{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "
\n", " 数値計算による常微分方程式解法(python版)\n", "
\n", "\n", "
\n", " ordinary differential equation(ODE)\n", "
\n", "\n", "
\n", " cc by Shigeto R. Nishitani, 2020-23\n", "
\n", "\n", "\n", "* /Users/bob/Desktop/maple_ode/python_ode.ipynb\n", "* origin\tgit@github.com:daddygongon/maple_ode.git (fetch)" ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true, "slideshow": { "slide_type": "slide" }, "toc": "true" }, "source": [ "

Table of Contents

\n", "
" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Euler法による落下運動\n", "\n", "## 重力場中の運動\n", "重力場中のボールの落下を考えて,1軸で考えた運動方程式を立てます.\n", "\n", "$$\n", "\\begin{aligned}\n", "v &= \\frac{dx}{dt} \\\\\n", "a &= \\frac{d^2 x}{dt^2}\n", "\\end{aligned}\n", "$$\n", "質量を$m$, 重力加速度を$g$として,働く力が$F=-mg$であるとすると,ニュートンの運動方程式$F=ma$は,\n", "\n", "$$ \n", "-mg = m \\frac{d^2 x}{dt^2}\n", "$$\n", "となります.\n", "\n", "\n", "\n", "![image.png](attachment:image.png)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Euler法\n", "1次の微分方程式の一般形は\n", "\n", "$$\n", "\\frac{dx}{dt}=f(x,t)\n", "$$\n", "と書けます.この微分方程式を簡単な近似から求めるオイラー法を示します.\n", "$x(t+\\delta t)$をテイラー級数展開すると,\n", "\n", "$$\n", "x(t+\\delta t) \\simeq x(t) + \\frac{dx}{dt} \\delta t\n", "$$\n", "となります.これらを代入すると,計算アルゴリズムはつぎのようになります,\n", "\n", "$$\n", "x_{i+1} = x_i + f_i\\,\\delta t\n", "$$\n", "ここで,$f_i$は点($x_i, t_i$)における関数の値です.このアルゴリズムを適用して,$t+\\delta t$の座標$x_{i+1}$を一つ前の時間の座標$x_i$から導くことができます.これを重力場中の運動方程式に適用します.\n", "\n", "## 重力場中の運動をEuler法で解いたら\n", "Euler法は一階の微分方程式に対する定式化をしています.ところが,重力場中の運動は2階の微分方程式です.このようなときには媒介変数を導入して1次連立方程式に置き直します.\n", "\n", "媒介変数として速度$v$を使って,2階の運動方程式\n", "$$\n", "\\frac{d^2x}{dt^2} = -g \n", "$$\n", "が,1階の連立方程式\n", "$$\n", "\\begin{aligned}\n", "\\frac{dv}{dt} & = -g \\\\\n", "\\frac{dx}{dt} & = v \n", "\\end{aligned}\n", "$$\n", "で置き換えられると考えることに相当します.アルゴリズムにすると,\n", "\n", "$$\n", "\\begin{aligned}\n", "v_{i+1} &= v_i - g\\, dt \\\\\n", "x_{i+1} &= x_i + v_i\\, dt\n", "\\end{aligned}\n", "$$\n", "なる連立方程式を解くことに置き換わります.これをpythonで関数にして,さらに計算結果を表示させてみます." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "def euler(x0, v0):\n", " v1 = v0 - g * dt\n", " x1 = x0 + v0 * dt\n", " return x1, v1" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Eulerは$x_i$, $v_i$を受け取って,先ほど導いた簡単な計算によって,$v_{i+1}$, $x_{i+1}$を順次計算して返します.結果は," ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "\n", "def my_plot(xx, vv, tt):\n", " plt.plot(tt, xx, color = 'b', linestyle='--',label=\"height\")\n", " plt.plot(tt, vv, color = 'r', label=\"velocity\")\n", " plt.legend()\n", " plt.xlabel('time')\n", " plt.ylabel('height and velocity')\n", " plt.grid()\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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jqqF1a/dZWOgSy9FHw4QJ0L69v3GZxFDhYy5VHauqPYGrVbVnwNJPVd+KYozGmCOQmemSyKZNcOqp8PLL9nLeRF6FyUREfuOtthKR35ddQrmoiFwiIotFZL+IdCmzb4SIrBCRZSLy64DyXK9shYjcEVDeWkQ+98oniEhqKLEZEw/OOQe+/tp1eLz2WvjNb2wiLhNZlb2AT/c+M4DMcpZQLAIuBA6ZuUFE2gGXAe2BXOAZEUkWkWTgaaA30A4Y5B0L8DDwuKqeAPwIXBtibMbEhWbNYMYMeOAB9+6kVi2/IzLxrMJ3Jqr6vPc5MtwXVdWlACJSdld/YLyq7ga+E5EVQFdv3wpVXemdNx7oLyJLgbNww70AjAXuBZ4Nd8zG1ETJyXDnnQcfcy1cCB995F7YH/7rZ0z1VTmcioiMBW5R1W3edkPgUVX9bQTiaQF8FrC9xisDWF2m/BdAY2Cbqu4r5/jDiMhQYChAVlYWeXl51QqyqKio2ufWVFbn+PDkkyfw1lvZTJiwidtuW0Zm5r5D9sdjnauSaHWOVH2DmQO+Y2kiAVDVH72mwpUSkVlAs3J23amqk4MPMXxU9QXgBYAuXbpojx49qvVz8vLyqO65NZXVOT6ceaab1fGOO5pyyy1NmTQJOgX8NsdjnauSaHWOVH2DSSZJItJQVX8EEJFGwZynqr2qEc9aoGXAdrZXRgXlW4AGIpLi3Z0EHm+MKUPEjT582mlwySXu88MPoVs3vyMzNV0wPeAfBT4VkftF5AHgE+CRCMUzBbhMRGqLSGugDfAFMA9o47XcSsW9pJ+iqgrMAS72zh8M+HLXY0xN8stfwpdfuvlROnf2OxoTD6pMJqr6Kq7l1QZgPXChqv4jlIuKyAARWQN0A6aJyAzvWouBicAS4H1gmKqWeHcdNwIzgKXARO9YgNuB33sv6xsDL4USmzGJomlTN6x9aips2QIXXQQ//JDmd1imhgrmMRdALQ4OpxJyA0NVfRt4u4J9DwIPllP+HvBeOeUrOdjiyxhTDd98A7NmwaxZnWnQAHJz/Y7I1DTBDEF/C/Aa0AQ4ChgnIjdFOjBjTPT86leQnw9NmuymTx+47z438ZYxwQrmzuRa4BequgNARB7GjRr8ZCQDM8ZE1wknwNNPf8nrr3fnnntg3z6XVIwJRjDJRICSgO0SDj7yMsbEkbS0/Ywd65oQ9+3rdzSmJgmmNdf/AZ+LyL0ici+uU6G95DYmTom48byystx4XgMGwLRpfkdlYl0wrbkeA64BtnrLNar6RITjMsbEgG3b4Pvv4fzzYfRoG33YVKyyybEaBWyu8pYD+1R1a+TCMsbEgqZN4V//cncqI0a4kYhfeskm3TKHq+ydST6gHPp+pHRbgeMiGJcxJkbUrQuvvw45OS6h7NoFb5fbsN8ksspGDW4dzUCMMbFLBG6/HTp0gBYVDqVqElkw/UxERH4jIn/2to8REeskaEwCOu88d4cCboyvF1/0NRwTQ4JpzfUMbtiT0jlDCnETVRljEtSePbBkCQwdCsOHQ0lJ1eeY+BZMMvmFqg4DdoEbgh6wqXGNSWCpqTB1qhsocswYN67Xjh1+R2X8FEwy2etNm6sAItIUsIEWjElwKSnw1FPw17/Cu++68bys6XDiCqYH/N9wgzIeJSIP4oZ7vyuiURljagQRuPlmOP549+jLpgJOXMFMcvWaiOQDZ+OaBV9QOoe7McaAezFf6pVXoFEj6NfPt3CMD4JpzfU3oJGqPq2qT1kiMcZUpKQEXngBLrgAHnvMHnslkmDemeQDd4nItyIyRkS6RDooY0zNlJzs5kUZMAD+8Af4n/9xow+b+BfM2FxjVbUPcCqwDHhYRJZHPDJjTI1Uty688Ybr5Pj88+4uxZoOx79gZ1oEOAH4GXAsbupcY4wpV1KSGxiydWvYtMndsZj4VmUyEZFHgAHAt8B44H5V3RbhuIwxceC66w6uf/45NG7sJuEy8SeYO5NvgW6qujnSwRhj4lNJCQweDFu3us6OXW1AprgTzDuT5y2RGGNCkZwMU6ZARgb06OESiokvwbTmMsaYkLVtC59+Cu3aQf/+rgmxiR+WTIwxUZOVBXl58OtfwwcfWD+UeFJhMhGRRpUtoVxURC4RkcUisj+w34qItBKRYhEp8JbnAvZ1FpGFIrJCRP4m4gZu8OKZKSLLvc+GocRmjImsjAyYPBnGjXPDr2zebH1R4kFldyb5wHzvcxPwH2C5t54f4nUXARcCc8vZ962q5njL9QHlzwJDgDbekuuV3wHMVtU2wGxv2xgTw2rVgrQ0N2tjz55wySVu3dRcFSYTVW2tqscBs4DzVbWJqjYG+gIfhHJRVV2qqsuCPV5EmgP1VPUzVVXgVeACb3d/YKy3Pjag3BgT49LSYMgQeOcd6NMHtm/3OyJTXaJVPLQUkYWqelJVZdW6uEge8EdVne9ttwIW4+6CtgN3qerH3qOw0arayzvuDOB2Ve0rIttUtYFXLsCPpdvlXG8oMBQgKyur8/jx46sVd1FRERkZGdU6t6ayOicGv+o8c+ZRjB79c044oYiHH15AgwZ7o3btRPueQ61vz54981X18GG1VLXSBZiBG3K+lbfcCcwI4rxZuMdZZZf+AcfkAV0CtmsDjb31zsBqoB7QBZgVcNwZwFRvfVuZ6/5YVWyqSufOnbW65syZU+1zayqrc2Lws85Tp6qmpakOGBDd6yba9xxqfYH5Ws7f1GA6LQ4C7sHNaQLuPcegqk5S7y7iSKjqbmC3t54vIt8CbYG1QHbAodleGcAGEWmuquu9x2Ebj/S6xhj/nXcezJ4Nxx7rdySmOoLptLhVVW9R1U7ecouqbo1EMCLS1JvVERE5DveifaWqrge2i8gvvUdZVwGTvdOmAIO99cEB5caYGua006BFC9e6a8gQmDfP74hMsIKZz6StiLwgIh+IyIelSygXFZEBIrIG6AZME5EZ3q7uwAIRKQDeBK4PSFw3AH8HVuCGeJnulY8GzvFGMu7lbRtjarCNG91Q9med5e5WTOwL5jHXG8BzuD/kYRlIWlXf5uBjs8DyScCkCs6ZD3Qop3wLbhZIY0ycOPpo+Pe/XefGPn1g4kTXa97ErmB6wO9T1WdV9QtVzS9dIh6ZMSahHX00fPQR5OTARRe5OVJM7AommbwrIjeISPNw9YA3xphgNGoEM2e6O5Ts7KqPN/4J5jFX6cvt4QFlChwX/nCMMeZQ9erBtGkHt7/6Cjp18i8eU75gWnO1LmexRGKMibopU+CUU+DRR/2OxJQV1LS9ItIBaAeklZap6quRCsoYY8qTm+vG8frjH2HnTrjrLjdYpPFfMNP23gP0wCWT94DewL9w42MZY0zUpKbC66+7Mb3uvtsllFGjLKHEgmBewF+Ma3r7g6peA5wM1I9oVMYYU4GUFHjlFTe//OjRbsIt479gkkmxqu4H9olIPdxwJS0jG5YxxlQsKQmefdY1HT7tNL+jMRBcMpkvIg2AF3HzmHwJ2P8LGGN8JQLdu7v1uXPh5pth/35/Y0pkVb4zUdUbvNXnROR93LwiCyIbljHGBC8vD558EoqL4fnn3Z2Lia6gWnOVUtVVEYrDGGOq7c9/hr174YEH3LzyL7xgCSXajiiZGGNMLBKB++5zn/ff7xLKiy9aQokmSybGmLggAiNHus8VK1xCMdETzBD0/wimzBhj/FaaUP7xD0hOhs2boSQsY52bqgRzE9g+cMObvKpzZMIxxpjQJSVBYSF06wbXXmsJJRoqTCYiMkJECoGOIrLdWwpx/UxsNkNjTEzLzIQrr4SxY+G3v7WEEmkVvjNR1YeAh0TkIVUdEcWYjDEmLO6+2z36uvtuqFXLWnlFUjD9TEaISAvg2MDjVXVuJAMzxphwKG02fP/9cPzxMML+1zgighnocTRwGbCEg9P2KmDJxBhTI4wcCU2awOWX+x1J/AqmafAA4ERV3R3pYIwxJhJE3HArAHv2wJtvWmIJt2CeHq4EakU6EGOMiYa//x2uuML1ljfhU+GdiYg8iXuctRMoEJHZwIG7E1W9OfLhGWNMeF1/PXzxhXuXUrs2nHqq3xHFh8oec833PvOBKVGIxRhjIi4pCV56CXbvhttug5tuakGPHn5HVfNV1jR4bKQuKiJ/Ac4H9gDfAteo6jZv3wjgWtzL/ptVdYZXngv8FUgG/q6qo73y1sB4oDEu8V2pqnsiFbsxpuZLToZXX3UJ5ZVXWnH33e4Fvam+YIZTWSgiC8osH4vI4yLSuJrXnQl0UNWOwH+AEd612uFajrUHcoFnRCTZ63X/NG7K4HbAIO9YgIeBx1X1BOBHXCIyxphK1aoF48fDU099ZYkkDIJ5AT8dmAZc4S3v4h6B/QC8Up2LquoHqrrP2/wMyPbW+wPjVXW3qn4HrAC6essKVV3p3XWMB/qLiABnAW96548FLqhOTMaYxJOaCsccsxOARx6Bt9/2OaAaLJimwb1U9ZSA7YUi8qWqniIivwlDDL8FJnjrLXDJpdQarwxgdZnyX+AebW0LSEyBxxtjTFD27IF33oH8fJg2DXr18juimieYZJIsIl1V9QsAETkV994CYF9FJ4nILKBZObvuVNXJ3jF3ej/jtSOKuppEZCgwFCArK4u8vLxq/ZyioqJqn1tTWZ0TQ6LW+ZNP8hgxIoVbb83h/PPr8OijX9Ou3Xa/Q4uIiH3HqlrpApwKLAS+A1YBC3CPndKBgVWdX8nPvRo3l3zdgLIRwIiA7RlAN2+ZUfY4QIDNQIpXfshxlS2dO3fW6pozZ061z62prM6JIdHrvH696vHHqzZooLpggX8xRVKo3zEwX8v5m1rlOxNVnaeqJwE5wMmq2lFVv1DVHao6sToJzGuZdRvQT1V3BuyaAlwmIrW9VlptgC+AeUAbEWktIqm4l/RTvIrNAS72zh+MjWhsjKmmZs1g1iw34vCXX/odTc1SWafF36jqOBH5fZlyAFT1sRCu+xRQG5jp/bzPVPV6VV0sIhNx44DtA4apaol33RtxdyrJwMuqutj7WbcD40XkAeAr4KUQ4jLGJLhWrWDpUkhPd9v799tIw8Go7J2J909JZrgvqq4Zb0X7HgQeLKf8PeC9cspX4h67GWNMWJQmkhkz4M474f33rR9KVSrrtPi89zkyeuEYY0zsSEuDxYuhd2+YPRvq1fM7otgVTKfFtiIyW0QWedsdReSuyIdmjDH+OvNMeOMNKCiAfv2guNjviGJXME8CX8S1nNoLoKoLcC/AjTEm7vXt66b+nTvXDVu/r8IOEYktmH4mdVX1i9IX7x775zTGJIzLL4ctW2DhQr8jiV3BJJPNInI8bjh6RORiYH1EozLGmBhz002g6ibaKiqCjAy/I4otwTzmGgY8D/xMRNYCtwL/E8mgjDEmFonAmjXQoQM8+6zf0cSWKu9MvKa3vUQkHUhS1cLIh2WMMbGpWTM46SQYNgyOOgouusjviGJDlclERGoDFwGtgJSATov3RTQyY4yJQSkpMGGCGwzy8stdXxSbXCu4x1yTcUPD7wN2BCzGGJOQ6taFqVPh+OOhf397MQ/BvYDPVtXciEdijDE1SKNG7q5k+HDIzq76+HgXzJ3JJyJyUsQjMcaYGqZlSzdbY8OGsGsXbN3qd0T+qWygx4W45sApwDUishLYjRv2XdVNuWuMMQlPFS680PVF+fDDg2N7JZLKHnP1jVoUxhhTg4nAddfBgAHupfxbb0FyctXnxZMKH3Op6veVLdEM0hhjYl3//vC3v8GUKXDLLe5uJZEE8wLeGGNMEG68EVatgkcfhTZtXFJJFJZMjDEmjB55xA0G2auX35FElyUTY4wJo6QkeOIJt67qhl9p2dLXkKLCJqM0xpgIeeAByMmBZcv8jiTyLJkYY0yEXHGFa9XVuzds2OB3NJFlycQYYyLkuOPcsCs//ADnnw874nggKksmxhgTQV27ul7y+flw5ZXx22TYXsAbY0yE9esHzzwDLVq4Do7xyJKJMcZEwXXXHVxftw6OPtq/WCLBHnMZY0wUTZvm3qXMmOF3JOHlSzIRkb+IyDciskBE3haRBl55KxEpFpECb3ku4JzOIrJQRFaIyN/Em6VLRBqJyEwRWe59NvSjTsYYE4zu3eHEE2HgQFi82O9owsevO5OZQAdv5OH/ACMC9n2rqjnecn1A+bPAEKCNt5TOsXIHMFtV2wCzvW1jjIlJmZmuhVfdutC3L2zc6HdE4eFLMlHVD1R1n7f5GVDp1DIi0hyop6qfqaoCrwIXeLv7A2O99bEB5cYYE5NatnQDQm7Y4AaI3L3b74hCJ+pzOzUReReYoKrjRKQVsBh3t7IduEtVPxaRLsBoVe3lnXMGcLuq9hWRbarawCsX4MfS7XKuNRQYCpCVldV5/Pjx1Yq5qKiIjIyMap1bU1mdE4PVObo++qgJa9bU5fLL/xu1Vl6h1rdnz575qtrlsB2qGpEFmAUsKmfpH3DMncDbHExqtYHG3npnYDVQD+gCzAo47wxgqre+rcx1fwwmvs6dO2t1zZkzp9rn1lRW58RgdfbP1q3RuU6o9QXmazl/UyPWNFi9u4iKiMjVuAm4zvYCRFV342ZzRFXzReRboC2wlkMfhWV7ZQAbRKS5qq73HofFyRNIY0yiWLTIvZh/6ik3uVZN5FdrrlzgNqCfqu4MKG8qIsne+nG4F+0rVXU9sF1Efuk9yroKmOydNgUY7K0PDig3xpgaoW1b6NgRrrkGPvnE72iqx6/WXE8BmcDMMk2AuwMLRKQAeBO4XlW3evtuAP4OrAC+BaZ75aOBc0RkOdDL2zbGmBojNRUmTYJjj4ULLoDva+Bctr70gFfVEyoonwRMqmDffKBDOeVbgLPDGqAxxkRZ48auhdcvf+laeP3rX1CT2kJYD3hjjIkRP/uZGxTypJPc0PU1iY3NFWDv3r2sWbOGXbt2VXpc/fr1Wbp0aZSiig2BdU5LSyM7O5tatWr5HJUx8Sc31y0Ae/dCTfk1s2QSYM2aNWRmZtKqVSukkkbfhYWFZGZmRjEy/5XWWVXZsmULa9asoXXr1n6HZUzcWrsWzj0X7r0XLrnE72iqZo+5AuzatYvGjRtXmkgSnYjQuHHjKu/ejDGhadIE6teHwYPhq6/8jqZqlkzKsERSNfs3MibyateGt95yL+b794/9aX8tmRhjTIxq1gwmT4bNm+HCC2N7DC9LJjFm1apVdOhwWAvoCj333HO8+uqrlR7zyiuvcOONN5a7b9SoUUcUnzEmuk45BV55BfbsgZ9+8juailkyqeGuv/56rrrqqmqfb8nEmNg3cCB89hkcdZTfkVTMkkklevQ4fHnmGbdv587y97/yitu/efPh+4JVUlLCkCFDaN++Peeeey7FxcV8++235Obm0rlzZ8444wy++eYbAO69917GjBkDwLx58+jYsSM5OTkMHz78kDucdevWkZubS5s2bbjtttsAuOOOOyguLiYnJ4crrriiGv9CxphoSU6G7dtdD/mZM/2O5nCWTGLQ8uXLGTZsGIsXL6ZBgwZMmjSJoUOH8uSTT5Kfn8+YMWO44YYbDjvvmmuu4fnnn6egoIDkMj2eCgoKmDBhAgsXLmTChAmsXr2a0aNHU6dOHQoKCnjttdeiVT1jTDUlJcHKlXDppe4zllg/k0rk5ZVfXljoZkmraD+4Zn2V7a9M69atycnJAaBz586sWrWKTz75hEsCGpvvLvMmbtu2bRQWFtKtWzcALr/8cqZOnXpg/9lnn039+vUBaNeuHd9//z0tW7asXoDGGF9kZMDbb0OXLjBggBsUMj3d76gcSyYxqHbt2gfWk5OT2bBhAw0aNKCgoCBsP3Pfvn2VHG2MiVXHHw///Cf06QO/+x28/jpRm1irMvaYqwaoV68erVu35o033gDchGZff/31Icc0aNCAzMxMPv/8cwCCnUWyVq1a7N27N7wBG2MiKjcXRo2COXNcT/lYYMmkhnjttdd46aWXOPnkk2nfvj2TJx8+bctLL73EkCFDyMnJYceOHQcea1Vm6NChdOzY0V7AG1PD3H67m1QrO7vqY6OivOkXE2Epb9reJUuWVDllparq9u3bgzou2goLCw+sP/TQQ3rzzTeH7WeXrXOw/1Y1WaxM5xpNVueaZ98+1ZEjVVeuDO74SE3ba3cmcWTatGnk5OTQoUMHPv74Y+666y6/QzLGRNjatfD4466H/M6dVR8fKfYCPo5ceumlXHrppX6HYYyJomOOcS/hzzsPhgyBceP8eSFvdybGGFPD9e4NDzzgksrjj/sTgyUTY4yJAyNGuEddf/4zbNwY/evbYy5jjIkDIm44p2XL/BnDy+5MjDEmTmRmut7xANOnR3fIeksmNVhGRka1zrv77ruZNWsWAE888QQ7/WwCYowJu4ULXQ/5W2+N3jUtmSSg++67j169egGWTIyJRyedBMOHw3PPQRXTHYWNb+9MROR+oD+wH9gIXK2q68TNCftXoA+w0yv/0jtnMFDaeeIBVR3rlXcGXgHqAO8Bt3ida6rv1luhgrGw6pSUuPGgj1RODjzxRIW777jjDlq2bMmwYcMAN7x8RkYGqsrEiRPZvXs3AwYMYOTIkYecp6rcdtttTJ8+HRHhrrvuOtBE+OGHH2bcuHEkJSXRu3dvRo8ezdVXX03fvn1Zt24d69ato2fPnjRp0oQrr7ySBQsW8IQX44svvsiSJUt43K/mIcaYahs1CubNg+uug5NPdksk+Xln8hdV7aiqOcBU4G6vvDfQxluGAs8CiEgj4B7gF0BX4B4Raeid8ywwJOC83CjVIawuvfRSJk6ceGB74sSJNG3alOXLl/PFF19QUFBAfn4+c+fOPeS8t956i4KCAr7++mtmzZrF8OHDWb9+PdOnT2fy5Ml8/vnnfP311wfmMSl18803c/TRRzNnzhzmzJnDwIEDeffddw+M1fV///d//Pa3v418xY0xYZeSAuPHQ6NGrpVXcXGErxfZH18xVd0esJkOlN5J9Ade9e4sPhORBiLSHOgBzFTVrQAiMhPIFZE8oJ6qfuaVvwpcAEwPKcBK7iCKCwvJzMwM6ceXp1OnTmzcuJF169axadMmGjZsyMKFC/nggw/o1KkTAEVFRSxfvpzu3bsfOO9f//oXgwYNIjk5maysLM4880zmzZvHRx99xDXXXEPdunUBaNSoUaXXz8jI4KyzzmLq1Kn8/Oc/Z+/evZx00klhr6cxJjqysuDNN2H5cqhTJ7LX8rVpsIg8CFwF/AT09IpbAKsDDlvjlVVWvqac8vKuNxR3t0NWVhZ5ZSYcqV+/PoWFhVXGXVJSEtRx1dGvXz/GjRvHxo0b6d+/P6tXr+Z///d/D7tDKL1+YWEhe/bsYdeuXQfK9u7dS3Fx8WHlpUr3FxYWoqoUFRUdGKJ+0KBBPProo7Rt25ZBgwYdOLdsnXft2nXYv1+8KSoqivs6lmV1jk/HHOPmV/rpp1okJ0eovuUN2BWuBZgFLCpn6V/muBHASG99KnB6wL7ZQBfgj8BdAeV/9sq6ALMCys8AplYVW6wO9Lho0SLt1q2btmnTRtetW6czZszQrl27HhjEcc2aNbphwwZVVU1PT1dV1UmTJum5556r+/bt040bN+oxxxyj69ev1+nTp2u3bt10x44dqqq6ZcsWVVUdPHiwvvHGG6qq2qFDB11ZZoS4Tp06aXZ2tm7durXCOttAj/HJ6hy/8vJU09NVx4wpCOnnUMFAjxG9M1HVXkEe+hruxfk9wFogcArAbK9sLe5RV2B5nleeXc7xNVL79u0pLCykRYsWNG/enObNm7N06dIDMyhmZGQwbtw4jgrolTRgwAA+/fRTTj75ZESERx55hGbNmpGbm0tBQQFdunQhNTWVPn36MGrUqEOuN3ToUHJzcw+8OwEYOHAgBQUFNGzYEGNMfOjSBVq3hn/+syV/+EMELlBehonGArQJWL8JeNNbPw/3vkOAXwJfeOWNgO+Aht7yHdDI2/eFd6x45/ap6vqxemcSC8477zydNWvWIWV2Z5IYrM7x7b//VX3//Y9C+hnE4BD0o0VkkYgsAM4FbvHK3wNWAiuAF4EbANS9eL8fmOct93lleMf83TvnW0J9+Z6gtm3bRtu2balTpw5nn3223+EYY8KsZUuoXXt/RH62n625LqqgXIFhFex7GXi5nPL5QIewBpiAGjRowH/+8x+/wzDG1EDWA74MDbGvYyKwfyNjTFmWTAKkpaWxZcsW+2NZCVVly5YtpKWl+R2KMSaG2BD0AbKzs1mzZg2bNm2q9Lhdu3Yl3B/TwDqnpaWRnZ1dxRnGmERiySRArVq1aN26dZXH5eXlHeiRnigSsc7GmODZYy5jjDEhs2RijDEmZJZMjDHGhEwSteWSiGwCvq/m6U2AzWEMpyawOicGq3P8C7W+x6pq07KFCZtMQiEi81W1i99xRJPVOTFYneNfpOprj7mMMcaEzJKJMcaYkFkyqZ4X/A7AB1bnxGB1jn8Rqa+9MzHGGBMyuzMxxhgTMksmxhhjQmbJ5AiJSK6ILBORFSJyh9/xRIOIrBKRhSJSICLz/Y4nEkTkZRHZKCKLAsoaichMEVnufcbNPMYV1PdeEVnrfc8FItLHzxjDTURaisgcEVkiIotF5BavPJ6/54rqHPbv2t6ZHAERSQb+A5wDrMHN+DhIVZf4GliEicgqoIuqxm3HLhHpDhQBr6pqB6/sEWCrqo72/sehoare7mec4VJBfe8FilR1jJ+xRYqINAeaq+qXIpIJ5AMXAFcTv99zRXUeSJi/a7szOTJdgRWqulJV9wDjgf4+x2TCQFXnAlvLFPcHxnrrY3G/hHGhgvrGNVVdr6pfeuuFwFKgBfH9PVdU57CzZHJkWgCrA7bXEKEvJsYo8IGI5IvIUL+DiaIsVV3vrf8AZPkZTJTcKCILvMdgcfO4pywRaQV0Aj4nQb7nMnWGMH/XlkxMME5X1VOA3sAw7xFJQlH3PDjenwk/CxwP5ADrgUd9jSZCRCQDmATcqqrbA/fF6/dcTp3D/l1bMjkya4GWAdvZXllcU9W13udG4G3c475EsMF75lz67Hmjz/FElKpuUNUSVd0PvEgcfs8iUgv3R/U1VX3LK47r77m8Okfiu7ZkcmTmAW1EpLWIpAKXAVN8jimiRCTde3GHiKQD5wKLKj8rbkwBBnvrg4HJPsYScaV/UD0DiLPvWUQEeAlYqqqPBeyK2++5ojpH4ru21lxHyGtC9wSQDLysqg/6G1FkichxuLsRcNM8vx6PdRaRfwI9cMNzbwDuAd4BJgLH4KYrGKiqcfHSuoL69sA99lBgFXBdwLuEGk9ETgc+BhYC+73iP+HeIcTr91xRnQcR5u/akokxxpiQ2WMuY4wxIbNkYowxJmSWTIwxxoTMkokxxpiQWTIxxhgTMksmxkSBiDQQkRu89aNF5E2/YzImnKxpsDFR4I2LNLV0hF5j4k2K3wEYkyBGA8eLSAGwHPi5qnYQkatxo9SmA22AMUAqcCWwG+ijqltF5HjgaaApsBMYoqrfRLsSxlTEHnMZEx13AN+qag4wvMy+DsCFwKnAg8BOVe0EfApc5R3zAnCTqnYG/gg8E42gjQmW3ZkY47853lwThSLyE/CuV74Q6OiN+Hoa8IYbagmA2tEP05iKWTIxxn+7A9b3B2zvx/2OJgHbvLsaY2KSPeYyJjoKgczqnOjNP/GdiFwCbiRYETk5nMEZEypLJsZEgapuAf4tIouAv1TjR1wBXCsiXwOLsemiTYyxpsHGGGNCZncmxhhjQmbJxBhjTMgsmRhjjAmZJRNjjDEhs2RijDEmZJZMjDHGhMySiTHGmJD9P9t/BZijMXDuAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#g, dt =9.8, 0.01\n", "g, dt =9.8, 0.1\n", "tt,xx,vv=[0.0],[10.0],[0.0] #for compare rain_drop\n", "#tt,xx,vv=[0.0],[0.0],[9.8]\n", "#tt,xx,vv=[10.0],[0.0],[0.0]\n", "\n", "\n", "t = 0.0\n", "\n", "for i in range(0,250): #250 for compare rain_drop\n", " t += dt\n", " x, v = euler(xx[-1],vv[-1])\n", " tt.append(t)\n", " xx.append(x)\n", " vv.append(v)\n", "\n", "# print(xx)\n", "# print(vv)\n", "my_plot(xx, vv, tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "位置(height:$x$)と速度($v$)の時間($t$)変化を表示させています.\n", "\n", "\n", "時間とともに位置は放物線状に変化し,速度は一定の傾きで増加していく,等加速度運動を再現しています.Euler法ではこのように非常に簡単なcodeによって微分方程式で表される現象をシミュレートできることがわかるでしょう." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "## 空気抵抗がある水滴の落下\n", "ballの落下ではわかりにくいですが,より小さな質量の水滴では,速度に比例する空気抵抗が効いてきます.この様子を見ましょう.微分方程式には,\n", "\n", "$$\n", "F_x = - C v_x\n", "$$\n", "\n", "項が付与されます.そうすると運動方程式は\n", "\n", "$$\n", "m \\frac{dv_x}{dt} = - C v_x - mg\n", "$$\n", "となります.これにともなったv_xの時間変化に対して,今までは単純に重力加速していたのが,v_xに比例する空気抵抗を記述する項が付与されます.この変化をEuler2に入れ込むと少しの修正ですが,結果は劇的に変化します.\n", "\n", "\n", "![image.png](attachment:image.png)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "その前に,ここで示した修正がどれほど普通の微分方程式の解法としてややこしいかを少し示しておきます.\n", "$$\n", "m \\frac{dv_x}{dt} = - C v_x - mg\n", "$$\n", "を整理すると,\n", "$$\n", "\\frac{dv_x}{dt} = - \\frac{C}{m} v_x - g\n", "$$\n", "です.右辺を$v_x$の係数でくくって,変形していくと,\n", "$$\n", "\\begin{aligned}\n", "\\frac{dv_x}{dt} & = - \\frac{C}{m}\\left(v_x - \\frac{m}{C}g\\right) \\\\\n", "\\frac{1}{\\left(v_x - \\frac{m}{C}g\\right)}dv_x & = - \\frac{C}{m}dt\n", "\\end{aligned}\n", "$$\n", "これで変数分離されているので積分をとって,\n", "公式$\\int \\frac{1}{x+a} dx = \\log |x+a| + C_1$を使うと\n", "$$\n", "\\log \\left|v_x - \\frac{m}{C}g \\right| = - \\frac{C}{m} t + C_1\n", "$$\n", "なんですが,両辺の指数をとって「適当」に変形すると\n", "$$\n", "\\begin{aligned}\n", "\\left| v_x - \\frac{m}{C}g\\right| & = \\exp(- \\frac{C}{m}t + C_1 ) \\\\\n", "v_x &= \\frac{gm}{C} + \\exp(- \\frac{C}{m}t + C_1 )\n", "\\end{aligned}\n", "$$\n", "となります.最後の絶対値の変形は怪しいんであまり信頼しないでね.\n", "\n", "これをpythonが用意している数式処理libraryのsympyを使うと次の通りとなります." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle v{\\left(t \\right)} = \\frac{- g m + e^{cc \\left(C_{1} - \\frac{t}{m}\\right)}}{cc}$" ], "text/plain": [ "Eq(v(t), (-g*m + exp(cc*(C1 - t/m)))/cc)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy import *\n", "v, f = symbols('v f', cls=Function)\n", "cc, t, m, x, g= symbols('cc t m x g')\n", "# dsolve(f(x).diff(x, x) + f(x), f(x))\n", "dsolve(v(t).diff(t)+cc/m*v(t)+g,v(t))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def euler2(x0, v0):\n", " v1 = v0 + (-cc * v0- g) * dt\n", " x1 = x0 + v0 * dt\n", " return [x1, v1]\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "g, dt, cc=9.8, 0.01, 1.0\n", "# tt,xx,vv=[0.0],[0.0],[-10]\n", "tt,xx,vv=[0.0],[10.0],[0.0]\n", "t = 0.0\n", "for i in range(0,500):\n", " t += dt\n", " x, v = euler2(xx[-1],vv[-1])\n", " tt.append(t)\n", " xx.append(x)\n", " vv.append(v)\n", "\n", "my_plot(xx, vv, tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ちょっと気をつけたいのは,$-Cv$の向きです.vは例えば自由落下の時には下向きのベクトルなんで,抵抗は反対向き,すなわち上むき,数値的には正,になります." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "# 高精度計算\n", "\n", "## バネの運動\n", "今度はバネの運動です.空気抵抗との違いはほんの少しで,\n", "$$\n", "F_x = -k x\n", "$$\n", "と今度は,位置xに力が比例することです.そうすると運動方程式は,\n", "\n", "$$\n", "m \\frac{dv_x}{dt} = - k x\n", "$$\n", "となります.\n", "\n", "連立方程式は\n", "$$\n", "\\begin{aligned}\n", "\\frac{dv}{dt} & = - \\frac{k}{m}x \\\\\n", "\\frac{dx}{dt} & = v\n", "\\end{aligned}\n", "$$\n", "となるんで,アルゴリズムに置き換えると,\n", "\n", "$$\n", "\\begin{aligned}\n", "v_{i+1} & = v_i - \\frac{k}{m} x_i\\, dt \\\\\n", "x_{i+1} & = x_i + v_i\\, dt\n", "\\end{aligned}\n", "$$\n", "なる連立方程式を解くことに置き換わります.これをpythonで関数にして,さらに計算結果を表示させてみます.\n", "\n", "\n", "![image.png](attachment:image.png)\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def euler3(x0,v0):\n", " v1 = v0 +(- k * x0) * dt\n", " x1 = x0 + v0 * dt\n", " return [x1, v1]\n", "\n", "t, dt, k=0.0, 0.01, 0.01\n", "tt,xx,vv=[0.0],[0.0],[0.01]\n", "for i in range(0,100000):\n", " t += dt\n", " x, v = euler3(xx[-1],vv[-1])\n", " tt.append(t)\n", " xx.append(x)\n", " vv.append(v)\n", "\n", "my_plot(xx, vv, tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "kはあらかじめ$m$で割られて正規化されているとします.これをEuler法で計算すると上のような結果が得られます.\n", "\n", "徐々に発散していく様子がわかると思います.本来,摩擦のないバネは定常的に振動します.この発散の原因は,Euler法の計算誤差が大きいせいです.そこで,より精度の高いRunge-Kutta法を導入します.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2次のRunge-Kuttaの導出\n", "一般にRunge-Kutta法と呼ばれる手法は,4次の古典的Runge-Kutta法を指します.