{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "
\n", " 数値計算による微分方程式解法(python版)\n", "
\n", "
\n", " cc by Shigeto R. Nishitani\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", "

1  Euler法による落下運動
1.1  重力場中の運動
1.2  Euler法
1.3  重力場中の運動をEuler法で解いたら
1.4  空気抵抗がある水滴の落下
2  高精度計算
2.1  バネの運動
2.2  2次のRunge-Kuttaの導出
2.3  Runge-Kutta2次公式
2.4  Runge-Kutta4次公式
2.5  連立方程式にRunge-Kutta4次公式を
3  RLC回路の応答
4  課題
4.1  雨粒
4.2  大砲
5  自由課題
5.1  RLC回路
5.2  RLC回路
" ] }, { "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", "![simple_gravitation_fall](./figs/ode.002.jpeg)\n", "\n" ] }, { "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": "code", "execution_count": 12, "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": 3, "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": 8, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": "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\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(0,22): #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." ] }, { "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", "![gravitation_fall_with_air_resistance](./figs/ode.003.jpeg)\n", "\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": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Eq(v(t), (-g*m + exp(cc*(C1 - t/m)))/cc)" ] }, "execution_count": 14, "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": 15, "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": 16, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "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." ] }, { "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", "![free_oscillation_mass_spring_system](./figs/ode.004.jpeg)\n", "\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": [ "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": 13, "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": 18, "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." ] }, { "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" ] }, { "cell_type": "code", "execution_count": 19, "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": 22, "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": 23, "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, 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 2019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": "3.6.1" }, "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": { "colors": { "hover_highlight": "#DAA520", "navigate_num": "#000000", "navigate_text": "#333333", "running_highlight": "#FF0000", "selected_highlight": "#FFD700", "sidebar_border": "#EEEEEE", "wrapper_background": "#FFFFFF" }, "moveMenuLeft": true, "nav_menu": { "height": "192px", "width": "252px" }, "navigate_menu": true, "number_sections": true, "sideBar": true, "threshold": 4, "toc_cell": true, "toc_section_display": "block", "toc_window_display": false, "widenNotebook": false } }, "nbformat": 4, "nbformat_minor": 2 }