{"id":9988,"date":"2025-01-22T12:00:54","date_gmt":"2025-01-22T03:00:54","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=9988"},"modified":"2025-01-22T12:18:59","modified_gmt":"2025-01-22T03:18:59","slug":"scipy-%e3%81%a7%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e9%81%8b%e5%8b%95%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e6%95%b0%e5%80%a4%e7%9a%84%e3%81%ab%e8%a7%a3%e3%81%8f","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e9%81%8b%e5%8b%95%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e6%95%b0%e5%80%a4%e7%9a%84%e3%81%ab%e8%a7%a3%e3%81%8f%e6%ba%96%e5%82%99\/scipy-%e3%81%a7%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e9%81%8b%e5%8b%95%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e6%95%b0%e5%80%a4%e7%9a%84%e3%81%ab%e8%a7%a3%e3%81%8f\/","title":{"rendered":"SciPy \u3067\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f"},"content":{"rendered":"<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Python \u306e SciPy \u3092\u4f7f\u3063\u3066\uff0c\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u3002\u904b\u52d5\u65b9\u7a0b\u5f0f\u306e\u5c0e\u51fa\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u306b\u307e\u3068\u3081\u3066\u3044\u308b\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e9%81%8b%e5%8b%95%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e6%95%b0%e5%80%a4%e7%9a%84%e3%81%ab%e8%a7%a3%e3%81%8f%e6%ba%96%e5%82%99\/\">\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u6e96\u5099<\/a><\/li>\n<\/ul>\n<p>\u306a\u304a\uff0c\u307b\u307c\u540c\u3058\u5185\u5bb9\u3067\u30b0\u30e9\u30d5\u306e\u307f <code>plt.***<\/code> \u306e\u307f\u3067\u63cf\u3044\u305f\u65e7\u7248\u306e\u30da\u30fc\u30b8\u306f\u4ee5\u4e0b\uff1a<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e9%81%8b%e5%8b%95%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e6%95%b0%e5%80%a4%e7%9a%84%e3%81%ab%e8%a7%a3%e3%81%8f%e6%ba%96%e5%82%99\/python-%e3%81%a7%e9%81%8b%e5%8b%95%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e8%a7%a3%e3%81%84%e3%81%a6%e6%8c%af%e5%b9%85%e3%81%a8%e5%91%a8%e6%9c%9f%e3%81%ae%e9%96%a2%e4%bf%82%e3%82%92%e8%aa%bf%e3%81%b9\/\">Python \u3067\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u632f\u5e45\u3068\u5468\u671f\u306e\u95a2\u4fc2\u3092\u8abf\u3079\u308b\uff08\u65e7\u7248\uff09<\/a><\/li>\n<\/ul>\n<p>\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\uff0c\uff08\u3061\u3087\u3063\u3068\u3060\u3051\u9762\u5012\u3060\u3051\u3069\uff09\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u306b\u5f93\u3044\uff0c<code>ax.***<\/code> \u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u3092\u4f5c\u6210\u3059\u308b\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/python-%e3%81%a7%e3%82%b0%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90\/matplotlib-%e3%81%a7%e3%82%b0%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90%ef%bc%9aax-%e7%b7%a8\/\">Matplotlib \u3067\u30b0\u30e9\u30d5\u4f5c\u6210\uff1aax \u7de8<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<p><!--more--><\/p>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u4e00\u69d8\u91cd\u529b\u5834\u4e2d\u306e\u5358\u632f\u308a\u5b50\">\u4e00\u69d8\u91cd\u529b\u5834\u4e2d\u306e\u5358\u632f\u308a\u5b50<\/h3>\n<p>\u5358\u632f\u308a\u5b50\u306e\u3072\u3082\u306e\u9577\u3055\u3092 $\\ell$\uff0c\u91cd\u529b\u52a0\u901f\u5ea6\u306e\u5927\u304d\u3055\u3092 $g$\uff0c\u925b\u76f4\u4e0b\u5411\u304d\u304b\u3089\u306e\u632f\u308c\u89d2\u3092 $\\theta$ \u3068\u3059\u308b\u3068\uff0c\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f<\/p>\n<p>$$\\frac{d^2\\theta}{dt^2} = &#8211; \\frac{g}{\\ell} \\sin\\theta$$<\/p>\n<p>\u3068\u306a\u308b\u3002\u5c0e\u51fa\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u3092\u53c2\u7167\u3002<\/p>\n<h4 id=\"\u632f\u308c\u89d2\u304c\u5c0f\u3055\u3044\u5834\u5408\u306b\u306f\u5358\u632f\u52d5\u3068\u306a\u308b\u3053\u3068\">\u632f\u308c\u89d2\u304c\u5c0f\u3055\u3044\u5834\u5408\u306b\u306f\u5358\u632f\u52d5\u3068\u306a\u308b\u3053\u3068<\/h4>\n<p>$|\\theta| \\ll 1$ \u306e\u5834\u5408\u306b\u306f\uff0c$\\sin\\theta \\simeq \\theta$ \u3068\u8fd1\u4f3c\u3059\u308b\u3053\u3068\u3067\uff0c\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f<\/p>\n<p>$$\\frac{d^2\\theta}{dt^2} = &#8211; \\frac{g}{\\ell} \\theta$$<\/p>\n<p>\u3068\u306a\u308a\uff0c\u3053\u308c\u306f\u5358\u632f\u52d5\u3068\u306a\u308b\u3002\u5358\u632f\u52d5\u306e\u5468\u671f $\\tau_0$ \u306f<\/p>\n<p>$$\\tau_0 = 2 \\pi \\sqrt{\\frac{\\ell}{g}}$$<\/p>\n<p>\u3068\u306a\u308a\uff0c\u5358\u632f\u308a\u5b50\u306e\u3072\u3082\u306e\u9577\u3055\u3068\u91cd\u529b\u52a0\u901f\u5ea6\u3060\u3051\u3067\u6c7a\u307e\u308a\uff0c\u521d\u671f\u6761\u4ef6\u3067\u4e0e\u3048\u3089\u308c\u308b\u632f\u308c\u89d2 $\\theta_0$ \u306b\u4f9d\u5b58\u3057\u306a\u3044\u3002\u3053\u308c\u3092\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u632f\u308a\u5b50\u306e\u7b49\u6642\u6027<\/strong><\/span>\u300d\u3068\u8a00\u3063\u305f\u308a\u3059\u308b\u3002<\/p>\n<h4 id=\"\u7121\u6b21\u5143\u5316\">\u7121\u6b21\u5143\u5316<\/h4>\n<p>\u5358\u632f\u52d5\u306e\u5468\u671f $\\tau_0$ \u3067\u7121\u6b21\u5143\u5316\u3057\u305f\u6642\u9593 $T$ \u3092<\/p>\n<p>$$T \\equiv \\frac{t}{\\tau_0}$$<\/p>\n<p>\u3068\u5b9a\u7fa9\u3059\u308b\u3002\u3053\u306e\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u6642\u9593\u5ea7\u6a19\u3067\u66f8\u3044\u305f\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f<\/p>\n<p>$$\\frac{d^2 \\theta}{dT^2} = &#8211; 4 \\pi^2 \\sin\\theta$$<\/p>\n<p>\u3068\u306a\u308b\u3002<\/p>\n<h4 id=\"\u632f\u308c\u89d2\u304c\u5927\u304d\u3044\u5834\u5408\u306e\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\">\u632f\u308c\u89d2\u304c\u5927\u304d\u3044\u5834\u5408\u306e\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5<\/h4>\n<p>\u632f\u308c\u89d2\u304c\u5927\u304d\u3044\uff0c\u3064\u307e\u308a $\\sin\\theta \\simeq \\theta$<br \/>\n\u3068\u8fd1\u4f3c\u3067\u304d\u306a\u3044\u5834\u5408\u306f\uff0c\u632f\u308a\u5b50\u306e\u5468\u671f\u306f\u4e00\u822c\u306b\u632f\u308c\u89d2\u306b\u4f9d\u5b58\u3059\u308b\u306e\u3067\u306f\u306a\u3044\u304b\u3068\u8003\u3048\u3089\u308c\u308b\u3002<\/p>\n<p>\u305d\u3053\u3067\uff0c$T = 0$ \u3067\u306e\u632f\u308c\u89d2 $\\theta_0$<br \/>\n\u3092\u305f\u3068\u3048\u3070 10\u00b0 \u304b\u3089 90\u00b0 \u307e\u3067 10\u00b0 \u304d\u3056\u307f\u3067\u5927\u304d\u304f\u3057\u3066\u3044\u3063\u305f\u5834\u5408\uff0c\u3075\u308a\u3053\u306e\u5468\u671f\u306f\u3069\u3046\u306a\u308b\u304b\uff1f\u3000\u3068\u3044\u3046\u306e\u304c\u554f\u984c\u3002<\/p>\n<p>\u904b\u52d5\u65b9\u7a0b\u5f0f\u306e\u53f3\u8fba\u304c $\\sin\\theta$ \u306e\u307e\u307e\u3067\u306f\u89e3\u6790\u7684\u306b\u89e3\u3051\u306a\u3044\u306e\u3067\uff0c\u4ee5\u4e0b\u3067\u306f\u6570\u5024\u7684\u306b\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u5358\u632f\u308a\u5b50\u306e\u632f\u5e45\uff08\u632f\u308c\u89d2\uff09\u3068\u5468\u671f\u306e\u95a2\u4fc2\u3092\u8abf\u3079\u308b\u3002<\/p>\n<h3 id=\"\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u6cd5\uff1asolve_ivp\">\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u6cd5\uff1a<code>solve_ivp<\/code><\/h3>\n<p><code>scipy.integrate.solve_ivp()<\/code> \u3092\u4f7f\u3063\u3066<br \/>\n2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u305f\u3081\u306b\u306f\uff0c\u9023\u7acb1\u968e\u5fae\u5206\u65b9\u7a0b\u5f0f\u7cfb\u306b\u306a\u304a\u3059\u3002<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\frac{d\\theta}{dT} &amp;=&amp; F_1(V) = \\dot{\\theta} \\\\<br \/>\n\\frac{dV}{dT} &amp;=&amp; F_2(\\theta) = &#8211; 4 \\pi^2 \\sin\\theta<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3053\u308c\u3092\u521d\u671f\u6761\u4ef6 $T = 0$ \u3067<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\theta(0) &amp;=&amp; \\theta_0 \\\\<br \/>\n\\dot{\\theta}(0) &amp;=&amp; 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3068\u3057\uff0c$T_0 = 0$ \u304b\u3089 $ T_1 = 2$ \u307e\u3067\u89e3\u304f\u3002<\/p>\n<p>\uff08\u304f\u3069\u3044\u3088\u3046\u3067\u3059\u304c\uff0c\u898f\u683c\u5316\u3055\u308c\u305f\u6642\u9593\u3067 $T_1 = 2$ \u3068\u3044\u3046\u306e\u306f\uff0c\u5358\u632f\u52d5\u306e\u5834\u5408\u306e\u5468\u671f $\\tau_0$ \u306e 2 \u500d\u306e\u6642\u9593\u307e\u3067\uff0c\u3068\u3044\u3046\u610f\u5473\u3067\u3059\u3088\u3002\uff09<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u30e9\u30a4\u30d6\u30e9\u30ea\u306e-import-\u3068\u8a2d\u5b9a\">\u30e9\u30a4\u30d6\u30e9\u30ea\u306e import \u3068\u8a2d\u5b9a<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># NumPy \u3082\u4f7f\u3044\u307e\u3059<\/span>\r\n<span class=\"kn\">import<\/span> <span class=\"nn\">numpy<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">np<\/span>\r\n\r\n<span class=\"c1\"># Matplotlib \u3067\u30b0\u30e9\u30d5\u3092\u63cf\u304d\u307e\u3059<\/span>\r\n<span class=\"kn\">import<\/span> <span class=\"nn\">matplotlib.pyplot<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">plt<\/span>\r\n<span class=\"c1\"># mathtext font \u306e\u8a2d\u5b9a<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">rcParams<\/span><span class=\"p\">[<\/span><span class=\"s1\">'mathtext.fontset'<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'cm'<\/span>\r\n\r\n<span class=\"c1\"># SciPy \u306b\u3088\u308b2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u6cd5<\/span>\r\n<span class=\"c1\"># solve_ivp<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">scipy.integrate<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">solve_ivp<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30e9\u30d5\u3092 SVG \u3067 Notebook \u306b\u30a4\u30f3\u30e9\u30a4\u30f3\u8868\u793a\u3055\u305b\u308b\u8a2d\u5b9a<\/span>\r\n<span class=\"o\">%<\/span><span class=\"k\">config<\/span> InlineBackend.figure_formats = ['svg']\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u904b\u52d5\u65b9\u7a0b\u5f0f\u306b\u51fa\u3066\u304f\u308b\u5186\u5468\u7387 $\\pi$ \u3084\u4e09\u89d2\u95a2\u6570 $\\sin\\theta$ \u306f NumPy \u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u3082\u306e\u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<div class=\"highlight\">\n<pre><span class=\"kn\">import<\/span> <span class=\"nn\">numpy<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">np<\/span>\r\n<\/pre>\n<\/div>\n<p>\u3068\u3057\u3066 import \u3057\u3066\u3044\u308b\u306e\u3067\uff0cNumPy \u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u3082\u306e\u3092\u4f7f\u3046\u5834\u5408\u306b\u306f <code>np.<\/code> \u3092\u3064\u3051\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\uff0c\u5186\u5468\u7387 $\\pi = $ <code>np.pi<\/code>\uff0c\u4e09\u89d2\u95a2\u6570 $\\sin\\theta = $ <code>np.sin(theta)<\/code> \u306a\u3069\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u9023\u7acb\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u53f3\u8fba\u3092\u5b9a\u7fa9\">\u9023\u7acb\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u53f3\u8fba\u3092\u5b9a\u7fa9<\/h4>\n<p><code>scipy.integrate.solve_ivp()<\/code> \u3092\u4f7f\u3063\u30662\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u305f\u3081\u306b\u306f\uff0c1\u968e\u9023\u7acb\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u66f8\u304d\u76f4\u3057\u307e\u3059\u3002<br \/>\n$T = $ <code>t<\/code>\uff0c$\\theta = $ <code>y[0]<\/code>\uff0c$\\dot{\\theta} = $ <code>y[1]<\/code> \u3068\u3057\u3066\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\frac{d\\theta}{dT} = \\frac{d}{dt} {\\tt y[0]} &amp;=&amp; F_1(t, y) = {\\tt y[1]} \\\\<br \/>\n\\frac{d^2\\theta}{dT^2} = \\frac{d}{dt} {\\tt y[1]} &amp;=&amp; F_2(t, y) = &#8211; 4 \\pi^2 \\sin({\\tt y[0]})<br \/>\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u9023\u7acb\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u53f3\u8fba<\/span>\r\n<span class=\"c1\"># scipy.integrate.solve_ivp() \u306f<\/span>\r\n<span class=\"c1\"># dy\/dt = F(t, y) \u306e\u5f62\u3092\u89e3\u304f<\/span>\r\n\r\n<span class=\"k\">def<\/span> <span class=\"nf\">F<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"c1\"># solve.ivp() \u306b\u6e21\u3059\u95a2\u6570\u306e\u5f15\u6570\u306e\u9806\u756a\u306b\u6ce8\u610f\u3002t \u304c\u5148<\/span>\r\n    <span class=\"c1\"># \u305f\u3068\u3048 t \u306b\u4f9d\u5b58\u3057\u306a\u304f\u3066\u3082\uff0c\u5fc5\u305a\u3053\u3046\u66f8\u304f\u3002<\/span>\r\n    <span class=\"c1\"># \u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30a4\u30f3\u30c7\u30f3\u30c8\uff08\u884c\u982d\u306e\u5b57\u4e0b\u3052\uff09\u90e8\u5206\u304c\u5b9a\u7fa9<\/span>\r\n    <span class=\"c1\"># Python \u3067\u306f\u30a4\u30f3\u30c7\u30f3\u30c8\u306b\u306f\u610f\u5473\u304c\u3042\u308b\u306e\u3067\u3057\u305f\u306d\u3002<\/span>\r\n    <span class=\"n\">theta<\/span> <span class=\"o\">=<\/span> <span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span>\r\n    <span class=\"n\">dottheta<\/span> <span class=\"o\">=<\/span> <span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span>\r\n    <span class=\"n\">F1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">dottheta<\/span>\r\n    <span class=\"n\">F2<\/span> <span class=\"o\">=<\/span> <span class=\"o\">-<\/span><span class=\"mi\">4<\/span> <span class=\"o\">*<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">pi<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">*<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"p\">[<\/span><span class=\"n\">F1<\/span><span class=\"p\">,<\/span> <span class=\"n\">F2<\/span><span class=\"p\">]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u6570\u5024\u89e3\u306e\u7cbe\u5ea6\u3092\u78ba\u8a8d\">\u6570\u5024\u89e3\u306e\u7cbe\u5ea6\u3092\u78ba\u8a8d<\/h4>\n<p>\u521d\u671f\u6761\u4ef6 $T = 0$ \u3067<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\theta(0) &amp;=&amp; \\theta_0 \\\\<br \/>\n\\dot{\\theta}(0) &amp;=&amp; 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u307e\u305a\uff0c$\\theta_0 = 80^{\\circ}$ \u306e\u5834\u5408\u306b\uff0c\u6570\u5024\u8a08\u7b97\u306e\u7cbe\u5ea6\u306b\u3064\u3044\u3066\u78ba\u8a8d\u3057\u3066\u304a\u304f\u3002<\/p>\n<p>SciPy \u306e <code>scipy.integrate.solve_ivp()<\/code> \u3067\u306f\uff0c\u6570\u5024\u8a08\u7b97\u306e\u7cbe\u5ea6\u306b\u95a2\u4fc2\u3059\u308b\u306e\u306f <code>rtol<\/code> \u3068 <code>atol<\/code> \u3067\u3042\u308b\u3002<\/p>\n<p>\u30de\u30cb\u30e5\u30a2\u30eb\u306b\u3088\u308b\u3068\uff0c\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u306f\uff08<code>rtol<\/code> <code>atol<\/code> \u3092\u6307\u5b9a\u3057\u306a\u3044\u3068\uff09 <code>rtol = 1e-3<\/code>, <code>atol = 1.e-6<\/code>\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u8a08\u7b97\u7bc4\u56f2<\/span>\r\n<span class=\"n\">T0<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"n\">T1<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>\r\n\r\n<span class=\"c1\"># \u521d\u671f\u6761\u4ef6<\/span>\r\n<span class=\"c1\">## \u632f\u5e45\uff08\u632f\u308c\u89d2\uff09\u306e\u521d\u671f\u5024<\/span>\r\n<span class=\"n\">th0<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">80<\/span>\r\n<span class=\"c1\">## \u632f\u308c\u89d2\u3092\u30e9\u30b8\u30a2\u30f3\u306b<\/span>\r\n<span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">radians<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\">## \u300c\u521d\u901f\u5ea6\u300d <\/span>\r\n<span class=\"n\">dottheta0<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n\r\n<span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>\r\n\r\n<span class=\"c1\"># \u8a08\u7b97\u7bc4\u56f2\uff1aT0 \u304b\u3089 T1 \u307e\u3067\u3092 N \u7b49\u5206\u3057\u305f\u30ea\u30b9\u30c8\u3092\u4f5c\u6210<\/span>\r\n<span class=\"c1\"># \u3053\u306e\u30ea\u30b9\u30c8\u306e\u6642\u523b\u3054\u3068\u306b\u8a08\u7b97\u7d50\u679c\u3092\u51fa\u529b\u3059\u308b<\/span>\r\n<span class=\"n\">t_list<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"n\">T0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"o\">+<\/span><span class=\"mi\">1<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">sol<\/span> <span class=\"o\">=<\/span> <span class=\"n\">solve_ivp<\/span><span class=\"p\">(<\/span><span class=\"n\">F<\/span><span class=\"p\">,<\/span> <span class=\"p\">[<\/span><span class=\"n\">T0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"n\">theta0<\/span><span class=\"p\">,<\/span> <span class=\"n\">dottheta0<\/span><span class=\"p\">],<\/span> \r\n                        <span class=\"n\">t_eval<\/span> <span class=\"o\">=<\/span> <span class=\"n\">t_list<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'\u30c7\u30d5\u30a9\u30eb\u30c8,  dottheta(T=2) = <\/span><span class=\"si\">%.10f<\/span><span class=\"s1\">'<\/span> \r\n          <span class=\"o\">%<\/span><span class=\"p\">(<\/span><span class=\"n\">sol<\/span><span class=\"o\">.<\/span><span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">][<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]))<\/span>\r\n<span class=\"c1\"># \u7cbe\u5ea6\u3092\u5909\u3048\u3066\u7d50\u679c\u3092\u78ba\u8a8d\u3002<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">TOL<\/span> <span class=\"ow\">in<\/span> <span class=\"p\">[<\/span><span class=\"mf\">1e-8<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-9<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-10<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-11<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-12<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-13<\/span><span class=\"p\">]:<\/span>\r\n    <span class=\"n\">sol<\/span> <span class=\"o\">=<\/span> <span class=\"n\">solve_ivp<\/span><span class=\"p\">(<\/span><span class=\"n\">F<\/span><span class=\"p\">,<\/span> <span class=\"p\">[<\/span><span class=\"n\">T0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"n\">theta0<\/span><span class=\"p\">,<\/span> <span class=\"n\">dottheta0<\/span><span class=\"p\">],<\/span> \r\n                        <span class=\"n\">t_eval<\/span> <span class=\"o\">=<\/span> <span class=\"n\">t_list<\/span><span class=\"p\">,<\/span> \r\n                        <span class=\"n\">rtol<\/span> <span class=\"o\">=<\/span> <span class=\"n\">TOL<\/span><span class=\"p\">,<\/span> \r\n                        <span class=\"n\">atol<\/span> <span class=\"o\">=<\/span> <span class=\"n\">TOL<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"c1\"># \u6700\u5f8c\u306e\u5024\u3092\u8868\u793a\u3057\uff0c\u8aa4\u5dee\u3092\u78ba\u8a8d\u3002<\/span>\r\n    <span class=\"c1\"># Python \u3067\u306f\u30ea\u30b9\u30c8\u306e\u6700\u5f8c\uff08\u6700\u5f8c\u5c3e\uff09\u306e\u5024\u306f [-1] \u3067\u53c2\u7167\u3059\u308b<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'TOL = <\/span><span class=\"si\">%.0e<\/span><span class=\"s1\">, dottheta(T=2) = <\/span><span class=\"si\">%.10f<\/span><span class=\"s1\">'<\/span> \r\n          <span class=\"o\">%<\/span><span class=\"p\">(<\/span><span class=\"n\">TOL<\/span><span class=\"p\">,<\/span> <span class=\"n\">sol<\/span><span class=\"o\">.<\/span><span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">][<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>\u30c7\u30d5\u30a9\u30eb\u30c8,  dottheta(T=2) = 8.0317781678\r\nTOL = 1e-08, dottheta(T=2) = 8.0634650784\r\nTOL = 1e-09, dottheta(T=2) = 8.0634655209\r\nTOL = 1e-10, dottheta(T=2) = 8.0634655717\r\nTOL = 1e-11, dottheta(T=2) = 8.0634655776\r\nTOL = 1e-12, dottheta(T=2) = 8.0634655783\r\nTOL = 1e-13, dottheta(T=2) = 8.0634655783\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u306f\u5c0f\u6570\u70b9\u4ee5\u4e0b1\u6841\u7a0b\u5ea6\u306e\u7cbe\u5ea6\u3057\u304b\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308b\u3002<br \/>\n\u4e0a\u306e\u7d50\u679c\u304b\u3089 <code>TOL = 1.e-12<\/code> \u3067\u5c0f\u6570\u70b9\u4ee5\u4e0b 10 \u6841\u7a0b\u5ea6\u306e\u7cbe\u5ea6\u304c\u3042\u308b\u3068\u308f\u304b\u308b\u3002\u4ee5\u5f8c\u306e\u8a08\u7b97\u306f\uff0c\u3053\u308c\u304f\u3089\u3044\u3067\u884c\u3046\u3002<\/p>\n<h4 id=\"$\\theta_0-=-80^{\\circ}$-\u306e\u5834\u5408\">$\\theta_0 = 80^{\\circ}$ \u306e\u5834\u5408<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u8a08\u7b97\u7bc4\u56f2<\/span>\r\n<span class=\"n\">T0<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"n\">T1<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>\r\n\r\n<span class=\"c1\"># \u521d\u671f\u6761\u4ef6<\/span>\r\n<span class=\"c1\">## \u632f\u5e45\uff08\u632f\u308c\u89d2\uff09\u306e\u521d\u671f\u5024<\/span>\r\n<span class=\"n\">th0<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">80<\/span>\r\n<span class=\"c1\">## \u632f\u308c\u89d2\u3092\u30e9\u30b8\u30a2\u30f3\u306b<\/span>\r\n<span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">radians<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\">## \u300c\u521d\u901f\u5ea6\u300d <\/span>\r\n<span class=\"n\">dottheta0<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n\r\n<span class=\"c1\"># \u3061\u3087\u3063\u3068 N \u304c\u5927\u304d\u3044\u304c\u3042\u3068\u3067\u610f\u5473\u304c\u308f\u304b\u308b<\/span>\r\n<span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">200000<\/span>\r\n<span class=\"n\">t_list<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"n\">T0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"o\">+<\/span><span class=\"mi\">1<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">sol80<\/span> <span class=\"o\">=<\/span> <span class=\"n\">solve_ivp<\/span><span class=\"p\">(<\/span><span class=\"n\">F<\/span><span class=\"p\">,<\/span> <span class=\"p\">[<\/span><span class=\"n\">T0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"n\">theta0<\/span><span class=\"p\">,<\/span> <span class=\"n\">dottheta0<\/span><span class=\"p\">],<\/span> \r\n                  <span class=\"n\">t_eval<\/span> <span class=\"o\">=<\/span> <span class=\"n\">t_list<\/span><span class=\"p\">,<\/span> \r\n                  <span class=\"n\">rtol<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.e-12<\/span><span class=\"p\">,<\/span> \r\n                  <span class=\"n\">atol<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.e-12<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><code>solve_ivp()<\/code> \u306b\u3088\u308b\u6570\u5024\u89e3\u306f <code>sol80<\/code> \u306b\u683c\u7d0d\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u5024\u3092\u53c2\u7167\u3059\u308b\u306b\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># t_eval \u3059\u306a\u308f\u3061 t_list \u306f<\/span>\r\n<span class=\"n\">sol80<\/span><span class=\"o\">.<\/span><span class=\"n\">t<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[5]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>array([0.00000e+00, 1.00000e-05, 2.00000e-05, ..., 1.99998e+00,\r\n       1.99999e+00, 2.00000e+00])<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># theta \u3059\u306a\u308f\u3061 y[0] \u306f<\/span>\r\n<span class=\"n\">sol80<\/span><span class=\"o\">.<\/span><span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[6]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>array([1.3962634 , 1.3962634 , 1.39626339, ..., 0.07562658, 0.07570721,\r\n       0.07578785])<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># dottheta \u3059\u306a\u308f\u3061 y[1] \u306f<\/span>\r\n<span class=\"n\">sol80<\/span><span class=\"o\">.<\/span><span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[7]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>array([ 0.00000000e+00, -3.88786517e-04, -7.77573034e-04, ...,\r\n        8.06352530e+00,  8.06349545e+00,  8.06346558e+00])<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u8a08\u7b97\u7d50\u679c\u306e\u30b0\u30e9\u30d5\">\u8a08\u7b97\u7d50\u679c\u306e\u30b0\u30e9\u30d5<\/h4>\n<p>\u6570\u5024\u8a08\u7b97\u3067\u304d\u305f\u3089\uff0c\u7d50\u679c\u3092\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u6a2a\u8ef8\u306b\u898f\u683c\u5316\u3055\u308c\u305f\u6642\u9593 $T =$ <code>sol80.t<\/code>\uff0c<\/li>\n<li>\u7e26\u8ef8\u306b\u632f\u308c\u89d2 $\\theta =$ <code>sol80.y[0]<\/code><\/li>\n<\/ul>\n<p>\u3092\u3068\u3063\u3066\u30b0\u30e9\u30d5\u306b\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[8]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># ax \u3092\u4f7f\u3046\u969b\u306e\u6700\u521d\u306e\u304a\u307e\u3058\u306a\u3044<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">sol80<\/span><span class=\"o\">.