導出は意外と面倒なので,2次の場合のさわりを紹介して,そこからの類推としましょう.$x,v,t$などのパラメータ名を変更しますのでご注意あれ.\n", "\n", "(「ANSI Cによる数値計算法」堀之内聰一,酒井幸吉,榎園茂,森北2002, p.133)\n", "テイラー展開により,$h^2$の精度まで展開する.\n", "$$\n", "y(x_0+h) = y(x_0) +y_0'h+\\frac{1}{2!}y_0''h^2 + O(h^3)\n", "$$\n", "\n", "この式において,$y_0' = f(x_0,y_0)$は既知とする.一方,$y_0''$は$f(x_0,y_0)$から直接的には求められない.したがって,この式の右辺と$h^2$の項まで一致する近似値を,$f(x_0,y_0)$だけを既知として算出する方法を考えよう.\n", "\n", "平均値の定理より,\n", "$$\n", "\\Delta y = y(x_0+h)-y(x_0) = hy'(x_0 + \\theta h), \\, 0<\\theta<1\n", "$$\n", "\n", "$y'(x_0 +\\theta h)$の近似値として,$\\theta=0, \\theta=1$の場合を考えると,\n", "$$\n", "\\begin{aligned}\n", "\\Delta y &\\simeq hy'(x_0) \\, &{\\textrm where}\\, &\\theta=0\\\\\n", "\\Delta y &\\simeq hy'(x_0+h) \\, &{\\textrm where}\\, &\\theta=1\n", "\\end{aligned}\n", "$$\n", "これらの値は単独では$\\Delta y$に対して$h^2$の精度をもつ近似値にならないが,これらの一次結合$\\alpha h y'(x_0)+\\beta hy'(x_0+h)$を$\\alpha, \\beta$をうまく定めることによって,$\\Delta y$の$h^2$の精度をもつ近似値にすることができる.実際,\n", "$$\n", "\\begin{aligned}\n", "\\alpha h y'(x_0)+\\beta hy'(x_0+h) & =\\alpha h y'(x_0)+\\beta h \\{y'(x+0)+y''(x_0)h+O(h^2)\\} \\\\\n", "& =(\\alpha+\\beta)hy'_0 + \\beta h^2 y_0'' + O(h^3)\n", "\\end{aligned}\n", "$$\n", "\n", "したがって,テイラー展開式と係数を比較して,\n", "$$\n", "\\begin{aligned}\n", "\\alpha + \\beta = 1, \\, \\beta = \\frac{1}{2}\\\\\n", "\\alpha = \\frac{1}{2}, \\, \\beta =\\frac{1}{2}\n", "\\end{aligned}$$\n", "となり,\n", "\n", "$$\n", "\\Delta y = \\frac{1}{2}hy'(x_0) + \\frac{1}{2}hy'(x_0+h)+O(h^3)\n", "$$\n", "\n", "いま,\n", "$$\n", "k_1 =hy'(x_0) =hf(x_0,y_0)\n", "$$\n", "\n", "とおこう.上式に代入して,\n", "$$\n", "\\begin{aligned}\n", "hy'(x_0+h) &= hf(x_0+h,y(x_0+h)) \\\\\n", "& =hf(x_0+h, y(x_0)+y'(x_o)h+O(h^2)) \\\\\n", "& =hf(x_0+h, y_0+k_1+O(h^2)) \\\\\n", "& =hf(x_0+h, y_0+k_1)+O(h^2)\n", "\\end{aligned}$$\n", "\n", "したがって,\n", "$$\n", "k_2 = hf(x_0+h, y_0+k_1)\n", "$$\n", "とおけば,\n", "$$\n", "\\Delta y = \\frac{1}{2}k_1 + \\frac{1}{2}k_2 + O(h^3)\n", "$$\n", "となる.これより,\n", "$$\n", "k = \\frac{1}{2}(k_1+k_2), y_1 = y_0 +k\n", "$$\n", "\n", "とおくと,$y(x_0+h) = y_1+O(h^3)$となり,$y_1$は$h^2$の精度の近似値となる." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Runge-Kutta2次公式\n", "こうして得られたRunge-Kuttaの2次の公式を定義すると次の通りです.\n", "\n", "微分方程式\n", "$$\n", "\\frac{dy}{dx} = f(x,y), \\, where \\, y(x_0)=y_0\n", "$$\n", "\n", "の数値解は,刻み幅を$h$,$x_n=x_0+nh$として,次の漸化式\n", "$$\n", "y_{n+1} = y_n +k (n=0,1,2,\\cdots)\n", "$$\n", "で与えられる.ここに,$k$は次で定める.\n", "$$\n", "\\begin{aligned}\n", "k_1 & = hf(x_n,y_n), \\\\\n", "k_2 & = hf(x_n+h, y_n+k_1), \\\\\n", "k & = \\frac{1}{2}(k_1+k_2)\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Runge-Kutta4次公式\n", "2次と同様の考え方で,$h^4$の精度を持つRunge-Kutta4次公式を作ることができる.\n", "\n", "微分方程式\n", "$$\n", "\\frac{dy}{dx} = f(x,y), \\, {\\textrm where}y(x_0)=y_0\n", "$$\n", "\n", "の数値解は,刻み幅を$h$,$x_n=x_0+nh$として,次の漸化式\n", "$$\n", "y_{n+1} = y_n +k (n=0,1,2,\\cdots)\n", "$$\n", "で与えられる.ここに,$k$は次で定める.\n", "$$\n", "\\begin{aligned}\n", "k_1 & = hf(x_n,y_n), \\\\\n", "k_2 & = hf(x_n+\\frac{h}{2}, y_n+\\frac{k_1}{2}), \\\\\n", "k_3 & = hf(x_n+\\frac{h}{2}, y_n+\\frac{k_2}{2}), \\\\\n", "k_4 & = hf(x_n+h, y_n+k_3), \\\\\n", "k & = \\frac{1}{6}(k_1+2k_2+2k_3+k_4)\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 連立方程式にRunge-Kutta4次公式を\n", "連立微分方程式\n", "$$\n", "\\begin{aligned}\n", "\\frac{dy}{dx} &= f(x,y,z), &\\, \\, where \\, y(x_0)=y_0 \\\\\n", "\\frac{dz}{dx} &= g(x,y,z), &\\, \\, where \\, z(x_0)=z_0 \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "の数値解は,刻み幅を$h$,$x_n=x_0+nh$として,次の漸化式\n", "$$\n", "\\begin{aligned}\n", "y_{n+1} & = y_n +k &\\, (n=0,1,2,\\cdots) \\\\\n", "z_{n+1} & = z_n +l &\\, (n=0,1,2,\\cdots) \\\\\n", "\\end{aligned}\n", "$$\n", "で与えられる.ここに,$k,l$は次で定める.\n", "$$\n", "\\begin{aligned}\n", "k_1 &= hf(x_n,y_n,z_n), \\,\n", "&l_1 &= hg(x_n,y_n,z_n), \\\\\n", "k_2 &= hf(x_n+\\frac{h}{2}, y_n+\\frac{k_1}{2}, z_n+\\frac{l_1}{2}), \\,\n", "&l_2 &= hg(x_n+\\frac{h}{2}, y_n+\\frac{k_1}{2}, z_n+\\frac{l_1}{2}), \\\\\n", "k_3 &= hf(x_n+\\frac{h}{2}, y_n+\\frac{k_2}{2}, z_n+\\frac{l_2}{2}), \\,\n", "&l_3 &= hg(x_n+\\frac{h}{2}, y_n+\\frac{k_2}{2}, z_n+\\frac{l_2}{2}), \\\\\n", "k_4 &= hf(x_n+h, y_n+k_3, z_n+l_3), \\,\n", "&l_4 &= hg(x_n+h, y_n+k_3, z_n+l_3), \\\\\n", "k &= \\frac{1}{6}(k_1+2k_2+2k_3+k_4), \\,\n", "&l &= \\frac{1}{6}(l_1+2l_2+2l_3+l_4)\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def runge_kutta4(x0,y0,z0,h):\n", " k1= h * ff(x0, y0, z0);\n", " l1= h * gg(x0, y0, z0);\n", " k2= h * ff(x0 + h/2, y0 + k1/2, z0 + l1/2)\n", " l2= h * gg(x0 + h/2, y0 + k1/2, z0 + l1/2)\n", " k3= h * ff(x0 + h/2, y0 + k2/2, z0 + l2/2)\n", " l3= h * gg(x0 + h/2, y0 + k2/2, z0 + l2/2)\n", " k4= h * ff(x0 + h, y0 + k3, z0 + l3)\n", " l4= h * gg(x0 + h, y0 + k3, z0 + l3)\n", " kk= 1.0/6*(k1 + 2*k2 + 2*k3 + k4)\n", " ll= 1.0/6*(l1 + 2*l2 + 2*l3 + l4)\n", " return [kk,ll]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Runge-Kuttaの4次公式をそのままcodingすると上のようになります.これを先ほどのバネ運動の問題に当てはめてみましょう.\n", "\n", "先ほど導出した運動方程式の漸化式\n", "$$\n", "\\begin{aligned}\n", "v_{i+1} & = v_i - \\frac{k}{m} x_i\\, dt \\\\\n", "x_{i+1} & = x_i + v_i\\, dt\n", "\\end{aligned}\n", "$$\n", "\n", "とRunge-Kutta4次公式を示した連立微分方程式\n", "$$\n", "\\begin{aligned}\n", "\\frac{dy}{dx} &= f(x,y,z), \\, where \\, y(x_0)=y_0 \\\\\n", "\\frac{dz}{dx} &= g(x,y,z), \\, where \\, z(x_0)=z_0 \\\\\n", "\\end{aligned}\n", "$$\n", "とを比べて,変数の表記の違いと関数$f,g$を具体的に書き下します.\n", "\n", "| 4次の公式 | 運動方程式 |\n", "|:-----:|:-----:|\n", "|x | t |\n", "|y | x |\n", "|z | v |\n", "|f(x,y,z) | f(t,x,v) = v |\n", "|g(x,y,z) | g(t,x,v) = -k x |\n", "\n", "この変数の書き換えを吸収する中間関数としてEuler3を書き換えます.RungeKutta4の仮引数を上の表に従って置き換えて,数値を渡しています.また,関数$f,g$も定義しておきます." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def ff(t,x,v):\n", " return v\n", "\n", "def gg(t,x,v):\n", " return -k*x\n", "\n", "def ode(x0, v0):\n", " kk,ll = runge_kutta4(0, x0, v0, dt)\n", " x1 = x0 + kk\n", " v1 = v0 + ll\n", " return [x1, v1]\n", "\n", "t, dt, k=0.0, 0.1, 0.1\n", "tt,xx,vv=[0.0],[0.0],[0.01]\n", "for i in range(0,10000):\n", " t += dt\n", " x, v = ode(xx[-1],vv[-1])\n", " tt.append(t)\n", " xx.append(x)\n", " vv.append(v)\n", "\n", "my_plot(xx, vv, tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "これを前と同様に走らせると\n", "発散も収束もすることなく,定常的に振動を繰り返していることが見て取れます." ] }, { "attachments": { "image-2.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "# 太陽系\n", "\n", "## 分子動力学=Verlet(ベルレ)法\n", "\n", "惑星の軌道は摩擦のない宇宙空間での2体の重力だけで考えることができる単純な動きなので,比較的容易に再現することができます.\n", "この運動を記述する方程式がニュートンの運動方程式\n", "$$\n", "F = ma\n", "$$\n", "です.ここで$F$はForce(力),\n", "$m$はmass(質量),\n", "$a$はaccelleration(加速度)です.\n", "\n", "$a$ を微分で明示すると,\n", "$$\n", "F = m \\frac{d^2}{dt^2}r(t)\n", "$$\n", "となります.\n", "$r(t)$がある時間での惑星の位置をさしているとします.\n", "これを微小時間$h$で級数展開して\n", "$$\n", "r(t + h) = r(t) + \\frac{dr}{dt} h + \\frac{1}{2} \\frac{d^2r}{dt^2} h^2 + O(h^3)\n", "$$\n", "と\n", "$$\n", "r(t - h) = r(t) - \\frac{dr}{dt} h + \\frac{1}{2} \\frac{d^2r}{dt^2} h^2 + O(h^3)\n", "$$\n", "での和をとって高次項を無視して,$r(t+h)$について解いて,$d^2r/dt^2=F/m$を代入すると,\n", "$$\n", "r(t + h) = 2r(t) - r(t-h) + \\frac{F}{m} h^2\n", "$$\n", "となり,$r(t+h)$の位置を$r(t - h)$と$r(t)$での情報から予測することができます.\n", "\n", "このように微分方程式を差分方程式に変換し,数値的に解いていく方法がVerlet法で,そのほかの種々の分子動力学法の手法の基本となる考え方です.\n", "\n", "![image-2.png](attachment:image-2.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 太陽系=重力\n", "\n", "実際の粒子(剛体球)の運動を記述するには粒子にかかる$F$(力)を知る必要があります.\n", "惑星の軌道を考えるときには太陽を中心とする重力\n", "$$\n", "F = -G\\frac{mM}{d^2}\n", "$$\n", "ですので非常に単純になります.\n", "$G$は重力定数,\n", "$m, M$は2体それぞれの質量,\n", "$d$は2体間の距離(distance)です.\n", "\n", "適当に規格化して,太陽が原点(0,0)にあり,\n", "惑星の位置をr=(x,y)とすると,距離 $d=\\sqrt{x^2+y^2}$ として,\n", "力は\n", "```python\n", "F=1/d** 2\n", "```\n", "で与えられます.\n", "その力ベクトルを位置によって分解すると,[-x/d,-y/d]となるので,\n", "```python\n", "L=(x*x+y*y)**(3/2)\n", "force=[-x/L,-y/L]\n", "```\n", "で求めることができます(たぶん).\n", "将来,現場で宇宙空間のシミュレーションを実行する際は,この導出が正しいか確かめて,間違ってたら教えてください.\n", "初期値r(0 - h), r(0)\n", "を適当におけば,後はVerlet式に従って芋ずる式で惑星の未来の軌跡をシミュレートすることができます.\n", "\n", "こうしてKeplerの第1(楕円軌道),第2(面積速度一定)法則が理解できます.\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "def force(pos):\n", " x=pos[0]\n", " y=pos[1]\n", " L=(x*x+y*y)**(3/2)\n", " return [-x/L,-y/L]\n", "\n", "def Verlet(r0,rh):\n", " f=force(r0)\n", " x=2*r0[0]-rh[0]+h**2/m*f[0]\n", " y=2*r0[1]-rh[1]+h**2/m*f[1]\n", " return [x,y]\n", "\n", "h=0.04\n", "dx, dy=0.0, h\n", "m=0.2\n", "xx=[2.0, 2.0-dx]\n", "yy =[0,-dy]\n", "for i in range(1,90): \n", " x1, y1 = Verlet([xx[-1],yy[-1]],[xx[-2],yy[-2]])\n", " xx.append(x1)\n", " yy.append(y1)\n", "\n", "plt.plot(xx,yy,'o',color='r')\n", "plt.show\n", "\n" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "# RLC回路の応答\n", "電気回路の応答を考えましょう.R(resistor,抵抗) L(inductor,コイル) C(capacitor,コンデンサー)をそれぞれふたつずつ組み合わせてみていくのが常套手段なんですが,一個ずつだと面倒なので,まずは全部入れた方程式を立てます.そこからパラメータを変えて回路の挙動を観察します.こんなとこから進めていけるのが,数値計算の利点です.どんなんでも解けるから.\n", "\n", "コンデンサに蓄えられた電荷を$Q(t)$, 回路に流れる電流を$I(t)$とします.\n", "\n", "* 自己インダクタンス$L$のコイルにかかる電圧は$L \\frac{dI}{dt}$\n", "* 容量$C$のコンデンサにかかる電圧は$\\frac{Q}{C}$\n", "* 抵抗値$R$の抵抗に掛かる電圧は$RI$\n", "\n", "となります.コイルにかかる電圧,コンデンサにかかる電圧,抵抗にかかる電圧の和が,この回路にかけた電圧$V(t)$であることを使うと,\n", "\n", "$$\n", "L \\frac{dI}{dt} + \\frac{Q}{C} + RI = V(t)\n", "$$\n", "\n", "となります.ここで電流$I$とコンデンサの電荷$Q$の関係$I=\\frac{dQ}{dt}$を使うと,\n", "\n", "$$\n", "L \\frac{d^2Q}{dt^2} + \\frac{Q}{C} + R\\frac{dQ}{dt} = V{t}\n", "$$\n", "が得られます.\n", "\n", "先ほどの重力系の問題と比べると\n", "\n", "$$\n", "v \\rightarrow i \\\\\n", "x \\rightarrow q\n", "$$\n", "と置き換えれば良さそうです.\n", "\n", "そうするとアルゴリズムは,\n", "$$\n", "\\begin{aligned}\n", "i_{i+1} & = i_i + (V - RR \\, i_i -qc \\, q_i) \\, dt \\\\\n", "q_{i+1} & = q_i + i_i \\, dt;\n", "\\end{aligned}\n", "$$\n", "となりそうです.RRやqcには適当に規格化した値をいれます.\n", "\n", "![rlc_circuit](./figs/ode.005.jpeg)\n", "\n", "![image.png](attachment:image.png)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def euler_rlc(q0, i0):\n", " i1 = i0 + (v - r * i0 - qc * q0) * dt\n", " q1 = q0 + i0 * dt\n", " return [q1, i1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "コンデンサー($C$),コンダクター($L$)を1として,抵抗値を0.5として,入力電圧を1Vと設定してコンデンサーにたまる電荷と電流の変化を確かめたのが次の図です.\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dt, r, qc, v =0.01, 0.5, 0,1\n", "ii=[0.0]\n", "qq=[0.0]\n", "tt=[0.0]\n", "t = 0\n", "for i in range(0,2000):\n", " t += dt\n", " q, i2 = euler_rlc(qq[i],ii[i])\n", " tt.append(t)\n", " qq.append(q)\n", " ii.append(i2)\n", "\n", "my_plot(qq,ii,tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "入力電圧を0V,コンデンサーにあらかじめ1クーロン貯めたと設定して電荷と電流の時間変化を確かめたのが次の図です.\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dt, r, qc, v =0.01, 1.0, 1, 0\n", "ii=[0.0]\n", "qq=[1.0]\n", "tt=[0.0]\n", "t = 0\n", "for i in range(0,2000):\n", " t += dt\n", " q, i2 = euler_rlc(qq[i],ii[i])\n", " tt.append(t)\n", " qq.append(q)\n", " ii.append(i2)\n", "\n", "my_plot(qq,ii,tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 課題\n", "\n", "## 雨粒\n", "空気抵抗を受ける雨粒の速度の変化を自分の言葉で説明しなさい.\n", "\n", "## 大砲\n", "free fallの初期設定を変えて,x=0から鉛直方向にv=9.8で投げ上げたボールの時間変化を示しなさい.\n", "\n", "# 自由課題\n", "以下は 2021年度は不要です.\n", "\n", "## RLC回路\n", "抵抗が0の場合の電荷,電流の変化を確認しなさい.\n", "\n", "## RLC回路\n", "抵抗が0の場合にも,エネルギー保存が成り立つようにコードを改良しなさい.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Raw Cell Format", "kernelspec": { "display_name": "Python 3", "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": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "base_numbering": 1, "nav_menu": { "height": "192px", "width": "252px" }, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": "block", "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }