu6cwtJ0mkHjdVD3zxCUycM1RcOHON2rCVpYkWRHrv0aH3xkHE6qHKIbv7yQe6HYQW5Wbrjq1N1ySd308TyQt3whf2075hkGc8/YoL+esE07TWyRKceMFrnH5mcb/egyiH69yVHar8xpdp7VIlu+tIBbl+lND9HD1x0mM45tFLDS/L089P2c/tPoVBIV5+0t374ub1UnJetUw4YrS9Pq/TU0Z3nT9XQwhxNLC/UVSfu7S4bVZavh//vCO07ulT5OWH98vQp7n1VdlZYfzj7IJ1ywGhJ0pkHj9XRu5e76355WqWmn7m/crJCmlBeqO99eg932X5jynT/1w9VWUH8+n/d5/dVXmL+s8LcbP31wmk6JPHo2NeOnOCpo6tP2lvnHjZekjS5osgNPyTpiMnl+vO5BysnK/644LWJOXWk+H3hA18/zL1//MYxk9xRPybkMI+V7T2qRGckAgNJOmtapS771O6S4n2cH1rHe3x5oe762jS3Hbv0+N3da0tOVli3nXeI254fVDlEJ+w7yl33kk9O1pmJeZ4Kc7P0f59IluWQ8UN1/Rf2c//9vU/v4dZRSX5OYt6k+HY+s89It45CoZB+ftoU7TM6/u/SRCBonDhllL5jzQn07eN2d/9/zJAC/f6sA91/n37wWPeR7qxwSH8852D3ejm6LF+fP3C0+7ff+sRkHbN7cnSkvY0pY8v0s1OT773zDh+vgtzk8f7j2Qe7/YfdRxTr0/skrw3XnrKP9h5V4u6DCZsk6XP7jdKXpo5z/33R0ZOUk8gKRpTk63dWWY7ZvUK7DY/PtxUOh/TbLx3oHqf8nLDndf7v2MmaMjZ5zpk5viRp3zGluvT4ZJ2dvP9ot0+Xl52lH5ywl9uO7gw9fizOXPxfeOEFXXvttfrLX/6i66+/Xt/4xjcUDmc8dVOP5ebmaurUqXrxxRc9w2NffPFFnXbaaTt9+4Yd1mz2dVyl+M1STVO7VtXEA5kKT3CSDIncCb1LgnMuZYX9gUJ8WVtHzH0UwBPIJC6i5pvrshJz5cTXTY6C2eyb58mem2aL73EmM4qosS2Zyg+3Aq3SFIFWuW9/G9s6Zear9wdETdFOtw5M42IvN9vMz0kGG+66vlFPdlnskSNmm3nZ8W9na++MaWXiuAwvtsqSuMGta25352VKNR+Of0J0z6N4vrBBigcK1fWtWlPbrM7EyuW+AMQTjqQK5xq9+2MuMlLyeNvbNDeqmxuTX3fsH7UTaeu0RlL5Hm1LEXaZfWpODPc035KWOmTzBkhD3G8dTPVoW7Is5nh7Ahl75JIvGLUDmVrf+ZduFJZ53K62ud0NGu36S/W6w1PUn/n+Bv/x7OhKfktfqtddsaXZMweUvay+xQ55++fIpd5uJ4zebi9SjopIvHdHWY+4mHPFjLSQ4iNAq+tbtbGhzR0BEpjzpr5VeTnex7q8I0e8ndr4HD15qmmKarH1LSKpHj3yB0j2MvP//vmY4nMFtnpeU4pPTL+1uT0eyHQTEq1vSDU3TXCEkXnd0vxsd+L9pdY3JnlGA62p84zoCQZlbe61KRlwxJdtboy6IxPNemYUzKqaZs+jW/5Aa0OKxwo9QZlv2cjS5GN85npUlJvlngtjhxboww2RlCOt7EDQvF6RL4SMh1bebWZnhTWyNF8bGtrcR4BTlqU+GG7aZfEHHPa5YL6ow/5gZ8yQAq1vaNMGe9SO2aYbuCbDkZSP+PnKUpibfIxv+ZZGa+RXqpFC3Y8aMx0Tf2i1xToX7Pfo6LIC1bV0JEIib8jmGenXzcgvz8jDRP0NK0o+xrd8c5NbD0V5yXUXrY8kRi6lDkbN/WF/dcIJJ+iEE07QI488op/97Ge6+eabdeONN+rMM8/cqdvt7fZCknYfUaK7vzYt5bLS/Bz9/LQp3a77hQPH6AsHjkm5bOqEofrvt4/q9nV//+UDUy7LCsfDnqtP2jvl8uP2GqHj9hqRctnuI0r09PeOTbksLztLv06MFvILhUK69PjdPZ1i26f2HqkPfvpZ929tI0vz9fT3jlHMkRuSGbnZYf3lK4fo92d1uSPjbeceNl5fOHCMCnKyAt/SO3XCML137acV7Yx55riV4teEf19ylGqbo+59ol2WG8+You8ct5uGl+QFtnvCfqP09lWfUnZW2P0Qxpg8vFiv/L/jtLGhTXuOLPEsy8kK694LD9XC6gbtObLEDSmMKz+7p06cMkplBclvtkyWZaheuvKTqmmK6qDKIZ5l5cV5evK7x2huVZ2OnFzhqYdQKKSbzjpQpx44WrsPLwm87nmHT9Duw4vV3hXzBDeSNKmiSE9ddozmrK13Jww38nOy9M9vHK7nF23UoZOGBe57f3DCXtprVInKCnIC59qn9xmpBy86TKtqmt2RPsawolz961tH6sl563Xy/qPdsEuK923/ct4h+se7a7Tb8GIdPrncs+55h49XXnZYW5vbdcFREz3L9h9XprsvmKZ3VtTqK4eN95xn+TlZuvfCQ3XXGyv1iT0rNLGiyLPuDV/YT+XFuSrMydaFR3tf9/i9R+gXp+2n+esadPln9vAsGzukQHeeP1WPzKrSFw4c48kbsrPCuu0rU/Xb5xdr9xHFOmnKKM+6lx6/e+KLltp07Sn7aFfqcbhk9NbFX4p/c8T555+vadOm6cgjj9Rdd92ltWvX6pJLLtnp2zbckTfWo1Am4DDLa5rak4GM9WYptsIR/4TeybmcOtQZM533+LIi62bdDAn1BjLJjqsUH/VgLgz2I2rBR6G6fwTN7FNjW6e7zeGpAq3aFsUScyUN8wVa9reS+UcRdcUcd6LSVK9rtllhhUCmQ+MtS/CxOP88RaasNU3t7ogy+5iZdVfXtrjfzGYu9nbYYL4q1T/yyw4U7G2adZclbhSHFeUqN/Gpgan7+paOQDiX6pE5cx5lJUK/JmsobqqRS+4Iraywuy175M0W30gq+9FBc24O950LGxra3Jte76N4yRFG/nDEBEQNLe2BxwrNiKjm9i53dJxdFtP5W1Pb4n7LnPuoY6JM8XDO1F+K+aNSjCIqTYRLZpv2aDNTD2auJ/t17ZFz7Z3eUXVmDpCumNNNWeKvu3xzo/uapmHyjFzyjfzqr3qznTB6s70YY02w6x95k58TH/lQ19KhJYlwxA5a4x3Q+vQTDTe0Bs5L06mta0k+qmy3HWOG5KumKeoGMuacjS9L8eiRf7RPQ3DkTWFutlsWE1qVeMqSrw83ROIjUrobVWI9RuUfrbIp0ua+D802Q6GQRpfla9nmJi3ZmBxVa26y7UfCghNSJzv+432BwrCi5NxT5prtr79VNc1aVZP8sMA/MmxDQ6s7t1TKRwd9I29yrKBnqVt/yQ7MWCsMSze6y/y/WXeUHVptMdfs5OuOGVKgDQ1tWl3b7D4abM5Be0RU4JFOt5zBgMM+F8x5bdffaCv0syf09palzd2Wf7Se+cZCe3+k+HuivqXDPRfMCKN4/aV5PDXVI2qJZfa5YN4v/qAsHvq1BUcRlSWPmel7FPnevxsa2tzH80ut83rskAKtrGl230tm5Fd8m8HJ6JOjzbyP1PV3p5xyisaOHasf/ehHOuuss9TVFfw6+R2tL/QvsG3pHuMJhULKSvOUT6pgybCvVX552VmegMKWFQ55+mP+/THBdSoj0nwrcGl+TiDMsrd5oC8csre535iybl+3clhht/s0rChXn9o79cjurHCo22WSAiGNbUJ5kTv6ym9oUa7OSYzwSrXN0w4am3KZJH1iz+H6RGIUl1/lsMJuQ8qyghx957jUy0KhkM6aVplymSQdv9cIHd9NqDpmSIFnFJetKC9b15zUfcBzfuJxwVSO3r1CR/tCO2N84lsLU8nNDusXp3cfSu9M2x0uGb1x8T/77LNVW1urn//859qwYYOmTJmiZ555RhMmTNj2yjuIO29Se/CxOCl5A7IqRcffrLu5MTm55Ej/hNStne5NpOkQ52SFVZCTpdaOruTImxQjouwRRoH9TTFXjrkZaora8zwlO+HuKCK3sxwcIWOWDS3MVbaZINUKepKjZ+LrFuQkO+ErEut6gx5Tf8EOurlxjn+rkXf0jOexuBRlKc7LToR+yZFL7jZNoJWoPzP5s5QMOOKTaMqzzcKUgULwUahliZtTe7SZCRSq6loCo5rKCuwQzTtPkSlrU7Szm5FL3mNWXpzrGZJsytLd/FuStLo2VWgVX74sEY6MtBpFs2xNbYv7rUSpHhfzj1wyy+PhUnCbZl3zLLz5lrn4NpPnWGBuqcSyaGfMM9F6cn+9xzvVeW3qNhxKBmT243bhRJ1WJLYZCoVUmp+tupYO93Xt0MrMubRsU/D8s0f6mTmr+utjcX690U4YvdlemK9pr2mKqr7FOwpGkkYlRj6kChTMyCbThtjruo/GNLS5YYo5Z0vyc1SSHx9tajr3xb6gZ/66BvccLPZ1liXzyJJ3hIwdnJjRFiYEkuKd/7qWDncCTPt1TVlWbmlOMaokGVSYa5RZt6I4+fXqdqDtliUxAfSSjRHPa9plqU4RKNjf+hbxjZ4xo5NWbkl27oOhn9ywIRSSChOdFTuoaPZtc2RZnkKh+PXIfEOgfS6MLouHS0tShBjpHm+zwyWznyXW6KRRpfla39DmlsV/vN9fU6fFG5JlcefnSjXnUsrQz4zo8b6ufS54Q6BkaOWve/uYuaPjehhgmqDHnAtmbikpOZdTPBj1Bnv242v+0YX2ueC+l3xBo+R9DDLVI4mm7TDbNNeFaGfMnSDYtCvx/c3Xyppmt/7sZe43HXrmXPKPnOuf4dK9996rRYsW6cMPP9SiRYtUXV2tUCik8ePH69RTT90l+9AX+hcAMBD0OFzqCxd/SfrOd76j73znO7tse37mBsJxkjf/I0qCHUW3s1xihzVmhFH8ZrkwN8u9YbEfXzOjNPyBQmtHVzKQKQmGLqlGTJhlm6yvxTVpuV2WVIGCPyjzP/4npe6g2xOF+0eyhELxkTcNrR3JEVG+ETL26/rrQJJWJDobZqLL+P4kAwXzLTjDU9RR6kDLjPYJ1p8djnQkRmHZz4ibQGFVikChzAQKm1MEgr4RWqX52e4nlPbIL/88RabcGxpSB5j+kUupzoWNkTb3W+bM8rzsLPeT2lSPi5l1TUfPrr8yN6xJhkCm42sCtub2LvdTVX89rG9oc49LutE+qQKZ+NdMeyflLk7MF+Y4Sj3qLrHu6hR1VOY7r4cV5VmjAJOPxSVDNG891LV0JN+HJcGgcbm7LHhcNjS0uqMI+utjcX2lnTB6q70wE3N3xpKTiPo72h9tiKQMFMyE1Oa9Fg7JnYPHnlC5zB0p6h3FsaStMeVoC7NuTzvLJowwj251dDluO+EPQBZWR1K+rgmQTChtjyqxR0SZ9sSsa3+b3OJU+5t4XXfkl9UJN6NVqra2uPP2mfeYqYM661sb/WVZuaXZCq2s0T5mmyasyc12rw32qJKwO9I2vm5edpaGF+dpc2M05fEeM6RAH6ytd0P0VEHZ2q0t7jXbfXQrsT+bIm1u8GAHSGOHFnjCpVRBj7ssL1kWzygsX3Bih36mXfOEI4lHt5Kvay9LdVy8gcz6+lb3d54RXIkAM9XrmrpP1l9wm+tThHN20LM2MYq6OOW50P17afnmRs9k32ZfTf2ZkUumzcnLDj6emi7A9L+3Jf+cVYnz2hq12Nre5c4T0l9cc801mjJlivbff3998Ytf1P77768pU6aoqCj1aIedpbf7FwAwEPQ4XOorF//elpcddjsN1Sk6y+amx9ysDC9OjvAwNy7m8bWRpfmBUSXmazQlbwe0OD9bmxujycfiSoNBj3k0K1UgY9azJ+WOD/VMfFVvJPgombmZTz7iZ41WSeyvfwJse5v2N5f496mhtSN1/eUnR8F0tz/mmyQ8YUNeMlCo2toaXO6rB09ZEvVn1ksVLplH1/z7W5oIFEz9pZpnx5QlVbi0OcVjUKZuY07yPEoVRqxOvG55inKudusvGPqZ86QgJ8szFLg0P0dtHdGUdW9ugJebxwpLgudCqvqLz1NhAszu68F9rNAKZMy8YSnXcwPB+P7Yk3KHwyGV5GUr0taZMrTyB5jlvkfm7NdNVX91ze3qcpzAuuZ4u3VvB41mcvLE+7uiyB4t5Q1xi3Kz+l3nwKCdiDMTc1fXt7ohkSdAMqGL+1hccISCOXeLrJEYng5xipEPY4bka8mmRrej7X0UyrvNYmvZuCHxYfL2aCnTluVkhTWiJF8bI21pAxBzbfWWsyCxzcRoKassppwNrR1q6+gKrDtmSPzr1VON7nKDshQd/7GJsthzS5nlpfnZKszNUkt7V7LurfozE5qmKqcZBbMsxfE0+7O5MeqGZ/462twYtcoSHJ1kltkhmgkqlqaYJ6u8OBlgmuPmWXdIgWapTotTjO4a7T//POdQMvRzg5PEcnNer6trTY6u8ZTFG8CZttV+3SUp5smyR3eZ9idVgGnKUpyi7k2A6a8DKR4utXV6J8i2g55UwdSYwDkWfC+Zcyw3O+x+0GXKWd/SoSx3Xkdv+FnTFLUeiQ0GmMngKRiUxR9J9I5cKs3P0dPfO0ZjygrcILo/2bRpU2/vAgBgB+lxuMTFPy4UCqkkMVrFSBWsuMtKgp1IE1SkGvFk5GWH3SHu8eXxmwjziV+qzn2q/TE3Ye56pXmeZ5ZLC3LcgEhKPVrFjNJIFQok1+t+WbH19fLm393tr3/d4Sn2J9V64XBIxbnZ7oSp/uUlKerB3WbgdYMjToy87LDnZrqsoPt98q+bKhxx17OCiPycsPvpsDuKLd055gkqut8ff93a56Ypy2brXEi1rv9b71K+rlV/WeGQSvNz3PklpNSPB6bapr/+Uo3WM+zz1uxTpK3Tmqup+/pL9Q1/qfbHlNM8xhgOJQMwe7m7rj1yqcC7f6kCLXdf+/F8S7QTSWZibnO9L04xisO0I6mCJzOxvt0OxDvEuappak+5runYGt5RRPFl7rerWctM596ECdnWN5bFXzceLvnnY5KSHfhU2zSjsDZGzATPyToozc9x54+L+jr+dlnMiB1PWYZ46y9ViGbY8zGFQiGNKsvXyi3N7ocfpSmCHiNVIGOugXbAUV6Uq9yssNq7Yslv+fK97tyqerfuU50L7mTfKcpi6sCegyfLCjDrU5wLJphKfuuYHWAmJ1OPr5dcFv/QS+4x8b/umLICratrdT8cShVMmeu9N5CJLzMfQhTlZrmP0tuju5LrBgNDU5bUxyX4mJ4JBM1In+A+xYMe95imOP+S525wmflQxD7/ivOyVVaQ4/lSCP98V/PWNbghWqr625JiVJ1ZZtaTvO1VunlWAADYVfrfRxx9gH3TaE/+LKUPQPyhij2ZW6E1uapZzw6BSnzrpnrMpyfLRvg6rqW+stidZX8nPG04kmKER6plqddNF86lCQVSBApGdjjkufHyH5dUcy65y0rsoCfLvZk3yzzhXJqyDCnwhyPJ4x0IMawgIv64Xc/LUtHD0C9dqJJq3XTHNF1Z7G36l+dkecuSLszxL0s1ws3dZlH32/SvG6yj7gMiT9iaGB1nDC3M9bxnA+sWdR+UpT8uA2O+pcHOhERGqpEuhmduFd8kn/6JRgPrpujAp9qmP3Qp9oVW/i+fsK9zo9MESGa0T3JZcBRWqvXiZfEt72HQM6as+2Vm7qlUy1JtM1UAkmqZv97tsoTDobTH21/36QJBe1lFUZ5yrW8D8pcl3TZNINOT/bHvA3Kzw57rcCgUfwTQGJ1m3XRl8de7/3o5dmj357V/WapHL1NtszgvO1Bn6db1zuvlX9b9eeK/zwosTzGCK/U2u78umNDPyMkK9ctRSgCAgY2WKQP2zbM9+bOUKljpPlwaWWLfwIU86w73hUDBzn33ozgq0oz28X+rgX3zEixLug569+U0j9ulWiZ5OxBmu+7rbkfw5A+X7OXlxbmer9IM1F+KScS72187JAqEcwXdlyV9wJE+HPF0MIrz0palPMUjVsl1tyf0Sy4PhdIfl5FpRn75v5LVDlaGF6cP54Z7Ri559y99uNR9gBkIgPO6r/t051848U19qZZJqQLD7oPG8h4G0ui/RpX6OsRpOtr2+ezvRAbDpe47vcFApvtwxP8esjvwgWVpXjcwWipNOf3Xfn84UpTbfSe8JF3H3x9UDOm+LP7jUmZdi9MFWsEgx7tNe3luVtjz7ULp6ihQTl9oZQdB6bYpee9N0gVI2yrLGGt5sTUfk7S94ab3/sK+L/Bfa9Md77HbEfT4y2If0yLfh3iBwDBNuGlf+0eW5Ml6GZWkOf+2tb+ekUtpwq7c7LDn/qM0PyftN2cBANAbCJcyUJKmgxkY7ZNiQmVjZGn3HYxAIGPfcIb8j6F1P8LIH2gFQ6vkPm2zLGlGLmX6umUFOZ6RQek62tvqhJem22a6kV9pRs+YfUy1nn+b/rKUpXmsK12I4d8n/+NraY9LmkArL9s7CivdyCX72//i2+w+pAwGjcHH7VLtj3+Z5H+UrPuyFOVme27uA8fF2id/aJqujoKjsLoPrfzHxX9M7QDJfy70dLQe+q9RZd1fg9J17v0jR7Y18iZtUGEtG+HrEPuDHntdO6RItc1Ucwa5y6xyFuVlezrI/uuwPQLJ3/FPFxqkG7nk3yf/+z3dyCX/CBnvY3zZ7nyFUor6K7NDoPQjWUpSPH7lvq6/jjzHxXculHZ/LvhHlHna5KL4xNyG/xpuhy7BEKj7YC9doGW+ga27baYLc/yjsIp9YWx360ne4+0/F4IjyroPgewPSbKzwt5vTA2cf1bQaM3H5F8WX9cKgNOEUpI0bmiyHvznGAAAfQHhUgbShUD+mwF7hEy60TP+df3L7Jue8uI8b2c5Tcff/7hdcJvdj5ZKNwomODdSz1/XO/rD/2hb9yO0/DeN/sev7HWDwV1yf0Oh9J17fx2VeUYudX9j7S+nf54d/+N2eb7H7Tyva+2vv269c7CEPfWyrdCvp+HItkZopRs5568jewTScN8ye9RAcV62Oyl3fL3uX9c/iihtObcRmnrP6+4f/4vvb/evay8rzffOM+YfhWWHVjlZYRVYf+uve/RP/muQHTAGR390H1T4z53RvrDBG8h039HOTkzMnWqZ5Bvts41H8ez30LCiXM/jOelCK3/Iao9A8o/Q8nfC7etBQW6Whhba77fuR8Fsa7SPva75Zrzkut5wxF43UEdpRkv5g5MyT5Cf46m/dOsOLer+XAiFpMKc7kdL2euaibkNf/2NHtJ9UJbuXBhRkp/23sQOevxBvn3OF1rzMUnB0M9+fH+bYaxVD8P89ZfmUUd/CDnU9z70BGVpzr9tPzKXXNf/GJ+/LHZg6C8LAAB9AeFSBorzexaOlBXkpJ3IOt3IpZEl3X8i6e98pnt8LRTydsLThSP+Zf5Pbe1h/ulGz0jeYeLpPqX3B0SBoMIKenKzw97H7Yr8I3q6D0c8naHCXHeCVykYlAXDkTShS5rjkm7kkn+76c6jYDjiDTi8E7SnP8fs/Q2OXLLKEliv++OSlfh2NmN4qT9kSzPyK80y801z6ZZn8rp2WbLCIU+nIT75b3KjI/1lsY5puvrz13vgsbg0gZd/f9E/+TuudthckJvlOZfSBSD+cyddB90fjqQLDQKd5TQjb+yAw0zSb4RCobSPodn763981R6B5A+l/PXn31/P6Jo08/ek25+87LAn2MnJCnvmvEoXsvlHNXoeJdtGoGC//0OhkK8eug8qhvnDuTSPrxXmZnsCiKFp1g2eCz0f+WW3T1nhkLf+0tSDv10ba43K8d8rDS3M8QTw/vYy3aODY9OES/4w1n4/5edkebYTDKaS6/qv2fb5t63H//z3BWPTBKN2uMTj0wCAvohwKQPp5l3xfutK+rmG0o2u2a4RRlan1v9tZv79TTtCJs0II/+ynKzwNkbepAvDrNdNM+KpxDeSJb6uPfJme7aZppy56YOydEFFuke+/J1C/w1zunVL8tKFLtb5l+Z4SukDzHSPfKU7ZqmOizek7HkdeZb5zoWscEj5VqAZOFfSjCLq6cil8iLv3Fz+ydT9kyt7Ri6l+LY9w//+LbQepzHbtdkdF3+4if7JPneKcr2PpPqX+98XdojhH8FnL0t1XR5mhZ6Bzr21rv/aMTbNIzd2KOUPMSTf6CR/GJFm5I0dovnfp0V52cq2thMcOZJc13/N6enIEf8XNEi+YCDNY1T+cNk+Lv599Qc7/rbBG7p41003cqnSOmb+a71/f/37ZK/rv16lG5Xjf9wuOOLMPne7H+3jP96e4+nbH/+oMX/QM6G8KOXrSOlDtPHDkusV52UH3qNj0tT9+GE9qz//vvqv/f738KSK5D75P5izj5n/AwoAAPoCwqUM2DcH/ht0/8SsNnu0jJRqFEzPOvfpgpOSFJM8plvXDqbShRipRlPEzPdWK3gD5emg+26Q7L8NTsrdfRAh+UeOdP9tccP9I2/SlNPfUfJ3BNKFBqVpwhE7UMjNCgeOi93pCc651P0xs28q/dvM890c+wMt+2Y/3TxP6QIifx34txMI2Qq7P6bpgjtJ6uhKfh22v5Nt/326wNVfFvs9m+rTX7sO/SO47HM33WNx/oDIf+ztEY3+/eexuIHBvu61W+exYXd6/R9EVFodV/91bnSaQEaSZ7RfIOix100zisM/94u9D50pymKf7/6RGZOsjn9g5NIQuw7Sh6oFvoDWDnP869oBh3/ZRGt/wikmRE43787k4cXu/wfDueTf+ueE8r//g+Fcch/9j9DZr+sPuydWJM+T3Kzg7VxW2L6Wefd3txHJsvivORPKk69bOcw/91D6x7Hs/bVfR5L2sLbpP+ft+YT8H15IUntn8rzzh0STK+xwybu/e4wo6XZ/7CCvKdoZ2KZ97tihjyTtNSr5uv7RXPb++OtrW23BniOTr2sHWJK09+hS9/8n+soCAEBfQLiUATu4CI68Sd9Ztvk/8fPPXWCzb3L8N0/2JKOpvprW3k66CUv9+2sHP/aNn9HRlQyX/MFZuq/Wtm8q04Vdeb6bLslbVn/HP12IZu+D/8bfz3/zZ3fQ/BOLlqYZSWW/TqrJN63qSxHIdF/3nvpL8QlvOnY9BOaESRMueeYa8X2SLXlDIP8n+vbrVvrOP+8cRsFOS2csWUn+sg1PE7LZAdw43w26XQf+8E3yBgHpRj34OxTbCuDSsTtL27su+iZ7FESq0Wj2CCP/+38vq4O5u9U5lvxhvSM//zcc2uzzd4Kvs2yHGv5vrbLfe6lCIPua5A+Q9h6d3H+74yx5R5wU5Qav96as/vea5O3s+zvh9nVmdyvQkLwhVaog134t//Vh/7Fl7v/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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_t_evol(out, labels):\n", " fig = plt.figure(figsize = (12, 6))\n", " \n", " max_abs = 8\n", " \n", " ncoord = out.shape[1]\n", " ncols = 3\n", " nrows = ncoord // ncols + (ncoord % ncols)\n", "\n", " for i in range(0, ncoord):\n", " ax = fig.add_subplot(nrows, ncols, i + 1)\n", " ax.plot(t_grid, out[:, i])\n", " ax.set_xlabel(\"Time\")\n", " ax.set_ylabel(labels[i])\n", " ax.set_ylim(-max_abs, max_abs)\n", " \n", " plt.tight_layout()\n", "\n", "plot_t_evol(out_cart, [\"$v_x$\", \"$v_y$\", \"$v_z$\", \"$x$\", \"$y$\", \"$z$\"])" ] }, { "cell_type": "markdown", "id": "fourth-walnut", "metadata": {}, "source": [ "Note that the oscillatory behaviour in these plots is a quasi-Keplerian motion driven by the central-force field. The additional constant acceleration has a longer-term secular effect which is however not immediately recognisable in these plots.\n", "\n", "## Spherical coordinates\n", "\n", "Let us now switch to a [spherical coordinate system](https://en.wikipedia.org/wiki/Spherical_coordinate_system). Because we are operating in the Hamiltonian framework, we cannot use directly the time derivatives $\\left( \\dot{r}, \\dot{\\theta}, \\dot{\\phi} \\right)$ of the spherical coordinates as new momenta, and we have to use instead a set of canonical momenta $\\left( p_r, p_\\theta, p_\\phi \\right)$. The coordinate transformation $\\left(v_x, v_y, v_z, x, y, z\\right) \\rightarrow \\left( p_r, p_\\theta, p_\\phi, r, \\theta, \\phi \\right)$ reads:\n", "\n", "$$\n", "\\begin{aligned}\n", "p_r & = \\dot{r}, & r & = \\sqrt{x^2+y^2+z^2}, \\\\\n", "p_\\theta & = r^2\\dot{\\theta}, & \\theta & = \\arccos \\frac{z}{r}, \\\\\n", "p_\\phi & = r^2\\dot{\\phi}\\sin^2\\theta, & \\phi & = \\arctan \\frac{y}{x}.\n", "\\end{aligned}\n", "$$\n", "\n", "The Hamiltonian of the Stark problem in spherical coordinates becomes:\n", "\n", "$$\n", "\\mathcal{H}_\\mathrm{sph} = \\frac{1}{2}\\left( p_r^2+\\frac{p_\\theta^2}{r^2} + \\frac{p_\\phi^2}{r^2\\sin^2\\theta} \\right) - \\frac{1}{r} - \\varepsilon r \\cos\\theta.\n", "$$\n", "\n", "Let us define a couple of functions to convert a state vector between Cartesian and spherical coordinates:" ] }, { "cell_type": "code", "execution_count": 8, "id": "prostate-physiology", "metadata": {}, "outputs": [], "source": [ "# Cartesian to spherical.\n", "def cart2sph(state):\n", " from numpy import sqrt, arccos, arctan2\n", " vx,vy,vz,x,y,z = state\n", " r = sqrt(x**2+y**2+z**2)\n", " th = arccos(z/r)\n", " phi = arctan2(y,x)\n", " vr = (vx*x+vy*y+vz*z)/r\n", " vth = (z*vr-vz*r)/(r**2*sqrt(1-z**2/r**2))\n", " vphi = (vy*x-vx*y)/(x**2+y**2)\n", " return vr,vth,vphi,r,th,phi\n", "\n", "# Spherical to Cartesian.\n", "def sph2cart(state):\n", " from numpy import sin, cos\n", " vr,vth,vphi,r,th,phi = state\n", " x = r*sin(th)*cos(phi)\n", " y = r*sin(th)*sin(phi)\n", " z = r*cos(th)\n", " vx = vr*sin(th)*cos(phi)+r*(vth*cos(th)*cos(phi)-vphi*sin(th)*sin(phi))\n", " vy = vr*sin(th)*sin(phi)+r*(vth*cos(th)*sin(phi)+vphi*sin(th)*cos(phi))\n", " vz = vr*cos(th)-r*vth*sin(th)\n", " return vx,vy,vz,x,y,z\n", "\n", "# Spherical to Hamiltonian spherical.\n", "def sph2spham(state):\n", " from numpy import sin\n", " vr,vth,vphi,r,th,phi = state\n", " return vr,r**2*vth,r**2*vphi*sin(th)**2,r,th,phi\n", "\n", "# Hamiltonian spherical to spherical.\n", "def spham2sph(state):\n", " from numpy import sin\n", " pr,pth,pphi,r,th,phi = state\n", " return pr,pth/r**2,pphi/(r**2*sin(th)**2),r,th,phi" ] }, { "cell_type": "markdown", "id": "bc0ecc24-1b85-4302-80d9-26edb02fd878", "metadata": {}, "source": [ "We are now almost ready to numerically integrate the Stark problem in spherical coordinates. There is one additional complication however that we need to take into account.\n", "\n", "Because now we are operating in spherical coordinates, two of the coordinates are angles $\\left(\\theta, \\phi \\right)$ whose numerical values can grow in principle unbounded even if the motion remains bounded. In this specific example, the angle $\\phi$ will keep on growing as the particle orbits around the origin.\n", "\n", "This constant growth can become a problem because heyoka.py uses the largest absolute value in the state vector to transform the relative integration tolerance into an absolute error allowed within the integration loop: in other words, if (the absolute value of) $\\phi$ keeps on growing, the integrator will progressively become less accurate.\n", "\n", "We can avoid this undesirable effect by periodically reducing $\\phi$ modulo $2\\pi$. One possible way of implementing this is to define a callback function to be called at the end of every integration timestep:" ] }, { "cell_type": "code", "execution_count": 9, "id": "eee6986e-a10a-4a03-b925-c89cc9b44c54", "metadata": {}, "outputs": [], "source": [ "def mod_cb_sph(ta):\n", " # Fetch the current value of phi\n", " # from the state vector.\n", " phi = ta.state[5]\n", " \n", " # If phi is outside the [-pi, pi] range,\n", " # bring it back to [-pi, pi].\n", " if phi < -np.pi or phi > np.pi:\n", " ta.state[5] = (phi + np.pi) % (2 * np.pi) - np.pi\n", " \n", " return True" ] }, { "cell_type": "markdown", "id": "360f746e-070c-4033-a30d-ae881ffe64f5", "metadata": {}, "source": [ "We can now proceed to the numerical integration:" ] }, { "cell_type": "code", "execution_count": 10, "id": "bearing-pepper", "metadata": {}, "outputs": [], "source": [ "# Create the spherical symbolic variables.\n", "pr, pth, pphi, r, th, phi = hy.make_vars(\"pr\", \"pth\", \"pphi\", \"r\", \"th\", \"phi\")\n", "\n", "# Define the Hamiltonian in spherical coordinates.\n", "Ham_sph = 0.5 * (pr**2+(pth/r)**2+(pphi/(r*hy.sin(th)))**2) - 1./r - eps*r*hy.cos(th)\n", "\n", "# Convert the initial Cartesian conditions.\n", "sph_ic = sph2spham(cart2sph(cart_ic))\n", "\n", "# Create the integrator object.\n", "ta_sph = hy.taylor_adaptive(\n", " [(pr, -hy.diff(Ham_sph, r)),\n", " (pth, -hy.diff(Ham_sph, th)),\n", " (pphi, -hy.diff(Ham_sph, phi)),\n", " (r, hy.diff(Ham_sph, pr)),\n", " (th, hy.diff(Ham_sph, pth)),\n", " (phi, hy.diff(Ham_sph, pphi))],\n", " sph_ic\n", ")\n", "\n", "# Run the integration.\n", "_, _, _, nsteps_sph, _, out_sph = ta_sph.propagate_grid(t_grid,\n", " # Callback to reduce the\n", " # value of phi to [-pi, pi].\n", " callback = mod_cb_sph)" ] }, { "cell_type": "markdown", "id": "50246960-55d9-45aa-9d0a-27d83bdcfa29", "metadata": {}, "source": [ "Let's take a look at the results:" ] }, { "cell_type": "code", "execution_count": 11, "id": "796ba995-39e8-4ad0-b30f-e4c7831cadc1", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_t_evol(out_sph, [\"$p_r$\", r\"$p_\\theta$\", r\"$p_\\phi$\", \"$r$\", r\"$\\theta$\", r\"$\\phi$\"])" ] }, { "cell_type": "markdown", "id": "0d373952-ad09-4da9-a2f9-5c55c6c29ea0", "metadata": {}, "source": [ "Comparing these plots with those for the Cartesian coordinates, we can see how the oscillatory quasi-Keplerian behaviour remains. However, the oscillation amplitude is reduced with respect to the Cartesian case, and one of the momenta ($p_\\phi$, top right panel) has become a constant. This reflects the fact that the $z$ component of the angular momentum in the Stark problem is a constant of motion.\n", "\n", "Note that the bottom right panel, referring to the time evolution of $\\phi$, does **not** represent an oscillatory motion around 0: the sine-like shape is a visual effect of the periodic reduction of $\\phi$ to the $\\left[ -\\pi, \\pi\\right]$ range, but in reality the time evolution of $\\phi$ is linear with a periodic modulation on top.\n", "\n", "The periodic modulations in these plots arise from the fact that the initial Keplerian orbit is not perfectly circular and planar, and thus all coordinates (except $p_\\phi$) oscillate as the motion deviates from a perfect planar circle within each orbit. For a circular planar orbit around the origin, all coordinates and momenta would be constants, except for $\\phi$ which would evolve linearly.\n", "\n", "The fact that the amplitude of the periodic modulations is reduced with respect to the Cartesian case has an effect on the number of timesteps necessary to integrate the system:" ] }, { "cell_type": "code", "execution_count": 12, "id": "a55ce671-925d-4d0d-b7b7-d4a8ac99d527", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of steps (Cartesian): 1002\n", "Number of steps (spherical): 899\n" ] } ], "source": [ "print(\"Number of steps (Cartesian): {}\".format(nsteps_cart))\n", "print(\"Number of steps (spherical): {}\".format(nsteps_sph))" ] }, { "cell_type": "markdown", "id": "a5e2c894-85b9-4382-b3c7-f1890bde33e9", "metadata": {}, "source": [ "The reduction is not dramatic, but nevertheless measurable.\n", "\n", "Spherical coordinates require fewer timesteps because the reduction in the amplitude of the oscillatory motions improves the convergence of the Taylor series that heyoka.py uses internally to propagate the motion at each timestep. In other words, when using spherical coordinates the Taylor series synthesised by heyoka.py at each timestep can describe accurately the solution of the system for longer intervals of time.\n", "\n", "## Delaunay elements\n", "\n", "The results of the previous section suggest that introducing another system of coordinates which further reduces the amplitude of periodic oscillations may further decrease the number of timesteps required by the integrator. Because we are dealing with a perturbed Keplerian system, an obvious choice is to use [Keplerian orbital elements](https://en.wikipedia.org/wiki/Orbital_elements).\n", "\n", "In the Hamiltonian formalism, we cannot use directly the Keplerian elements as coordinates as they are not canonical variables. Instead, we can use the [Delaunay elements](https://en.wikipedia.org/wiki/Orbital_elements#Delaunay_variables), which are closely-related to the Keplerian elements via the following relations (valid in adimensional units):\n", "\n", "$$\n", "\\begin{aligned}\n", "L & = \\sqrt{a}, & l & = M, \\\\\n", "G & = \\sqrt{a\\left( 1 - e^2\\right)}, & g & = \\omega, \\\\\n", "H & = \\sqrt{a\\left( 1 - e^2\\right)} \\cos i, & h & = \\Omega.\n", "\\end{aligned}\n", "$$\n", "\n", "In these formulae, $\\left( a, e, i, M, \\omega, \\Omega \\right)$ are the usual Keplerian elements: semi-major axis, eccentricity, inclination, mean anomaly, longitude of pericentre and longitude of the ascending node.\n", "\n", "When employing Delaunay elements, a major complication is the appearance of the mean anomaly $l$, which is related to the eccentric anomaly $E$ via [Kepler's equation](https://en.wikipedia.org/wiki/Kepler%27s_equation), which, in terms of Delaunay elements, reads:\n", "\n", "$$\n", "l = E - \\sqrt{1-\\frac{G^2}{L^2}} \\sin E.\n", "$$\n", "\n", "This equation cannot be inverted in finite terms using elementary functions, thus, from now on, we will regard the eccentric anomaly $E$ as an unspecified function of $l$, $G$ and $L$:\n", "\n", "$$\n", "E = E\\left( l, G, L \\right).\n", "$$\n", "\n", "The cartesian coordinate $z$ can be written in terms of Delaunay elements as\n", "\n", "$$\n", "z = L\\sqrt{1-\\frac{H^2}{G^2}}\\left[ L\\left( \\cos E - \\sqrt{1-\\frac{G^2}{L^2}} \\right)\\sin g + G\\sin E \\cos g \\right],\n", "$$\n", "\n", "while the two-body problem Hamiltonian is simply\n", "\n", "$$\n", "\\mathcal{H}_\\mathrm{2bp} = -\\frac{1}{2L^2}.\n", "$$\n", "\n", "Thus, the full Hamiltonian for the Stark problem in Delaunay elements reads:\n", "\n", "$$\n", "\\mathcal{H}_\\mathrm{Del} \\left( L, G, H, l, g, h \\right) = -\\frac{1}{2L^2}-\\varepsilon L\\sqrt{1-\\frac{H^2}{G^2}}\\left[ L\\left( \\cos E - \\sqrt{1-\\frac{G^2}{L^2}} \\right)\\sin g + G\\sin E \\cos g \\right].\n", "$$\n", "\n", "In order to write the equations of motion, we will have to take into account that $E$ is a function of $\\left( l, G, L \\right)$ whose derivatives can be explicitly computed from Kepler's equation:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\frac{\\partial E}{\\partial l} & = \\frac{1}{1-\\sqrt{1-\\frac{G^2}{L^2}}\\cos E},\\\\\n", "\\frac{\\partial E}{\\partial L} & = \\frac{G^2\\sin E}{L^3\\sqrt{1-\\frac{G^2}{L^2}}\\left(1-\\sqrt{1-\\frac{G^2}{L^2}}\\cos E\\right)},\\\\\n", "\\frac{\\partial E}{\\partial G} & = \\frac{-G\\sin E}{L^2\\sqrt{1-\\frac{G^2}{L^2}}\\left(1-\\sqrt{1-\\frac{G^2}{L^2}}\\cos E\\right)}.\n", "\\end{aligned}\n", "$$\n", "\n", "We can now proceed to formulate the equations of motion:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\frac{dL}{dt} & =-\\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial E}\\frac{\\partial E}{\\partial l}, & \\frac{dl}{dt} & = \\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial L}+\\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial E}\\frac{\\partial E}{\\partial L}, \\\\\n", "\\frac{dG}{dt} & = -\\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial g}, & \\frac{dg}{dt} & = \\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial G}+\\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial E}\\frac{\\partial E}{\\partial G}, \\\\\n", "\\frac{dH}{dt} & = -\\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial h}=0, & \\frac{dh}{dt} & = \\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial H} .\n", "\\end{aligned}\n", "$$\n", "\n", "Note that the Hamiltonian does not depend directly on $l$ (only indirectly via $E$). Thus, in the numerical integration, we will be replacing the differential equation for $l$ with the differential equation for $E$:\n", "\n", "$$\n", "\\frac{dE}{dt}=\\frac{\\partial E}{\\partial l}\\frac{dl}{dt}+\\frac{\\partial E}{\\partial L}\\frac{dL}{dt} + \\frac{\\partial E}{\\partial G}\\frac{dG}{dt}.\n", "$$\n", "\n", "The value of $l$ for a given $E$ can be obtained via Kepler's equation.\n", "\n", "On the implementation side, let us begin with a couple of functions to convert between Cartesian coordinates and Delaunay elements. We will be using [pykep](https://esa.github.io/pykep/) for the conversion between cartesian coordinates and Keplerian elements:" ] }, { "cell_type": "code", "execution_count": 13, "id": "57fa693f-3d97-46fa-8961-3b713480d5be", "metadata": {}, "outputs": [], "source": [ "# Cartesian to Delaunay.\n", "def cart2del(state):\n", " import pykep as pk\n", " \n", " vx,vy,vz,x,y,z = state\n", "\n", " a,e,i,Om,om,E = pk.ic2par([x, y, z], [vx, vy, vz])\n", " \n", " L = np.sqrt(a)\n", " G = np.sqrt(a*(1-e**2))\n", " H = G*np.cos(i)\n", " \n", " g = om\n", " h = Om\n", " \n", " return [L, G, H, E, g, h]\n", "\n", "# Delaunay to cartesian.\n", "def del2cart(state):\n", " import pykep as pk\n", " \n", " L,G,H,E,g,h = state\n", " \n", " a = L**2\n", " e = np.sqrt(1-G**2/L**2)\n", " i = np.arccos(H/G)\n", " \n", " Om = h\n", " om = g\n", " \n", " ret = pk.par2ic([a, e, i, Om, om, E])\n", " \n", " return [ret[1][0], ret[1][1], ret[1][2], ret[0][0], ret[0][1], ret[0][2]]" ] }, { "cell_type": "markdown", "id": "47407cff-e083-41fe-8634-e4cc64fdb695", "metadata": {}, "source": [ "Next, we formulate the Hamiltonian and the equations of motion:" ] }, { "cell_type": "code", "execution_count": 14, "id": "0e44e17b-4b7d-495c-a7d7-b9b3167d967f", "metadata": {}, "outputs": [], "source": [ "# Symbolic variables for the Delaunay elements.\n", "L, G, H, E, g, h = hy.make_vars(\"L\", \"G\", \"H\", \"E\", \"g\", \"h\")\n", "\n", "# The Hamiltonian.\n", "Ham_del = -0.5*L**-2 - eps*L*hy.sqrt(1.-H**2*G**-2)*(L*(hy.cos(E)-hy.sqrt(1.-G**2*L**-2))*hy.sin(g)+G*hy.sin(E)*hy.cos(g))\n", "\n", "# Derivatives of E wrt l, L and G.\n", "dE_dl = (1. - hy.sqrt(1.-G**2*L**-2)*hy.cos(E))**-1\n", "dE_dL = G**2*hy.sin(E)/(L**3*hy.sqrt(1.-G**2*L**-2)*(1. - hy.sqrt(1.-G**2*L**-2)*hy.cos(E)))\n", "dE_dG = -G*hy.sin(E)/(L**2*hy.sqrt(1.-G**2*L**-2)*(1. - hy.sqrt(1.-G**2*L**-2)*hy.cos(E)))\n", "\n", "# Equations of motion.\n", "dL_dt = -hy.diff(Ham_del, E) * dE_dl\n", "dG_dt = -hy.diff(Ham_del, g)\n", "dH_dt = hy.expression(0.)\n", "dl_dt = hy.diff(Ham_del, L) + hy.diff(Ham_del, E) * dE_dL\n", "dg_dt = hy.diff(Ham_del, G) + hy.diff(Ham_del, E) * dE_dG\n", "dh_dt = hy.diff(Ham_del, H)\n", "dE_dt = dE_dl * dl_dt + dE_dL * dL_dt + dE_dG * dG_dt" ] }, { "cell_type": "markdown", "id": "455eb1ec-d130-4a2e-88a3-b5c9fa51c172", "metadata": {}, "source": [ "Like in the case of spherical coordinates, we will also need to prevent $E$ from growing indefinitely:" ] }, { "cell_type": "code", "execution_count": 15, "id": "4200061c-7506-4837-986f-c7b8627d9183", "metadata": {}, "outputs": [], "source": [ "# Callback to reduce E to the\n", "# [-pi, pi] range.\n", "def mod_cb_del(ta):\n", " E = ta.state[3]\n", " if E < -np.pi or E > np.pi:\n", " ta.state[3] = (E + np.pi) % (2 * np.pi) - np.pi\n", " \n", " return True" ] }, { "cell_type": "markdown", "id": "a52cf7b4-dc66-40b6-a049-a72e07929167", "metadata": {}, "source": [ "We are now ready to create the integrator object:" ] }, { "cell_type": "code", "execution_count": 16, "id": "6a19bc78-a99b-42bf-a6f3-7e9ac60c0a11", "metadata": {}, "outputs": [], "source": [ "# Convert the initial conditions\n", "# into Delaunay elements.\n", "del_ic = cart2del(cart_ic)\n", "\n", "# Create the integrator.\n", "ta_del = hy.taylor_adaptive(\n", " [(L, dL_dt),\n", " (G, dG_dt),\n", " (H, dH_dt),\n", " (E, dE_dt),\n", " (g, dg_dt),\n", " (h, dh_dt)],\n", " del_ic\n", ")" ] }, { "cell_type": "markdown", "id": "76103dc7-ab9a-4b40-8039-b854eb943630", "metadata": {}, "source": [ "Let us proceed to the numerical integration:" ] }, { "cell_type": "code", "execution_count": 17, "id": "c5622eda-bbcd-4c60-bc7e-768dfe0c7c9a", "metadata": {}, "outputs": [], "source": [ "_, _, _, nsteps_del, _, out_del = ta_del.propagate_grid(t_grid, callback = mod_cb_del)" ] }, { "cell_type": "markdown", "id": "f2839f24-8220-48e3-bcf9-06420cb0eb1f", "metadata": {}, "source": [ "We can now take a look at the time evolution of the orbital elements:" ] }, { "cell_type": "code", "execution_count": 18, "id": "8758a7a5-9250-4d43-9865-492bcb0a5690", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_t_evol(out_del, [\"$L$\", \"$G$\", \"$H$\", \"$E$\", \"$g$\", \"$h$\"])" ] }, { "cell_type": "markdown", "id": "867f0669-43f1-451a-a20e-318befd087be", "metadata": {}, "source": [ "The plots for $L$, $G$, $H$, $g$ and $h$ clearly show how the Keplerian oscillations for these elements have been removed thanks to the use of orbital elements as a coordinate system. These elements would be constant in a perfectly Keplerian orbit, while in the Stark problem they undergo short-term oscillations with amplitude $\\sim\\varepsilon$ and long-term evolution with timescale $\\sim 1/\\varepsilon$. We can see the perturbation induced by the constant acceleration field by zooming into, e.g., the plot for the $g$ angle (the argument of pericentre):" ] }, { "cell_type": "code", "execution_count": 19, "id": "abcdc48c-bc6d-4524-971e-45cfeb3ae2b3", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (6, 3))\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.plot(t_grid[:100], out_del[:100, 4])\n", "ax.set_xlabel(\"Time\")\n", "ax.set_ylabel(\"$g$\");" ] }, { "cell_type": "markdown", "id": "facfa4ec-0849-43e1-9611-555236b7f26e", "metadata": {}, "source": [ "Let us now zoom into the plot for $E$:" ] }, { "cell_type": "code", "execution_count": 20, "id": "27210f10-341e-4ecc-b15f-ce6067e464ac", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (6, 3))\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.plot(t_grid[:100], out_del[:100, 3])\n", "ax.set_xlabel(\"Time\")\n", "ax.set_ylabel(\"$E$\");" ] }, { "cell_type": "markdown", "id": "6135ee1f-6525-442d-9a1b-8ee24c47cb50", "metadata": {}, "source": [ "We can see how $E$ is still subject to Keplerian oscillations. Indeed, even in a perfectly Keplerian orbit, the time evolution of $E$ is linear only for circular orbits.\n", "\n", "Because of the presence of Keplerian oscillations in $E$, the reduction in number of integration timesteps after switching to Delaunay elements is measurable but not very large:" ] }, { "cell_type": "code", "execution_count": 21, "id": "b5f2f844-798e-4cbc-8b58-4899dbe07a9a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of steps (Cartesian): 1002\n", "Number of steps (spherical): 899\n", "Number of steps (Delaunay) : 764\n" ] } ], "source": [ "print(\"Number of steps (Cartesian): {}\".format(nsteps_cart))\n", "print(\"Number of steps (spherical): {}\".format(nsteps_sph))\n", "print(\"Number of steps (Delaunay) : {}\".format(nsteps_del))" ] }, { "cell_type": "markdown", "id": "9f980864-f8ba-4d5e-b276-f21ad9167c5b", "metadata": {}, "source": [ "In order to further reduce the number of timesteps, we will have to implement one final trick." ] }, { "cell_type": "markdown", "id": "5f73a4e7-33ec-4167-87b3-6fa8b985fccb", "metadata": {}, "source": [ "## Delaunay + Sundman\n", "\n", "The idea we will be exploring in this section is to replace the time $t$ with a fictitious time $\\tau$ defined by the differential relation\n", "\n", "$$\n", "\\frac{dt}{d\\tau} = r,\n", "$$\n", "\n", "where $r$ is the distance from the Keplerian centre of force (i.e., the origin). This time transformation belongs to the class of [Sundman transformations](https://en.wikipedia.org/wiki/Karl_F._Sundman), which were originally introduced for regularisation purposes: the fictitious time $\\tau$ flows slower close to the centre of force, so that it is impossible for a test particle to reach the gravitational singularity as that would take an infinite amount of fictitious time $\\tau$.\n", "\n", "Here, however, we are not interested in the regularisation properties of this transformation. Rather, what is of interest to us in this context is that, in Keplerian orbits, $E$ evolves *linearly* with $\\tau$. In other words, by replacing the time coordinate $t$ with $\\tau$, we will be able to remove the Keplerian oscillations of $E$ in the Stark problem.\n", "\n", "We can introduce the new time coordinate $\\tau$ directly in the definition of the equations of motion. $r$ can be expressed in terms of Delaunay elements as\n", "\n", "$$\n", "r = L^2\\left( 1 - \\sqrt{1-\\frac{G^2}{L^2}}\\cos E\\right).\n", "$$\n", "\n", "For each Delaunay element $D_i$ we can then write:\n", "\n", "$$\n", "\\frac{dD_i}{d\\tau} = \\frac{dD_i}{dt}\\frac{dt}{d\\tau} = \\frac{dD_i}{dt} L^2\\left( 1 - \\sqrt{1-\\frac{G^2}{L^2}}\\cos E\\right).\n", "$$\n", "\n", "We will also append the differential equation for $dt/d\\tau$ to the ODE system, so that we can track the evolution of the real time $t$ in fictitious time $\\tau$:" ] }, { "cell_type": "code", "execution_count": 22, "id": "56a06947-164a-4f91-b977-e5926e3a1a90", "metadata": {}, "outputs": [], "source": [ "# Expression for dt/dtau.\n", "dt_dtau = L**2*(1 - hy.sqrt(1.-G**2*L**-2) * hy.cos(E))\n", "\n", "# Additional dynamical variable to\n", "# integrate t(tau).\n", "t = hy.make_vars(\"t\")\n", "\n", "ta_del_e = hy.taylor_adaptive(\n", " [(L, dL_dt*dt_dtau),\n", " (G, dG_dt*dt_dtau),\n", " (H, dH_dt*dt_dtau),\n", " (E, dE_dt*dt_dtau),\n", " (g, dg_dt*dt_dtau),\n", " (h, dh_dt*dt_dtau),\n", " (t, dt_dtau)\n", " ],\n", " # Both t and tau\n", " # start at zero.\n", " del_ic + [0.]\n", ")" ] }, { "cell_type": "markdown", "id": "905d9b86-5cf2-4aaa-b8bd-f42da7d646dd", "metadata": {}, "source": [ "In order to prevent the real time $t$ from growing indefinitely, we will periodically reset its value:" ] }, { "cell_type": "code", "execution_count": 23, "id": "5f2a30a0-6045-4230-a708-f217d7915b97", "metadata": {}, "outputs": [], "source": [ "def mod_cb_del_e(ta):\n", " # Reduce E to the [-pi, pi] range.\n", " E = ta.state[3]\n", " if E < -np.pi or E > np.pi:\n", " ta.state[3] = (E + np.pi) % (2 * np.pi) - np.pi\n", "\n", " # Modulo reduction of t when it\n", " # grows past 5.\n", " t = ta.state[6]\n", " if t > 5:\n", " ta.state[6] = t % 5\n", " \n", " return True" ] }, { "cell_type": "markdown", "id": "9f112023-526d-4dec-8da3-9827b2e2e7d2", "metadata": {}, "source": [ "We can now proceed to the integration:" ] }, { "cell_type": "code", "execution_count": 24, "id": "0249bafb-1cfa-4845-94c0-92e898be650d", "metadata": {}, "outputs": [], "source": [ "_, _, _, nsteps_del_e, _, out_del_e = ta_del_e.propagate_grid(t_grid, callback = mod_cb_del_e)" ] }, { "cell_type": "markdown", "id": "3f4b7531-bfb3-46e7-8f24-af3b021c24c5", "metadata": {}, "source": [ "Let us plot the results:" ] }, { "cell_type": "code", "execution_count": 25, "id": "1fd0289a-8cbd-41bd-b98e-b543e8a2e4ac", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_t_evol(out_del_e, [\"$L$\", \"$G$\", \"$H$\", \"$E$\", \"$g$\", \"$h$\", \"$t$\"])" ] }, { "cell_type": "markdown", "id": "62f36759-6e45-4cf6-93c0-4a07c65ebd3b", "metadata": {}, "source": [ "And let us zoom into the plot for $E$:" ] }, { "cell_type": "code", "execution_count": 26, "id": "ca36771b-5759-4d07-bf93-3271733062a7", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (6, 3))\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.plot(t_grid[:100], out_del_e[:100, 3])\n", "ax.set_xlabel(\"Time\")\n", "ax.set_ylabel(\"$E$\");" ] }, { "cell_type": "markdown", "id": "48e5d8ba-be06-429a-87d8-489b00d09b44", "metadata": {}, "source": [ "The plot indeed confirms that the Keplerian oscillations for $E$ are gone.\n", "\n", "What about the number of steps?" ] }, { "cell_type": "code", "execution_count": 27, "id": "536551b3-6d01-43c1-b113-a188c0ebf183", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of steps (Cartesian): 1002\n", "Number of steps (spherical): 899\n", "Number of steps (Delaunay) : 764\n", "Number of steps (D + S) : 388\n" ] } ], "source": [ "print(\"Number of steps (Cartesian): {}\".format(nsteps_cart))\n", "print(\"Number of steps (spherical): {}\".format(nsteps_sph))\n", "print(\"Number of steps (Delaunay) : {}\".format(nsteps_del))\n", "print(\"Number of steps (D + S) : {}\".format(nsteps_del_e))" ] }, { "cell_type": "markdown", "id": "af4898ae-72a0-4bcb-b007-9bf3ec92599c", "metadata": {}, "source": [ "We can see how, after the removal of the short-term Keplerian oscillations from $E$, the reduction in number of steps is substantial. Indeed, in the Delaunay + Sundman setup, the evolution of the coordinates in fictitious time deviates from constant or linear behaviour only through the external perturbation, whose magnitude $\\varepsilon$ is small.\n", "\n", "Let us conclude by summarising in a plot the number of steps required by each coordinate system:" ] }, { "cell_type": "code", "execution_count": 28, "id": "01beaa65-65aa-47e8-bb61-2eddb230d312", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (6, 6))\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.bar(range(4), [nsteps_cart, nsteps_sph, nsteps_del, nsteps_del_e], tick_label=[\"Cartesian\", \"Spherical\", \"Delaunay\", \"D + S\"])\n", "ax.set_ylabel(\"N of steps\");" ] }, { "cell_type": "markdown", "id": "ab28c328-df90-4a77-b9cd-2140b21e5fed", "metadata": {}, "source": [ "## Conclusions\n", "\n", "In this example we have shown how the choice of coordinate system and time coordinate can influence the behaviour of a Taylor integrator. Intuitively, the closer the time evolution of a coordinate is to a polynomial, the longer the Taylor series can approximate the ODE solution, and the fewer number of steps is required.\n", "\n", "In these experiments we focused only on the number of steps as a performance metric. Clearly, the use of more sophisticated coordinate systems (such as the Delaunay elements) can lead to more complicated equations of motion, which in turn may lead to overall longer integration times. Nevertheless, the minimisation of the number of timestpes may be of interest in some cases (e.g., to reduce the accumulation of numerical errors in long-term integrations)." ] } ], "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": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 5 }