<\/span><span class=\"n\">t<\/span><span class=\"p\">,<\/span> <span class=\"n\">sol80<\/span><span class=\"o\">.<\/span><span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-10056\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Furi-01.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u7e26\u8ef8\u306e\u5358\u4f4d\u3092\u5ea6\u306b\u5909\u3048\u305f\u30b0\u30e9\u30d5\">\u7e26\u8ef8\u306e\u5358\u4f4d\u3092\u5ea6\u306b\u5909\u3048\u305f\u30b0\u30e9\u30d5<\/h4>\n<p>\u7e26\u8ef8\u306e\u632f\u308c\u89d2\u3092\u30e9\u30b8\u30a2\u30f3\u304b\u3089\u5ea6\u306b\u5909\u3048\u305f\u30b0\u30e9\u30d5\u3092\u63cf\u304d\u307e\u3059\u3002\u5ea6\u304b\u3089\u30e9\u30b8\u30a2\u30f3\u3078\u306e\u5909\u63db\u306f <code>np.radians()<\/code> \u3067\u3057\u305f\u3002\u30e9\u30b8\u30a2\u30f3\u304b\u3089\u5ea6\u3078\u306f <code>np.degrees()<\/code> \u3067\u3059\u3002<\/p>\n<p>\u307e\u305f\uff0c\u521d\u671f\u6761\u4ef6\u3092\u51e1\u4f8b\u306b\u8a18\u3057\uff0c\u30b5\u30a4\u30a8\u30f3\u30c6\u30a3\u30d5\u30a3\u30c3\u30af\u306a\u30b0\u30e9\u30d5\u3089\u3057\u304f grid\uff08\u683c\u5b50\u7dda\uff09\u7b49\u3092\u3064\u3051\u3066\u307f\u307e\u3059\u3002<\/p>\n<p>\u53c2\u8003\uff1a\u51e1\u4f8b\u3084\u6a2a\u8ef8\u7e26\u8ef8\u306e\u30e9\u30d9\u30eb\u306b $\\LaTeX$ \u8a18\u6cd5\u3092\u4f7f\u3063\u3066\u3044\u307e\u3059\u3002\u304d\u308c\u3044\u306a\u6570\u5f0f\u7528\u66f8\u4f53\u3067\u8868\u793a\u3055\u308c\u307e\u3059\u3002$\\LaTeX$ \u8a18\u6cd5\u3067\u306f \\$ \u3067\u631f\u3093\u3060\u9593\u306b\u6570\u5f0f\u3084 \\ \uff08\u30d0\u30c3\u30af\u30b9\u30e9\u30c3\u30b7\u30e5\uff09\u3067\u306f\u3058\u307e\u308b\u30b3\u30de\u30f3\u30c9\u3092\u66f8\u304d\u307e\u3059\u3002\u4e00\u90e8\uff0c\\ \uff08\u30d0\u30c3\u30af\u30b9\u30e9\u30c3\u30b7\u30e5\uff09\u304c\u8aa4\u8a8d\u8b58\u3055\u308c\u3066\u3057\u307e\u3046\u5834\u5408\u304c\u3042\u308b\u306e\u3067\uff0c\u5b89\u5168\u306e\u305f\u3081\u306b\u6587\u5b57\u5217\u306e\u524d\u306b <code>r<\/code> \u3092\u3064\u3051\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># ax \u3092\u4f7f\u3046\u969b\u306e\u6700\u521d\u306e\u304a\u307e\u3058\u306a\u3044<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"c1\"># LaTeX \u8a18\u6cd5<\/span>\r\n<span class=\"c1\"># \\ \u3092\u6b63\u3057\u304f\u8a8d\u8b58\u3057\u3066\u3082\u3089\u3046\u305f\u3081\u306b r \u3092\u3064\u3051\u308b<\/span>\r\n<span class=\"n\">key<\/span> <span class=\"o\">=<\/span> <span class=\"sa\">r<\/span><span class=\"s2\">\"$\\theta_0 = 80^{\\circ}$\"<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">sol80<\/span><span class=\"o\">.<\/span><span class=\"n\">t<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">degrees<\/span><span class=\"p\">(<\/span><span class=\"n\">sol80<\/span><span class=\"o\">.<\/span><span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"n\">key<\/span><span class=\"p\">);<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u7e26\u8ef8\u306e\u30e9\u30d9\u30eb\u3002<\/span>\r\n<span class=\"c1\"># LaTeX \u8a18\u6cd5<\/span>\r\n<span class=\"c1\"># \\ \u3092\u6b63\u3057\u304f\u8a8d\u8b58\u3057\u3066\u3082\u3089\u3046\u305f\u3081\u306b r \u3092\u3064\u3051\u308b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u898f\u683c\u5316\u3055\u308c\u305f\u6642\u9593 $T$\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylabel<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"\u632f\u308c\u89d2 $\\theta$ (\u00b0)\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09\u306e\u8868\u793a\u3002\u79c1\u306f\u70b9\u7dda\u304c\u597d\u307f\u3002<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">ls<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u306e\u8868\u793a<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/span><span class=\"p\">();<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-10057\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Furi-02.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u632f\u308c\u89d2\u306e\u521d\u671f\u5024\u3092\u5909\u3048\u3066\u8a08\u7b97\">\u632f\u308c\u89d2\u306e\u521d\u671f\u5024\u3092\u5909\u3048\u3066\u8a08\u7b97<\/h4>\n<p>$\\theta_0 = 80^{\\circ}$ \u306e\u5834\u5408\u306f\u6570\u5024\u8a08\u7b97\u3067\u304d\u305f\u306e\u3067\uff0c$\\theta_0 = 70^{\\circ}, 60^{\\circ}, 45^{\\circ}$\uff0c\u305d\u3057\u3066\u6bd4\u8f03\u306e\u305f\u3081\u306b\uff0c\u307b\u307c\u5358\u632f\u52d5\u3068\u601d\u308f\u308c\u308b $\\theta_0 = 1^{\\circ}$ \u306e\u5834\u5408\u3082\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>$\\theta_0 = 80^{\\circ}$ \u306e\u5834\u5408\u306e\u30b3\u30fc\u30c9\u30924\u56de\u5206\u30b3\u30d4\u30da\u3057\u3066&#8230; \u3068\u3044\u3046\u306e\u3082\u306a\u3093\u3067\u3059\u306e\u3067\uff0c<code>for<\/code> \u6587\u3092\u4f7f\u3063\u3066\u7e70\u308a\u8fd4\u3057\u51e6\u7406\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[10]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u8a08\u7b97\u7d50\u679c\u3092\u4fdd\u5b58\u3057\u3066\u304a\u304f\u30ea\u30b9\u30c8<\/span>\r\n<span class=\"c1\"># sols \u306b [th0, theta, dottheta] \u306e\u9806\u306b\u4fdd\u5b58\u3057\u3066\u304a\u304f<\/span>\r\n<span class=\"n\">sols<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n\r\n<span class=\"n\">th0s<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">80<\/span><span class=\"p\">,<\/span> <span class=\"mi\">70<\/span><span class=\"p\">,<\/span> <span class=\"mi\">60<\/span><span class=\"p\">,<\/span> <span class=\"mi\">45<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">th0<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">th0s<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">radians<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">sol<\/span> <span class=\"o\">=<\/span> <span class=\"n\">solve_ivp<\/span><span class=\"p\">(<\/span><span class=\"n\">F<\/span><span class=\"p\">,<\/span> <span class=\"p\">[<\/span><span class=\"n\">T0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"n\">theta0<\/span><span class=\"p\">,<\/span> <span class=\"n\">dottheta0<\/span><span class=\"p\">],<\/span> \r\n                    <span class=\"n\">t_eval<\/span> <span class=\"o\">=<\/span> <span class=\"n\">t_list<\/span><span class=\"p\">,<\/span> \r\n                    <span class=\"n\">rtol<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.e-12<\/span><span class=\"p\">,<\/span> \r\n                    <span class=\"n\">atol<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.e-12<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">sols<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">([<\/span><span class=\"n\">th0<\/span><span class=\"p\">,<\/span> <span class=\"n\">sol<\/span><span class=\"o\">.<\/span><span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">],<\/span> <span class=\"n\">sol<\/span><span class=\"o\">.<\/span><span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">]])<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"$\\theta$-\u306e\u30b0\u30e9\u30d5\">$\\theta$ \u306e\u30b0\u30e9\u30d5<\/h4>\n<p>\u8a08\u7b97\u7d50\u679c\u3092\u3042\u308f\u305b\u3066\u30b0\u30e9\u30d5\u306b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[11]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># ax \u3092\u4f7f\u3046\u969b\u306e\u6700\u521d\u306e\u304a\u307e\u3058\u306a\u3044<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">sol<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">sols<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"c1\"># \u51e1\u4f8b label \u306e\u8a2d\u5b9a\u3002LaTeX \u8868\u8a18\u306f $ \u3067\u56f2\u3080\u3002<\/span>\r\n    <span class=\"n\">key<\/span> <span class=\"o\">=<\/span> <span class=\"sa\">r<\/span><span class=\"s2\">\"$\\theta_0 = <\/span><span class=\"si\">%2d<\/span><span class=\"s2\">^{\\circ}$\"<\/span> <span class=\"o\">%<\/span> <span class=\"n\">sol<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span>\r\n    <span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">t_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">degrees<\/span><span class=\"p\">(<\/span><span class=\"n\">sol<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">]),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"n\">key<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u7e26\u8ef8\u306e\u30e9\u30d9\u30eb\u3002<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u898f\u683c\u5316\u3055\u308c\u305f\u6642\u9593 $T$\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylabel<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"\u632f\u308c\u89d2 $\\theta$ (\u00b0)\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09\u306e\u8868\u793a\u3002\u79c1\u306f\u70b9\u7dda\u304c\u597d\u307f\u3002<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">ls<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlim<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u306e\u8868\u793a<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/span><span class=\"p\">();<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-10058\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Furi-03.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u25cb\u7df4\u7fd2\uff1a$\\dot{\\theta}$-\u306e\u30b0\u30e9\u30d5\">\u25cb\u7df4\u7fd2\uff1a$\\dot{\\theta}$ \u306e\u30b0\u30e9\u30d5<\/h4>\n<p>$\\dot{\\theta}$ \u306e\u8a08\u7b97\u7d50\u679c\u3082\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u3088\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[12]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># ax \u3092\u4f7f\u3046\u969b\u306e\u6700\u521d\u306e\u304a\u307e\u3058\u306a\u3044<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">()<\/span>\r\n\r\n...\r\n...\r\n...\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u7e26\u8ef8\u306e\u30e9\u30d9\u30eb\u3002<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u898f\u683c\u5316\u3055\u308c\u305f\u6642\u9593 $T$\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylabel<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"$\\dot{\\theta}$\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09\u306e\u8868\u793a\u3002<\/span>\r\n\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u306e\u8868\u793a<\/span>\r\n\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-10059\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Furi-04.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u5468\u671f\u306f\u901f\u5ea6\u306e\u5411\u304d\u304c\u5909\u308f\u308b\u6642\u523b\u304b\u3089...\">\u5468\u671f\u306f\u901f\u5ea6\u306e\u5411\u304d\u304c\u5909\u308f\u308b\u6642\u523b\u304b\u3089&#8230;<\/h4>\n<p>\u5358\u632f\u308a\u5b50\u306e\u5468\u671f\u306b\u3064\u3044\u3066\u306f\uff0c$\\dot{\\theta}(t) = 0$ \u3068\u306a\u308b $t$ \u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u3066\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u4ee5\u4e0b\u3067\u3084\u3063\u3066\u307e\u3057\u305f\u306d\u3002<\/p>\n<ul>\n<li>\u53c2\u8003\uff1a<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%E3%82%B3%E3%83%B3%E3%83%94%E3%83%A5%E3%83%BC%E3%82%BF%E6%BC%94%E7%BF%92\/python-%E3%81%A7%E6%95%B0%E5%80%A4%E8%A7%A3%E6%9E%90\/scipy-%E3%81%A7%E6%95%B0%E5%80%A4%E8%A7%A3%E6%9E%90\/#i-6\">\u25cb\u7df4\u7fd2\uff1a\u5358\u632f\u308a\u5b50\u306e\u5468\u671f<\/a><\/li>\n<\/ul>\n<p>\u3053\u3053\u3067\u306f\uff0c\u3082\u3046\u5c11\u3057\u539f\u59cb\u7684\u306a\u65b9\u6cd5\u3067\u8003\u3048\u3066\u307f\u308b\u3002<\/p>\n<p>\u521d\u901f\u5ea6 $\\dot{\\theta}(0) = 0$ \u3067\u306f\u3058\u307e\u308b\u632f\u308a\u5b50\u306e\u904b\u52d5\u306f\uff0c\u534a\u5468\u671f\u3054\u3068\u306b $\\dot{\\theta} = 0$ \u3068\u306a\u308b\u306f\u305a\u3067\u3042\u308b\u3002\u5b9f\u969b\u306e\u6570\u5024\u8a08\u7b97\u3067\u306f\uff0c\u523b\u307f\u5e45<\/p>\n<p>$$h \\equiv \\frac{T_1 &#8211; T_0}{N}$$<\/p>\n<p>\u3092\u4f7f\u3063\u3066\u96e2\u6563\u7684\u306a\u6642\u523b $T_i = T_0 + i h$ \u3067\u306e\u5024\u3092\u6c42\u3081\u3066\u3044\u308b\u306e\u3067\uff0c\u53b3\u5bc6\u306b $\\dot{\\theta}=0$ \u3068\u306a\u308b\u77ac\u9593\u304c\u5f97\u3089\u308c\u308b\u3068\u306f\u9650\u3089\u306a\u3044\u3002\u3057\u305f\u304c\u3063\u3066\uff0c\u901f\u5ea6\u306e\u5411\u304d\u304c\u5909\u308f\u308b\u6642\u523b\uff0c<br \/>\n\u3064\u307e\u308a<\/p>\n<p>$$\\dot{\\theta}(T_i) &gt; 0, \\quad \\dot{\\theta}(T_{i+1}) \\leq 0$$<\/p>\n<p>\u3068\u306a\u308b\u6642\u523b $T_i$ \u304a\u3088\u3073 $T_{i+1}$ \u3092\u63a2\u3057\uff0c$\\dot{\\theta}(\\tau) = 0$ \u3068\u306a\u308b\u6642\u523b\u3067\u3042\u308b\u5468\u671f $\\tau$ \u3092\uff0c$T_i$ \u3068 $T_{i+1}$ \u3092 $\\dot{\\theta} (T_i) : \\bigl| \\dot{\\theta}(T_{i+1})\\bigr|$ \u306b\u5185\u5206\u3059\u308b\u70b9\u3068\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u6c42\u3081\u308b\u3053\u3068\u306b\u3059\u308b\u3002<\/p>\n<p>$$ \\tau = \\frac{\\bigl| \\dot{\\theta}(T_{i+1})\\bigr|\\,T_i + \\dot{\\theta} (T_i)\\, T_{i+1}}{\\dot{\\theta} (T_i) + \\bigl| \\dot{\\theta}(T_{i+1})\\bigr|}$$<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/naibunten.png\" alt=\"iwaki\" width=\"75%\" \/><\/p>\n<p>\u305f\u3060\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u305f\u3081\u3060\u3051\u306a\u3089\uff0c<code>N = 200000<\/code> \u306a\u3069\u3068\u3044\u3046\u5927\u304d\u306a\u5024\u3092\u3068\u308b\u5fc5\u8981\u306f\u306a\u3044\u306e\u3060\u304c\uff0c\u3053\u306e\u3088\u3046\u306b\u901f\u5ea6\u306e\u5411\u304d\u304c\u5909\u308f\u308b\u77ac\u9593\u3092\u3068\u3089\u3048\u305f\u3044\u3068\u304d\u306b\u306f\uff0c\u306a\u308b\u3079\u304f\u523b\u307f\u5e45\u3092\u5c0f\u3055\u304f\u3059\u308b\u3068\u826f\u3044\u306f\u305a\u3002<\/p>\n<p>\u3053\u306e\u3088\u3046\u306a\u7406\u7531\u3067 <code>N<\/code> \u306e\u5024\u3092\u5927\u304d\u304f\u3057\u3066\u3044\u308b\u3053\u3068\u306f\u7406\u89e3\u3057\u3066\u304a\u3053\u3046\u3002<\/p>\n<p>\u3067\u306f\uff0c$\\theta_0 = 80^{\\circ}$ \u306e\u5834\u5408\u306e\u6570\u5024\u8a08\u7b97\u306e\u7d50\u679c\u3092\u4f7f\u3044\uff0c\u4e0a\u3067\u8ff0\u3079\u305f\u65b9\u6cd5\u3067\u5468\u671f\u3092\u6c42\u3081\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[13]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># th0 = 80 \u306e\u6570\u5024\u89e3\u3092\u78ba\u8a8d<\/span>\r\n<span class=\"c1\"># theta<\/span>\r\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"n\">sol80<\/span><span class=\"o\">.<\/span><span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">])<\/span>\r\n<span class=\"c1\"># dot theta<\/span>\r\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"n\">sol80<\/span><span class=\"o\">.<\/span><span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">])<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>[1.3962634  1.3962634  1.39626339 ... 0.07562658 0.07570721 0.07578785]\r\n[ 0.00000000e+00 -3.88786517e-04 -7.77573034e-04 ...  8.06352530e+00\r\n  8.06349545e+00  8.06346558e+00]\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[14]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">th0<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">80<\/span>\r\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'\u03b80 = <\/span><span class=\"si\">%2d<\/span><span class=\"s1\">\u00b0 \u306e\u3068\u304d\uff0c'<\/span> <span class=\"o\">%<\/span> <span class=\"n\">th0<\/span><span class=\"p\">,<\/span> <span class=\"n\">end<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">''<\/span><span class=\"p\">)<\/span> <span class=\"c1\"># end = '' \u306a\u3089\u6539\u884c\u305b\u305a<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"c1\"># i \u306e\u7e70\u308a\u8fd4\u3057\u306f\u3053\u306e\u30a4\u30f3\u30c7\u30f3\u30c8<\/span>\r\n    <span class=\"c1\"># \u901f\u5ea6\u306e\u5411\u304d\u304c\u5909\u308f\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a<\/span>\r\n    <span class=\"k\">if<\/span> <span class=\"p\">(<\/span><span class=\"n\">sol80<\/span><span class=\"o\">.<\/span><span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">&gt;<\/span> <span class=\"mi\">0<\/span><span class=\"p\">)<\/span> <span class=\"o\">&amp;<\/span> <span class=\"p\">(<\/span><span class=\"n\">sol80<\/span><span class=\"o\">.<\/span><span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"o\">+<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"mi\">0<\/span><span class=\"p\">):<\/span>\r\n        <span class=\"c1\"># if \u304c\u6210\u308a\u7acb\u3064\u6642\u306e\u5b9f\u884c\u6587\u306f\u3053\u306e\u30a4\u30f3\u30c7\u30f3\u30c8<\/span>\r\n        <span class=\"c1\"># \u5185\u5206\u70b9\u306e\u5f0f\u304b\u3089\u5468\u671f\u3092\u8a08\u7b97<\/span>\r\n        <span class=\"n\">m<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sol80<\/span><span class=\"o\">.<\/span><span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span>\r\n        <span class=\"n\">n<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">abs<\/span><span class=\"p\">(<\/span><span class=\"n\">sol80<\/span><span class=\"o\">.<\/span><span class=\"n\">y<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"o\">+<\/span><span class=\"mi\">1<\/span><span class=\"p\">])<\/span>\r\n        <span class=\"n\">tau<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"n\">n<\/span><span class=\"o\">*<\/span><span class=\"n\">t_list<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">+<\/span> <span class=\"n\">m<\/span><span class=\"o\">*<\/span><span class=\"n\">t_list<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"o\">+<\/span><span class=\"mi\">1<\/span><span class=\"p\">])<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">m<\/span> <span class=\"o\">+<\/span> <span class=\"n\">n<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'\u5468\u671f \u03c4 = <\/span><span class=\"si\">%.7f<\/span><span class=\"s1\">'<\/span> <span class=\"o\">%<\/span> <span class=\"n\">tau<\/span><span class=\"p\">)<\/span>    \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>\u03b80 = 80\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f \u03c4 = 1.1374926\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4ee5\u4e0a\u306e\u7d50\u679c\u304b\u3089\uff0c\u4f8b\u3048\u3070\u632f\u308c\u89d2\u306e\u521d\u671f\u6761\u4ef6\u3092 $\\theta_0 = 80^{\\circ}$ \u3068\u3057\u305f\u6642\u306e\u5468\u671f\u306f $\\tau = 1.1374926$\uff0c\u3059\u306a\u308f\u3061\u5358\u632f\u52d5\u306e\u5834\u5408\u306e\u5468\u671f<\/p>\n<p>$$\\tau_0 = 2\\pi \\sqrt{\\frac{\\ell}{g}}$$<\/p>\n<p>\u306e $1.1374926$ \u500d\u3060\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u25cb\u7df4\u7fd2\uff1a\u5358\u632f\u308a\u5b50\u306e\u5468\u671f\">\u25cb\u7df4\u7fd2\uff1a\u5358\u632f\u308a\u5b50\u306e\u5468\u671f<\/h4>\n<p>\u3067\u306f\u672c\u984c\u3002$\\theta_0 = 10^{\\circ}$ \u304b\u3089 $10^{\\circ}$ \u304d\u3056\u307f\u3067 $90^{\\circ}$ \u307e\u3067\uff0c $T = 0$ \u304b\u3089 $ T = 2$ \u307e\u3067\u89e3\u304d\uff0c\u305d\u306e\u7d50\u679c\u304b\u3089\u632f\u308c\u89d2 $\\theta_0$ \u306b\u5bfe\u3059\u308b\u5468\u671f $\\tau$ \u3092\u6c42\u3081\u3066\u307f\u3088\u3002<\/p>\n<p>\u307e\u305f\uff0c\u6a2a\u8ef8\u306b\u632f\u308c\u89d2 $\\theta_0$\uff0c\u7e26\u8ef8\u306b\u5468\u671f $\\tau$ \u3092\u3068\u3063\u305f\u30b0\u30e9\u30d5\u3092\u63cf\u3051\u3002<\/p>\n<p>\u30b0\u30e9\u30d5\u306b\u3059\u308b\u305f\u3081\u306b\u306f\u632f\u5e45 <code>th0<\/code> \u306e\u30ea\u30b9\u30c8\u3068\uff0c\u632f\u5e45\u306e\u5404\u8981\u7d20\u306b\u5bfe\u5fdc\u3059\u308b\u5468\u671f <code>tau<\/code> \u306e\u30ea\u30b9\u30c8\u304c\u5fc5\u8981\u3067\u3059\u3088\u3002<\/p>\n<p><code>th0<\/code> \u306e\u30ea\u30b9\u30c8\u4f5c\u6210\u4f8b\u306f\u4ee5\u4e0b\u306e\u901a\u308a\uff1a<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[15]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># [10, 20, ...] \u3068\u5168\u90e8\u624b\u66f8\u304d\u3059\u308b\u3088\u308a\u697d\uff1f<\/span>\r\n<span class=\"n\">th0s<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">10<\/span><span class=\"o\">*<\/span><span class=\"n\">i<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">10<\/span><span class=\"p\">)]<\/span>\r\n<span class=\"n\">th0s<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[15]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>[10, 20, 30, 40, 50, 60, 70, 80, 90]<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u305d\u308c\u305e\u308c\u306e $\\theta_0$ \u306b\u5bfe\u3059\u308b\u5468\u671f $\\tau$ \u3082\u30ea\u30b9\u30c8\u306b\u3059\u308b\u3093\u3067\u3059\u3088\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5927\u5b66\u306e\u529b\u5b66\u7b49\u3067\u3082\uff0c\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f\uff0c\u632f\u308c\u89d2\u304c\u975e\u5e38\u306b\u5c0f\u3055\u304f\u3066 $\\sin\\theta \\simeq \\theta$ \u3068\u8fd1\u4f3c\u3067\u304d\u308b\u3068\u304d\u306e\u8a71\u3057\u304b\u3057\u306a\u3044\u304b\u3082\u3057\u308c\u306a\u3044\u3002<\/p>\n<p>\u8fd1\u4f3c\u3057\u306a\u3044\u3068\u304d\u306b\u306f\uff0c\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f\u89e3\u6790\u7684\u306b\u89e3\u3051\u306a\u3044\u304b\u3089\u3067\u3042\u308b\u3002<\/p>\n<p>\u3053\u3053\u3067\u306f\uff0c2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u3053\u3068\u306b\u3088\u3063\u3066\uff0c\u5358\u632f\u308a\u5b50\u306e\u5468\u671f\u306f\u632f\u308c\u89d2\u306b\u4f9d\u5b58\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u3002<\/p>\n<p style=\"text-align: center;\">\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u632f\u308a\u5b50\u306e\u7b49\u6642\u6027\u306f\u6210\u308a\u7acb\u305f\u306a\u3044<\/strong><\/span>\u300d<\/p>\n<p>\u3068\u3044\u3046\u3053\u3068\u3092\u7406\u89e3\u3067\u304d\u305f\uff01\u3068\u3044\u3046\u610f\u5473\u3067\uff0c\u3053\u308c\u306f\u8cb4\u91cd\u306a\u7d4c\u9a13\u3060\u3068\u601d\u3046\u304c\uff0c\u3044\u304b\u304c\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Python \u306e SciPy \u3092\u4f7f\u3063\u3066\uff0c\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u3002\u904b\u52d5\u65b9\u7a0b\u5f0f\u306e\u5c0e\u51fa\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u306b\u307e\u3068\u3081\u3066\u3044\u308b\u3002<\/p>\n<ul>\n<li>\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u6e96\u5099<\/li>\n<\/ul>\n<p>\u306a\u304a\uff0c\u307b\u307c\u540c\u3058\u5185\u5bb9\u3067\u30b0\u30e9\u30d5\u306e\u307f plt.*** \u306e\u307f\u3067\u63cf\u3044\u305f\u65e7\u7248\u306e\u30da\u30fc\u30b8\u306f\u4ee5\u4e0b\uff1a<\/p>\n<ul>\n<li>Python \u3067\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u632f\u5e45\u3068\u5468\u671f\u306e\u95a2\u4fc2\u3092\u8abf\u3079\u308b\uff08\u65e7\u7248\uff09<\/li>\n<\/ul>\n<p>\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\uff0c\uff08\u3061\u3087\u3063\u3068\u3060\u3051\u9762\u5012\u3060\u3051\u3069\uff09\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u306b\u5f93\u3044\uff0cax.*** \u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u3092\u4f5c\u6210\u3059\u308b\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e9%81%8b%e5%8b%95%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e6%95%b0%e5%80%a4%e7%9a%84%e3%81%ab%e8%a7%a3%e3%81%8f%e6%ba%96%e5%82%99\/scipy-%e3%81%a7%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e9%81%8b%e5%8b%95%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e6%95%b0%e5%80%a4%e7%9a%84%e3%81%ab%e8%a7%a3%e3%81%8f\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n<ul>\n<li>Matplotlib \u3067\u30b0\u30e9\u30d5\u4f5c\u6210\uff1aax \u7de8<\/li>\n<\/ul>\n","protected":false},"author":33,"featured_media":0,"parent":4940,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-9988","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/9988","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=9988"}],"version-history":[{"count":11,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/9988\/revisions"}],"predecessor-version":[{"id":10061,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/9988\/revisions\/10061"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4940"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=9988"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}