{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# 121 代数計算機による常微分方程式の解法\n", "## 読み込み" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "import sympy as sy\n", "sy.init_printing(use_latex=True)\n", "\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "import warnings\n", "warnings.filterwarnings(\"ignore\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 変数定義\n", "\\begin{align}\n", " m\\ddot{x}+c\\dot{x}+kx &= f(t) \\\\\n", " LC\\frac{d^2v_o}{dt^2}+RC\\frac{dv_o}{dt}+v_o(t) &= v_i(t)\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAATkAAAAvBAMAAABqN6DwAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nHKR8pj/5H+XjlcY89OzZAAAAAElFTkSuQmCC\n", "text/latex": [ "$$c \\frac{d}{d t} x{\\left (t \\right )} + k x{\\left (t \\right )} + m \\frac{d^{2}}{d t^{2}} x{\\left (t \\right )} = f{\\left (t \\right )}$$" ], "text/plain": [ " 2 \n", " d d \n", "c⋅──(x(t)) + k⋅x(t) + m⋅───(x(t)) = f(t)\n", " dt 2 \n", " dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAAvBAMAAAAcIdA+AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$C L \\frac{d^{2}}{d t^{2}} \\operatorname{v_{o}}{\\left (t \\right )} + C R \\frac{d}{d t} \\operatorname{v_{o}}{\\left (t \\right )} + \\operatorname{v_{o}}{\\left (t \\right )} = \\operatorname{v_{i}}{\\left (t \\right )}$$" ], "text/plain": [ " 2 \n", " d d \n", "C⋅L⋅───(vₒ(t)) + C⋅R⋅──(vₒ(t)) + vₒ(t) = vᵢ(t)\n", " 2 dt \n", " dt " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = sy.Symbol('t', real=True)\n", "\n", "# バネマスダンパ系\n", "x, f = sy.symbols('x, f', real=True)\n", "m, c, k = sy.symbols('m c k', real=True, positive=True)\n", "mech_eq = sy.Eq(m*x(t).diff(t,2)+c*x(t).diff(t,1)+k*x(t), f(t))\n", "\n", "#LRC直列回路\n", "v_o, v_i = sy.symbols('v_o v_i')\n", "L, R, C = sy.symbols('L R C', real=True, positive=True)\n", "LRC_eq = sy.Eq(L*C*v_o(t).diff(t,2)+R*C*v_o(t).diff(t,1)+v_o(t), v_i(t))\n", "\n", "display(mech_eq, LRC_eq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 一般解" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAcQAAAAcBAMAAAANa9LaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAGQ0lEQVRYCb1Yb4hUVRT/vdk3f3d297GKJLb5\nHCspW91UCqPihZSR1G4IEn3Il0QYtTiJIf1ZmEwj/JADabGgOQmVpMuOKRgVOPghKmidzLIwcylS\n8Is7rWZEsZ3z7rvv3Zl5M407qwfm3nN+59z7e+e+d++5u0BzoqcnNz5qXeG45VcY74ZfMY9Ho/e4\n6goPqlAWTtQVLKmIDzY9Hj0fHIBQXZqJscZ4AiaPmi64PcDJUNimJvn0IdYDZWYgWgl6PHGr0uXa\nq7j/4lnLNau6xniqhgFrTwowWgxwMtRqcIPHfHceobO+hYipGDVVyYOBWiEH2JEPZzx/K7DA9qwG\nefx4T4u5WszyoHJlD5txzOZMHUmUgC3SoF4bVYyaquTB5hohCZMdWY1md2XYQKxPGo3y+PGeJl//\ngx5SoeSFvdeDZ5SgPAfBOzxXHUXy6JnyoBZp0jtjSWScjhptnaEsLAEN8cjRSj8UFUa3gqlqNO1Y\nmr9V55SgfE3k7Vfja+mSJ1Qsj3AzAzYKfKYl/SH6cJTt0SCPHK30y24UxmEfW5PyddqFAAHTDIkl\n3yshUjzag4FXUsXU5wS/KF31esnTKpaMQyMpk3e5K3kH0G6XNr6mFPuTc4N4RIHb4IU2pmz1wmJ9\nI66u54BbQRtiRDsxQ/oj9JXGX3q0hBcu4zdjLsH+Nyxj6vSxnOfckhx1U3wICBFOQNd9tvTblOI7\n7882AnhWODEtlgz1e23+4jt127f9QgT87sGncL2rr6JdR4tLQGziL+nfQCl23A3onRlcwg8EH5Mu\nr+88uDj9gGdB5Wnvk3hbXiuIFMO062YBDGybyLj+qEUpjhcCeWjXaJuhZeVUfr8gjcQvad9WNUox\n8RnJAZz3NLyNNnoiAliEWzMpxZH5OaDFpLewlRxVKYbOAUP0CxJOcR8TGe05YOngu4ODJuI2vgcY\nYBHuTjprkr9+GsTDBS4xRhtIxCvtrFfJOGP5iFrQ+VmFXJQKsNpYRoYC0NSnT/+bnp8cLaC9EMrr\nYwV4Z4JTXihe+8SgV6KMUnn8D7XDolixF8MlvvwIgEGWodNnTobyI8lqHsQsmj8L3OAEqs1uYsYT\nCqIWdP+42YE2GRMvLiFVAdihl/BxMmOjl95jNG/7x41MMc6lLTxKjSsqj3/cxPtQlMfNLt5XApCD\ngF6j1fwyUs0DLnAx2xngR7PW9je333DjilrQ+yWIh+fNkXr4Ei2uCrDj5fHcdiwqYCXiln4HLRvv\nRxaZ4pkcGUl6fCkqT8TD9ePraXCrE7R6JXUCkIMQPXJX3Gq5rYync+79N5voBlYeOWjSwe4FC6U3\nw/10YcxInWBlLwY+HHj8OdLKKpCIoXa35am1lZ2uy01Rd04mTYzU1nSz4vOEM2QqIlKMX1SgWupO\naHZ0UywL/uKG6RfNcugzgyy7WF1nckvrS47wZvCJRwV9T7Y99wGp/H1Xy9FqqArRMy7kphj5Q9iR\nU9/Sylm6XcZTeYETKSZNd446nZ5BxIiUEpZzxv1Ekf5NyB22reAoye8ywCM57WeyqKC3FK7j0ww1\nr+HOoHpNxHS9boqxf4T9FJZCP4+uQhlP5TVcdwf/f0c8GuJ5CuQC9zr9kmMVoy4YDBhO7veun0cW\nF/QYhpDJkeMQeycj4vZJn8ubg4Nv0QTtzkVao9d1zGo5l3q+gqfVmgwJjXF4OkzSKEXtEvVVKW4j\nEImCk+I46+CCPg03YZFFxgpGJiPe2si36KztfvprpLevo4dnLOPR85MhoTEOz7ECaVTgwmP0ssS+\nXvsGy2s8q1MR28QX/CcD5dL8PzbcFEVFLNLsw0aHXU7C1vJqqBEkatGjGwsRMvi4iWTpZYnjRhnc\na5PxpEjxLF0KFdfUqG6KOq9fxKBmE9ptwCRtimR17givUD9VwJ5OauyKeROX6cpAzHwO3UL7sMLd\nvOmmiGG6J9JhymUrlEWX1fzMcoZpqc6TaafA6YepjxekQ/ZdB+/pI51TDB3fKNGp62WK2qnFfEY7\nZ2f3PHqUqRZZ4PiWEyic4lURmaI7edgOF64Kj1fg1tSaPjFay9MkPr18/Fcf7TPKkSmzxCEe9MeU\nQ6H/OG5OGVe9iS5MTNRzN+MTBW7SFbYZ6ms1dnL/2LhWT9cMz38TEMcGgeLJdAAAAABJRU5ErkJg\ngg==\n", "text/latex": [ "$$x{\\left (t \\right )} = C_{1} e^{\\frac{t}{2 m} \\left(- c - \\sqrt{c^{2} - 4 k m}\\right)} + C_{2} e^{\\frac{t}{2 m} \\left(- c + \\sqrt{c^{2} - 4 k m}\\right)}$$" ], "text/plain": [ " ⎛ ____________⎞ ⎛ ____________⎞\n", " ⎜ ╱ 2 ⎟ ⎜ ╱ 2 ⎟\n", " t⋅⎝-c - ╲╱ c - 4⋅k⋅m ⎠ t⋅⎝-c + ╲╱ c - 4⋅k⋅m ⎠\n", " ──────────────────────── ────────────────────────\n", " 2⋅m 2⋅m \n", "x(t) = C₁⋅ℯ + C₂⋅ℯ " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAh0AAAAhBAMAAACPaQQrAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nD0q5z8x0L+I/pBfLsMXQhuT/av8CZqJ2PO72I1AAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\operatorname{v_{o}}{\\left (t \\right )} = C_{1} e^{\\frac{t}{2 L} \\left(- R - \\frac{1}{\\sqrt{C}} \\sqrt{C R^{2} - 4 L}\\right)} + C_{2} e^{\\frac{t}{2 L} \\left(- R + \\frac{1}{\\sqrt{C}} \\sqrt{C R^{2} - 4 L}\\right)}$$" ], "text/plain": [ " ⎛ ____________⎞ ⎛ ____________⎞\n", " ⎜ ╱ 2 ⎟ ⎜ ╱ 2 ⎟\n", " ⎜ ╲╱ C⋅R - 4⋅L ⎟ ⎜ ╲╱ C⋅R - 4⋅L ⎟\n", " t⋅⎜-R - ───────────────⎟ t⋅⎜-R + ───────────────⎟\n", " ⎝ √C ⎠ ⎝ √C ⎠\n", " ──────────────────────── ────────────────────────\n", " 2⋅L 2⋅L \n", "vₒ(t) = C₁⋅ℯ + C₂⋅ℯ " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#理解を助けるため左辺のみ考え斉次とする\n", "mech_gen_ans = sy.dsolve(mech_eq.lhs)\n", "LRC_gen_ans = sy.dsolve(LRC_eq.lhs)\n", "\n", "display(mech_gen_ans, LRC_gen_ans)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 特殊解\n", "### 初期条件の設定" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHkAAAARBAMAAAALcx5NAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nQmCC\n", "text/latex": [ "$$C_{1} + C_{2} = x_{0}$$" ], "text/plain": [ "C₁ + C₂ = x₀" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfgAAAAqBAMAAACth1TcAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nPyc15PHL4uItEbJyeEvAEpEJ61r+BxoIiHJcc9z9AAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\frac{C_{1}}{2 m} \\left(- c - \\sqrt{c^{2} - 4 k m}\\right) + \\frac{C_{2}}{2 m} \\left(- c + \\sqrt{c^{2} - 4 k m}\\right) = \\dot{x}_0$$" ], "text/plain": [ " ⎛ ____________⎞ ⎛ ____________⎞ \n", " ⎜ ╱ 2 ⎟ ⎜ ╱ 2 ⎟ \n", "C₁⋅⎝-c - ╲╱ c - 4⋅k⋅m ⎠ C₂⋅⎝-c + ╲╱ c - 4⋅k⋅m ⎠ \n", "───────────────────────── + ───────────────────────── = \\dot{x}₀\n", " 2⋅m 2⋅m " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH8AAAARBAMAAAAGbW4KAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nZgtQS5f4BwEHbg0ylVfuAAAAAElFTkSuQmCC\n", "text/latex": [ "$$C_{1} + C_{2} = v_{o0}$$" ], "text/plain": [ "C₁ + C₂ = vₒ₀" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmwAAAAyBAMAAAAToJq4AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nPP3OKwAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\frac{C_{1}}{2 L} \\left(- R - \\frac{1}{\\sqrt{C}} \\sqrt{C R^{2} - 4 L}\\right) + \\frac{C_{2}}{2 L} \\left(- R + \\frac{1}{\\sqrt{C}} \\sqrt{C R^{2} - 4 L}\\right) = \\dot{v}_{o0}$$" ], "text/plain": [ " ⎛ ____________⎞ ⎛ ____________⎞ \n", " ⎜ ╱ 2 ⎟ ⎜ ╱ 2 ⎟ \n", " ⎜ ╲╱ C⋅R - 4⋅L ⎟ ⎜ ╲╱ C⋅R - 4⋅L ⎟ \n", "C₁⋅⎜-R - ───────────────⎟ C₂⋅⎜-R + ───────────────⎟ \n", " ⎝ √C ⎠ ⎝ √C ⎠ \n", "───────────────────────── + ───────────────────────── = \\dot{v}_{o0}\n", " 2⋅L 2⋅L " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_0, d_x_0 = sy.symbols('x_0 \\dot{x}_0', real=True)\n", "mech_init_condition = sy.Eq(mech_gen_ans.rhs.subs(t, 0), x_0) #x(0) = x_0\n", "mech_init_condition_dot = sy.Eq(mech_gen_ans.rhs.diff(t).subs(t, 0), d_x_0) #\\dot{x}(0) = d_x_0\n", "\n", "v_o0, d_v_o0 = sy.symbols('v_o0 \\dot{v}_{o0}', real=True)\n", "LRC_init_condition = sy.Eq(LRC_gen_ans.rhs.subs(t, 0), v_o0) #v_o(0) = v_o0\n", "LRC_init_condition_dot = sy.Eq(LRC_gen_ans.rhs.diff(t).subs(t, 0), d_v_o0) #\\dot{v}_o(0) = d_v_0\n", "\n", "display(mech_init_condition, mech_init_condition_dot, LRC_init_condition, LRC_init_condition_dot)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 積分定数について解く" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA60AAAAyBAMAAABFUyDnAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nTgFAFrdNAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left \\{ C_{1} : \\frac{1}{\\sqrt{c^{2} - 4 k m}} \\left(- \\dot{x}_0 m - \\frac{c x_{0}}{2} + \\frac{x_{0}}{2} \\sqrt{c^{2} - 4 k m}\\right), \\quad C_{2} : \\frac{1}{\\sqrt{c^{2} - 4 k m}} \\left(\\dot{x}_0 m + \\frac{x_{0}}{2} \\left(c + \\sqrt{c^{2} - 4 k m}\\right)\\right)\\right \\}$$" ], "text/plain": [ "⎧ ____________ ⎛ ____\n", "⎪ ╱ 2 ⎜ ╱ 2 \n", "⎪ c⋅x₀ x₀⋅╲╱ c - 4⋅k⋅m x₀⋅⎝c + ╲╱ c \n", "⎪ -\\dot{x}₀⋅m - ──── + ────────────────── \\dot{x}₀⋅m + ───────────────\n", "⎨ 2 2 2 \n", "⎪C₁: ───────────────────────────────────────, C₂: ────────────────────────────\n", "⎪ ____________ ____________ \n", "⎪ ╱ 2 ╱ 2 \n", "⎩ ╲╱ c - 4⋅k⋅m ╲╱ c - 4⋅k⋅m \n", "\n", "________⎞⎫\n", " ⎟⎪\n", "- 4⋅k⋅m ⎠⎪\n", "─────────⎪\n", " ⎬\n", "─────────⎪\n", " ⎪\n", " ⎪\n", " ⎭" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABH4AAAAyBAMAAADYTgEuAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left \\{ C_{1} : \\frac{1}{\\sqrt{C R^{2} - 4 L}} \\left(- \\sqrt{C} L \\dot{v}_{o0} - \\frac{R v_{o0}}{2} \\sqrt{C} + \\frac{v_{o0}}{2} \\sqrt{C R^{2} - 4 L}\\right), \\quad C_{2} : \\frac{1}{\\sqrt{C R^{2} - 4 L}} \\left(\\sqrt{C} L \\dot{v}_{o0} + \\frac{v_{o0}}{2} \\left(\\sqrt{C} R + \\sqrt{C R^{2} - 4 L}\\right)\\right)\\right \\}$$" ], "text/plain": [ "⎧ ____________ \n", "⎪ ╱ 2 \n", "⎪ √C⋅R⋅vₒ₀ vₒ₀⋅╲╱ C⋅R - 4⋅L \n", "⎪ -√C⋅L⋅\\dot{v}_{o0} - ──────── + ─────────────────── √C⋅L⋅\\dot{v}_{o0\n", "⎨ 2 2 \n", "⎪C₁: ───────────────────────────────────────────────────, C₂: ────────────────\n", "⎪ ____________ \n", "⎪ ╱ 2 \n", "⎩ ╲╱ C⋅R - 4⋅L \n", "\n", " ⎛ ____________⎞⎫\n", " ⎜ ╱ 2 ⎟⎪\n", " vₒ₀⋅⎝√C⋅R + ╲╱ C⋅R - 4⋅L ⎠⎪\n", "} + ────────────────────────────⎪\n", " 2 ⎬\n", "────────────────────────────────⎪\n", " ____________ ⎪\n", " ╱ 2 ⎪\n", "╲╱ C⋅R - 4⋅L ⎭" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "C1, C2 = sy.symbols('C1, C2')\n", "mech_C1C2_solution = sy.solve([mech_init_condition, mech_init_condition_dot], [C1, C2])\n", "LRC_C1C2_solution = sy.solve([LRC_init_condition, LRC_init_condition_dot], [C1, C2])\n", "\n", "display(mech_C1C2_solution, LRC_C1C2_solution)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 積分定数を戻す" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABFoAAAA1BAMAAACD/ZI8AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$x{\\left (t \\right )} = \\frac{e^{- \\frac{c t}{m}}}{2 \\sqrt{c^{2} - 4 k m}} \\left(\\left(2 \\dot{x}_0 m + x_{0} \\left(c + \\sqrt{c^{2} - 4 k m}\\right)\\right) e^{\\frac{t}{2 m} \\left(c + \\sqrt{c^{2} - 4 k m}\\right)} + \\left(- 2 \\dot{x}_0 m - c x_{0} + x_{0} \\sqrt{c^{2} - 4 k m}\\right) e^{\\frac{t}{2 m} \\left(c - \\sqrt{c^{2} - 4 k m}\\right)}\\right)$$" ], "text/plain": [ " ⎛ ⎛ ____________⎞ \n", " ⎜ ⎜ ╱ 2 ⎟ \n", " ⎜ t⋅⎝c + ╲╱ c - 4⋅k⋅m ⎠ \n", " ⎜⎛ ⎛ ____________⎞⎞ ─────────────────────── ⎛\n", " ⎜⎜ ⎜ ╱ 2 ⎟⎟ 2⋅m ⎜\n", " ⎝⎝2⋅\\dot{x}₀⋅m + x₀⋅⎝c + ╲╱ c - 4⋅k⋅m ⎠⎠⋅ℯ + ⎝\n", "x(t) = ───────────────────────────────────────────────────────────────────────\n", " __\n", " ╱ \n", " 2⋅╲╱ c\n", "\n", " ⎛ ____________⎞⎞ \n", " ⎜ ╱ 2 ⎟⎟ \n", " t⋅⎝c - ╲╱ c - 4⋅k⋅m ⎠⎟ -c⋅t \n", " ____________⎞ ───────────────────────⎟ ─────\n", " ╱ 2 ⎟ 2⋅m ⎟ m \n", "-2⋅\\dot{x}₀⋅m - c⋅x₀ + x₀⋅╲╱ c - 4⋅k⋅m ⎠⋅ℯ ⎠⋅ℯ \n", "───────────────────────────────────────────────────────────────────────────\n", "__________ \n", "2 \n", " - 4⋅k⋅m " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABZsAAAA2BAMAAABTmlrNAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nejFEIDYC7f/WENvUUGGIQNII/D8E55Fb3s9mWAAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\operatorname{v_{o}}{\\left (t \\right )} = \\frac{e^{- \\frac{R t}{L}}}{2 \\sqrt{C R^{2} - 4 L}} \\left(\\left(2 \\sqrt{C} L \\dot{v}_{o0} + v_{o0} \\left(\\sqrt{C} R + \\sqrt{C R^{2} - 4 L}\\right)\\right) e^{\\frac{t}{2 \\sqrt{C} L} \\left(\\sqrt{C} R + \\sqrt{C R^{2} - 4 L}\\right)} + \\left(- 2 \\sqrt{C} L \\dot{v}_{o0} - \\sqrt{C} R v_{o0} + v_{o0} \\sqrt{C R^{2} - 4 L}\\right) e^{\\frac{t}{2 \\sqrt{C} L} \\left(\\sqrt{C} R - \\sqrt{C R^{2} - 4 L}\\right)}\\right)$$" ], "text/plain": [ " ⎛ ⎛ __\n", " ⎜ ⎜ ╱ \n", " ⎜ t⋅⎝√C⋅R + ╲╱ C\n", " ⎜⎛ ⎛ ____________⎞⎞ ───────────────\n", " ⎜⎜ ⎜ ╱ 2 ⎟⎟ 2⋅√C⋅\n", " ⎝⎝2⋅√C⋅L⋅\\dot{v}_{o0} + vₒ₀⋅⎝√C⋅R + ╲╱ C⋅R - 4⋅L ⎠⎠⋅ℯ \n", "vₒ(t) = ──────────────────────────────────────────────────────────────────────\n", " \n", " \n", " \n", "\n", "__________⎞ ⎛ \n", " 2 ⎟ ⎜ \n", "⋅R - 4⋅L ⎠ t⋅⎝√C⋅R\n", "─────────── ⎛ ____________⎞ ───────\n", "L ⎜ ╱ 2 ⎟ \n", " + ⎝-2⋅√C⋅L⋅\\dot{v}_{o0} - √C⋅R⋅vₒ₀ + vₒ₀⋅╲╱ C⋅R - 4⋅L ⎠⋅ℯ \n", "──────────────────────────────────────────────────────────────────────────────\n", " ____________ \n", " ╱ 2 \n", " 2⋅╲╱ C⋅R - 4⋅L \n", "\n", " ____________⎞⎞ \n", " ╱ 2 ⎟⎟ \n", " - ╲╱ C⋅R - 4⋅L ⎠⎟ -R⋅t \n", "───────────────────⎟ ─────\n", " 2⋅√C⋅L ⎟ L \n", " ⎠⋅ℯ \n", "───────────────────────────\n", " \n", " \n", " " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mech_special_ans = mech_gen_ans.subs(mech_C1C2_solution)\n", "LRC_special_ans = LRC_gen_ans.subs(LRC_C1C2_solution)\n", "\n", "display(mech_special_ans.simplify(), LRC_special_ans.simplify())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### パラメータ代入" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAATkAAAAZBAMAAAC4FERAAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nTkSuQmCC\n", "text/latex": [ "$$x{\\left (t \\right )} = - 0.15 e^{- 6.193 t} + 1.15 e^{- 0.807 t}$$" ], "text/plain": [ " -6.193⋅t -0.807⋅t\n", "x(t) = - 0.15⋅ℯ + 1.15⋅ℯ " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVkAAAAZBAMAAABp80AwAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nsdWz3S9/Sm8WHsD/T/wLRh9fakBTED0AAAAASUVORK5CYII=\n", "text/latex": [ "$$\\operatorname{v_{o}}{\\left (t \\right )} = - 0.017 e^{- 6.884 t} + 1.017 e^{- 0.116 t}$$" ], "text/plain": [ " -6.884⋅t -0.116⋅t\n", "vₒ(t) = - 0.017⋅ℯ + 1.017⋅ℯ " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def round_sympyeq(eq, digit):\n", " eq_rounded = eq\n", " for value in sy.preorder_traversal(eq):\n", " if value.is_number:\n", " eq_rounded = eq_rounded.subs(value, round(value, digit))\n", " return eq_rounded\n", "\n", "mech_params = [(m, 0.5), (c, 3.5), (k, 2.5), (x_0, 1), (d_x_0, 0)]\n", "#mech_param_dict = {m:0.5, c:3.5, k:2.5, x_0:0, d_x_0:0} # for evalf(subs=args)\n", "mech_special_ans_specified = mech_gen_ans.subs(mech_params)\\\n", " .subs(sy.solve([mech_init_condition.subs(mech_params), \n", " mech_init_condition_dot.subs(mech_params)], \n", " [C1, C2]))\n", "mech_ans_rounded = round_sympyeq(mech_special_ans_specified, 3)\n", " \n", "LRC_params = [(L, 0.5),(R, 3.5), (C, 2.5), (v_o0, 1), (d_v_o0, 0)]\n", "LRC_special_ans_specified = LRC_gen_ans.subs(LRC_params)\\\n", " .subs(sy.solve([LRC_init_condition.subs(LRC_params), \n", " LRC_init_condition_dot.subs(LRC_params)], \n", " [C1, C2]))\n", "LRC_ans_rounded = round_sympyeq(LRC_special_ans_specified, 3) \n", " \n", "display(mech_ans_rounded)\n", "display(LRC_ans_rounded)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## グラフ化" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEECAYAAAA/L9PCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sy.plot(mech_ans_rounded.rhs, LRC_ans_rounded.rhs, (t, 0, 50), xlabel='Time',legend=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python [conda env:py3.6]", "language": "python", "name": "conda-env-py3.6-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.4" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }