{"id":5093,"date":"2025-01-21T10:30:00","date_gmt":"2025-01-21T01:30:00","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=5093"},"modified":"2025-01-21T17:36:58","modified_gmt":"2025-01-21T08:36:58","slug":"scipy-%e3%81%a7%e9%ab%98%e3%81%95-h-%e3%81%8b%e3%82%89%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%81%ae%e6%9c%80%e5%a4%a7%e5%88%b0%e9%81%94%e8%b7%9d%e9%9b%a2%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b","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\/%e9%ab%98%e3%81%95-h-%e3%81%8b%e3%82%89%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%81%ae%e6%9c%80%e5%a4%a7%e5%88%b0%e9%81%94%e8%b7%9d%e9%9b%a2%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e6%ba%96\/scipy-%e3%81%a7%e9%ab%98%e3%81%95-h-%e3%81%8b%e3%82%89%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%81%ae%e6%9c%80%e5%a4%a7%e5%88%b0%e9%81%94%e8%b7%9d%e9%9b%a2%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b\/","title":{"rendered":"SciPy \u3067\u9ad8\u3055 h \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u5230\u9054\u8ddd\u96e2\u3092\u6c42\u3081\u308b"},"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>\u5730\u9762\u304b\u3089\u9ad8\u3055 $h$ \u306e\u5730\u70b9\u304b\u3089\u7a7a\u6c17\u62b5\u6297\u306a\u3057\u306e\u659c\u65b9\u6295\u5c04\u3092\u884c\u3046\u3068\uff0c\u521d\u901f\u5ea6\u306e\u5927\u304d\u3055\u3092\u4e00\u5b9a\u3068\u3057\u305f\u5834\u5408\uff0c\u6c34\u5e73\u65b9\u5411\u306e\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f\u6253\u3061\u4e0a\u3052\u89d2\u5ea6\uff08\u4ef0\u89d2\uff09\u304c\u4f55\u5ea6\u306e\u3068\u304d\u304b\u3092 Python \u306e SciPy \u3068 NumPy \u3092\u4f7f\u3063\u3066\uff08\u304b\u3064 SymPy \u3092\u4f7f\u308f\u305a\u306b\uff09\u6c42\u3081\u308b\u3002<\/p>\n<p>Python \u306e Matplotlib \u306b\u3088\u308b\u30b0\u30e9\u30d5\u4f5c\u6210\u306b\u306f\uff0c<code>plt.***<\/code> \u3068\u3044\u3046\u95a2\u6570\u306e\u307f\u3092\u4f7f\u3063\u305f <strong>plt (pyplot) \u6d41<\/strong>\uff08pyplot \u30a4\u30f3\u30bf\u30fc\u30d5\u30a7\u30fc\u30b9\u3068\u3082\uff09\u3068\uff0c<code>ax.***<\/code> \u3068\u3044\u3046\u95a2\u6570\u306e\u307f\u3092\u4f7f\u3063\u305f <strong>ax \u6d41<\/strong>\uff08\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u6307\u5411\u30a4\u30f3\u30bf\u30fc\u30d5\u30a7\u30fc\u30b9\u3068\u3082\uff09\u306e2\u3064\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u306f <code>ax.***<\/code> \u306e\u307f\u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n<p><code>ax.***<\/code> \u306e\u307f\u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u3092\u4f5c\u6210\u3059\u308b\u65b9\u6cd5\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u306b\u307e\u3068\u3081\u3066\u3044\u307e\u3059\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<p style=\"text-align: right;\">update: 2025.01.21<\/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<h3 id=\"\u30e9\u30a4\u30d6\u30e9\u30ea\u306e-import\">\u30e9\u30a4\u30d6\u30e9\u30ea\u306e import<\/h3>\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 \u3092\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\r\n<span class=\"c1\"># \u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3 <\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">scipy.optimize<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">root_scalar<\/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<h3 id=\"\u904b\u52d5\u65b9\u7a0b\u5f0f\u306e\u89e3\">\u904b\u52d5\u65b9\u7a0b\u5f0f\u306e\u89e3<\/h3>\n<p>\u521d\u671f\u6761\u4ef6\u3092 $t = 0$ \u3067<\/p>\n<p>$$x(0) = 0, \\quad y(0) = h, \\quad v_x(0)\u00a0 = v_0 \\cos\\theta, \\quad v_y(0) = v_0 \\sin \\theta$$<\/p>\n<p>\u3068\u3057\u305f\u3068\u304d\u306e\u89e3\u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\nx(t) &amp;=&amp; v_0 \\cos\\theta\\cdot t \\\\<br \/>\ny(t) &amp;=&amp; h + v_0 \\sin\\theta\\cdot t &#8211; \\frac{1}{2} g t^2<br \/>\n\\end{eqnarray}<\/p>\n<h3 id=\"\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u659c\u65b9\u6295\u5c04\u306e\u89e3\">\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u659c\u65b9\u6295\u5c04\u306e\u89e3<\/h3>\n<p>\u3053\u306e\u7cfb\u306b\u7279\u5fb4\u7684\u306a\u6642\u9593 $\\displaystyle \\tau \\equiv \\frac{v_0}{g}$ \u304a\u3088\u3073\u9577\u3055 $\\displaystyle \\ell \\equiv v_0 \\tau = \\frac{v_0^2}{g}$ \u3067\u89e3\u3092\u7121\u6b21\u5143\u5316\u3059\u308b\u3068\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\nT &amp;\\equiv&amp; \\frac{t}{\\tau} \\\\<br \/>\nH &amp;\\equiv&amp; \\frac{h}{\\ell} \\\\<br \/>\nX &amp;\\equiv&amp; \\frac{x}{\\ell} = \\cos\\theta\\cdot T \\\\<br \/>\nY&amp;\\equiv&amp; \\frac{y}{\\ell} = H+ \\sin\\theta\\cdot T &#8211; \\frac{1}{2} T^2<br \/>\n\\end{eqnarray}<\/p>\n<p>\u8a73\u7d30\u306f\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8<\/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\/%e9%ab%98%e3%81%95-h-%e3%81%8b%e3%82%89%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%81%ae%e6%9c%80%e5%a4%a7%e5%88%b0%e9%81%94%e8%b7%9d%e9%9b%a2%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e6%ba%96\/\">\u9ad8\u3055 h \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u5230\u9054\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u6e96\u5099<\/a><\/li>\n<\/ul>\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<h3 id=\"\u95a2\u6570\u306e\u5b9a\u7fa9\">\u95a2\u6570\u306e\u5b9a\u7fa9<\/h3>\n<p>\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u89e3 $X(T, \\theta), Y(T, \\theta)$ \u304a\u3088\u3073\u6ede\u7a7a\u6642\u9593 $T_1$ \u3068\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L$ \u3092\u95a2\u6570\u3068\u3057\u3066\u5b9a\u7fa9\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[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u89d2\u5ea6 th \u306f\u5ea6\u3067 <\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">theta<\/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\">th<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"n\">T<\/span>\r\n\r\n<span class=\"k\">def<\/span> <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">theta<\/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\">th<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">H<\/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><span class=\"o\">*<\/span><span class=\"n\">T<\/span> <span class=\"o\">-<\/span> <span class=\"n\">T<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span>\r\n\r\n<span class=\"k\">def<\/span> <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">theta<\/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\">th<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/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> <span class=\"o\">+<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/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><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">H<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"k\">def<\/span> <span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">theta<\/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\">th<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">),<\/span> <span class=\"n\">th<\/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<h3 id=\"$H-=-0$-\u306e\u5834\u5408\u306e\u8ecc\u9053\">$H = 0$ \u306e\u5834\u5408\u306e\u8ecc\u9053<\/h3>\n<p>$\\theta = 45^{\\circ}$ \u524d\u5f8c\u306e\u89d2\u5ea6\u3067\u306e\u659c\u65b9\u6295\u5c04\u306e\u8ecc\u9053\u3092\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3002<\/p>\n<p>\u307e\u305a\u306f\uff0c\u3068\u308a\u3042\u3048\u305a\u306e\u30b0\u30e9\u30d5\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[3]:<\/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\"># \u03b8 = 45\u00b0 \u306e\u30b0\u30e9\u30d5<\/span>\r\n<span class=\"n\">th<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">45<\/span>\r\n<span class=\"n\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n\r\n<span class=\"c1\"># \u6ede\u7a7a\u6642\u9593 T1<\/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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/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\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/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-10041\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/axNhtosha-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<p>\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3057\u3066\uff0c\u3082\u3046\u5c11\u3057\u4f53\u88c1\u3092\u6574\u3048\u307e\u3059\u3002<\/p>\n<ul>\n<li>$\\theta$ \u306e\u5024\u3092\u51e1\u4f8b\u306b<\/li>\n<li>\u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09\u3092\u30c9\u30c3\u30c8\u306b<\/li>\n<li>\u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb<\/li>\n<li>\u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/li>\n<li>\u5ea7\u6a19\u8ef8\u306e\u76ee\u76db\u306e\u9593\u9694<\/li>\n<li>\u7e26\u8ef8\u6a2a\u8ef8\u306e\u30a2\u30b9\u30da\u30af\u30c8\u6bd4<\/li>\n<\/ul>\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\"># 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\"># \u03b8 = 45\u00b0 \u306e\u30b0\u30e9\u30d5<\/span>\r\n<span class=\"n\">th<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">45<\/span>\r\n<span class=\"n\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n\r\n<span class=\"c1\"># \u6ede\u7a7a\u6642\u9593<\/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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b<\/span>\r\n<span class=\"n\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'\u03b8 = <\/span><span class=\"si\">%2d<\/span><span class=\"s1\">\u00b0'<\/span> <span class=\"o\">%<\/span> <span class=\"n\">th<\/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\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/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\"># \u30b0\u30e9\u30d5\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b<\/span>\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\u30c9\u30c3\u30c8\u3067<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb<\/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\">\"X\"<\/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=\"s2\">\"Y\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"H = 0 \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u7e26\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=\"mf\">1.1<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylim<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u76ee\u76db\u306e\u9593\u9694\u3092\u624b\u52d5\u3067\u8a2d\u5b9a\u3059\u308b\u5834\u5408<\/span>\r\n<span class=\"c1\"># \u9593\u9694\u3092\u6307\u5b9a\u3057\u3066 np.arange() \u3092\u4f7f\u3046\u4f8b<\/span>\r\n<span class=\"c1\"># 0 \u304b\u3089 0.1 \u9593\u9694\u3067 1.1 \u672a\u6e80\uff08\u3064\u307e\u308a 1.0\uff09\u307e\u3067<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.1<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># \u8981\u7d20\u6570\u3092\u6307\u5b9a\u3057\u3066 np.linspace() \u3092\u4f7f\u3046\u4f8b<\/span>\r\n<span class=\"c1\"># (0, 0.5) \u533a\u9593\u3092 5 \u7b49\u5206<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_yticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"o\">+<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># 45\u00b0\u304c45\u00b0\u306b\u898b\u3048\u308b\u3088\u3046\u306b<\/span>\r\n<span class=\"c1\"># \u7e26\u8ef8\u6a2a\u8ef8\u306e\u30a2\u30b9\u30da\u30af\u30c8\u6bd4\u3092 'equal' \u306b\u3002<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_aspect<\/span><span class=\"p\">(<\/span><span class=\"s1\">'equal'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\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-10042\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/axNhtosha02.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<p>$\\theta$ \u306e\u5024\u3092 $43^{\\circ}$ \u304b\u3089 $47^{\\circ}$ \u307e\u3067 $1^{\\circ}$ \u523b\u307f\u3067\u5909\u3048\u3066\uff0c\u8907\u6570\u306e\u66f2\u7dda\u3092\u4e00\u5ea6\u306b\u63cf\u304f\u4f8b\u3002<\/p>\n<p><code>for<\/code> \u3067\u7e70\u308a\u8fd4\u3057\u51e6\u7406\u3055\u305b\u3066\u307f\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\uff0c\u7d30\u304b\u3044\u3053\u3068\u3067\u3059\u304c\uff0c\u30b0\u30e9\u30d5\u306e\u6700\u9ad8\u70b9\u306f $\\theta$ \u306e\u5024\u304c\u5927\u304d\u3044\u3068\u304d\u3067\u3059\u306e\u3067\uff0c\u5148\u306b $47^{\\circ}$ \u304b\u3089\u63cf\u304d\u306f\u3058\u3081\u3066\uff0c$1^{\\circ}$ \u305a\u3064\u6e1b\u3089\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[5]:<\/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\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n\r\n<span class=\"c1\"># \u8907\u6570\u306e\u30b0\u30e9\u30d5\u3092\u4e00\u5ea6\u306b\u63cf\u304f\u5834\u5408\uff0c<\/span>\r\n<span class=\"c1\"># for \u30eb\u30fc\u30d7\u3067\u7e70\u308a\u8fd4\u3057\u51e6\u7406<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">th<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">47<\/span><span class=\"p\">,<\/span> <span class=\"mi\">42<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">):<\/span>\r\n\r\n    <span class=\"c1\"># \u6ede\u7a7a\u6642\u9593<\/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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">))<\/span>\r\n\r\n    <span class=\"c1\"># \u51e1\u4f8b<\/span>\r\n    <span class=\"n\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'\u03b8 = <\/span><span class=\"si\">%2d<\/span><span class=\"s1\">\u00b0'<\/span> <span class=\"o\">%<\/span> <span class=\"n\">th<\/span>\r\n\r\n    <span class=\"c1\"># plot \u3067\u30b0\u30e9\u30d5\u3092\u63cf\u304f<\/span>\r\n    <span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/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=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/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\">\"X\"<\/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=\"s2\">\"Y\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"H = 0 \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2\u3068\u76ee\u76db<\/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=\"mf\">1.1<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylim<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.1<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_aspect<\/span><span class=\"p\">(<\/span><span class=\"s1\">'equal'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\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-10043\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/axNhtosha03.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<p>\u6700\u5927\u5230\u9054\u8ddd\u96e2\u3068\u306a\u308b\u89d2\u5ea6 $\\theta$ \u3092\u8abf\u3079\u308b\u305f\u3081\u306b\uff0c\u7740\u5730\u70b9\u4ed8\u8fd1\u3092\u62e1\u5927\u8868\u793a\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[6]:<\/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\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n\r\n<span class=\"c1\"># \u8907\u6570\u306e\u30b0\u30e9\u30d5\u3092\u4e00\u5ea6\u306b\u63cf\u304f\u5834\u5408\uff0c<\/span>\r\n<span class=\"c1\"># for \u30eb\u30fc\u30d7\u3067\u7e70\u308a\u8fd4\u3057\u51e6\u7406<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">th<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">47<\/span><span class=\"p\">,<\/span> <span class=\"mi\">42<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">):<\/span>\r\n\r\n    <span class=\"c1\"># \u6ede\u7a7a\u6642\u9593<\/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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">))<\/span>\r\n\r\n    <span class=\"c1\"># \u51e1\u4f8b<\/span>\r\n    <span class=\"n\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'\u03b8 = <\/span><span class=\"si\">%2d<\/span><span class=\"s1\">\u00b0'<\/span> <span class=\"o\">%<\/span> <span class=\"n\">th<\/span>\r\n\r\n    <span class=\"c1\"># plot \u3067\u30b0\u30e9\u30d5\u3092\u63cf\u304f<\/span>\r\n    <span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/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=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/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\">\"X\"<\/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=\"s2\">\"Y\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"H = 0 \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u7740\u5730\u70b9\u4ed8\u8fd1\u3092\u62e1\u5927\u8868\u793a<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlim<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.99<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.0<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylim<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.01<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\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-10044\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/axNhtosha04.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<p>\u4e0a\u306e\u30b0\u30e9\u30d5\u304b\u3089\uff0c$H=0$ \u306e\u5834\u5408\u306b\u306f\u78ba\u304b\u306b $\\theta=45^{\\circ}$ \u306e\u6642\u306b\u6700\u5927\u5230\u9054\u8ddd\u96e2\u306b\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\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<h3 id=\"$H-=-0.2$-\u306e\u5834\u5408\u306e\u8ecc\u9053\">$H = 0.2$ \u306e\u5834\u5408\u306e\u8ecc\u9053<\/h3>\n<p>\u4eca\u5ea6\u306f\uff0c$H=0.2$ \u3068\u3057\u3066\u3084\u3063\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[7]:<\/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\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.2<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">th<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">47<\/span><span class=\"p\">,<\/span> <span class=\"mi\">37<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">):<\/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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">))<\/span>\r\n    <span class=\"n\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'\u03b8 = <\/span><span class=\"si\">%2d<\/span><span class=\"s1\">\u00b0'<\/span> <span class=\"o\">%<\/span> <span class=\"n\">th<\/span>\r\n    <span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/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=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/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\">\"X\"<\/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=\"s2\">\"Y\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"H = 0.2 \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2\u3092\u8abf\u6574\u3059\u308b<\/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=\"mf\">1.5<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylim<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.7<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_aspect<\/span><span class=\"p\">(<\/span><span class=\"s1\">'equal'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\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-10045\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/axNhtosha05.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<p>\u6700\u5927\u5230\u9054\u8ddd\u96e2\u3068\u306a\u308b\u89d2\u5ea6 $\\theta$ \u3092\u8abf\u3079\u308b\u305f\u3081\u306b\uff0c\u7740\u5730\u70b9\u4ed8\u8fd1\u3092\u62e1\u5927\u8868\u793a\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\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.2<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">th<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">47<\/span><span class=\"p\">,<\/span> <span class=\"mi\">37<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">):<\/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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">))<\/span>\r\n    <span class=\"n\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'\u03b8 = <\/span><span class=\"si\">%2d<\/span><span class=\"s1\">\u00b0'<\/span> <span class=\"o\">%<\/span> <span class=\"n\">th<\/span>\r\n    <span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/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=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/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\">\"X\"<\/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=\"s2\">\"Y\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"H = 0.2 \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u7740\u5730\u70b9\u4ed8\u8fd1\u3092\u62e1\u5927\u8868\u793a<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlim<\/span><span class=\"p\">(<\/span><span class=\"mf\">1.15<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.19<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylim<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.02<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\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-10046\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/axNhtosha06.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<p>\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f $\\theta=45^{\\circ}$ \u306e\u3068\u304d<strong>\u3067\u306f\u306a\u3044\uff01<\/strong>\u3053\u3068\u304c\u308f\u304b\u308b\u3060\u308d\u3046\u3002<\/p>\n<h3 id=\"\u6c34\u5e73\u5230\u9054\u8ddd\u96e2-$L$\">\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L$<\/h3>\n<p>\u5b9a\u91cf\u7684\u306b\u8abf\u3079\u308b\u305f\u3081\u306b\uff0c\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 <code>L(th, H)<\/code> \u3092\u30b0\u30e9\u30d5\u306b\u3057\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[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=\"n\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.2<\/span>\r\n<span class=\"n\">th_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=\"mi\">38<\/span><span class=\"p\">,<\/span> <span class=\"mi\">48<\/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\">th_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">th_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/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\">\"\u6253\u3061\u51fa\u3057\u89d2\u5ea6 (\u00b0)\"<\/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=\"s2\">\"\u898f\u683c\u5316\u3055\u308c\u305f\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"H = 0.2 \u306e\u5834\u5408\u306e\u6253\u3061\u51fa\u3057\u89d2\u5ea6\u3068\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2\u3092\u8abf\u6574\u3059\u308b<\/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\">38<\/span><span class=\"p\">,<\/span> <span class=\"mi\">48<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">38<\/span><span class=\"p\">,<\/span> <span class=\"mi\">48<\/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_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-10047\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/axNhtosha07.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<p>\u4e0a\u306e\u30b0\u30e9\u30d5\u3092\u307f\u308b\u3068\uff0c$H=0.2$ \u306e\u5834\u5408\u306b\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f $\\theta=45^{\\circ}$ \u306e\u3068\u304d\u3067\u306f\u306a\u304f&#8230; \u3069\u306e\u304f\u3089\u3044\uff1f<\/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=\"L-\u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u3092\u6570\u5024\u5fae\u5206\u3067\u6c42\u3081\u308b\">L \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u3092\u6570\u5024\u5fae\u5206\u3067\u6c42\u3081\u308b<\/h4>\n<p>\u6570\u5024\u5fae\u5206\u3057\u3066 $\\displaystyle \\frac{dL(\\theta, H)}{d\\theta} = 0$ \u3068\u306a\u308b\u89d2\u5ea6 $\\theta$ \u3092\u6c42\u3081\u3066\u307f\u308b\u3002<\/p>\n<p>$\\theta \\rightarrow x$ \u3068\u3057\u3066\uff0c<\/p>\n<p>$$\\frac{dL(x, H)}{dx} \\simeq \\frac{L(x + \\delta) &#8211; L(x &#8211; \\delta)}{2 \\delta}, \\quad |\\delta| &lt;&lt; 1$$<\/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\"># \u3068\u308a\u3042\u3048\u305a\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u3066\u304a\u304f\u3002<\/span>\r\n<span class=\"c1\"># \u6570\u5024\u5fae\u5206: delta \u306f\u5c0f\u3055\u3044\u307b\u3069\u3088\u3044\uff0c\u3068\u3044\u3046\u308f\u3051\u3067\u306f\u306a\u3044 <\/span>\r\n<span class=\"c1\"># scipy.optimize.root_scalar \u3092\u4f7f\u3046\u3068\u304d\u306f<\/span>\r\n<span class=\"c1\"># x \u306e\u95a2\u6570\u3068\u3057\u3066\u5b9a\u7fa9<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">dL<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">delta<\/span><span class=\"o\">=<\/span><span class=\"mf\">1e-5<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"p\">(<\/span><span class=\"n\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">+<\/span><span class=\"n\">delta<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">)<\/span> <span class=\"o\">-<\/span> <span class=\"n\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">-<\/span><span class=\"n\">delta<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">delta<\/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>$dL(x) = 0$ \u306e\u89e3\u3092 $x$ \u306b\u3064\u3044\u3066\u6570\u5024\u7684\u306b\u6c42\u3081\u308b\u306b\u306f\uff0c<code>scipy.optimize.root_scalar<\/code> \u3092\u4f7f\u3044\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[11]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.2<\/span>\r\n\r\n<span class=\"c1\"># delta \u304c\u30c7\u30d5\u30a9\u30eb\u30c8\u306e\u5834\u5408<\/span>\r\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"n\">root_scalar<\/span><span class=\"p\">(<\/span><span class=\"n\">dL<\/span><span class=\"p\">,<\/span> <span class=\"n\">bracket<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">38<\/span><span class=\"p\">,<\/span> <span class=\"mi\">48<\/span><span class=\"p\">],<\/span> <span class=\"n\">args<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">))<\/span><span class=\"o\">.<\/span><span class=\"n\">root<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># delta \u3092\u5909\u3048\u3066\u307f\u308b<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">delta<\/span> <span class=\"ow\">in<\/span> <span class=\"p\">[<\/span><span class=\"mf\">1.e-3<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.e-4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.e-5<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.e-6<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.e-7<\/span><span class=\"p\">]:<\/span>\r\n    <span class=\"c1\"># x \u4ee5\u5916\u306e\u5909\u6570\u306f args \u306b<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"n\">root_scalar<\/span><span class=\"p\">(<\/span><span class=\"n\">dL<\/span><span class=\"p\">,<\/span> <span class=\"n\">bracket<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">38<\/span><span class=\"p\">,<\/span> <span class=\"mi\">48<\/span><span class=\"p\">],<\/span> <span class=\"n\">args<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">delta<\/span><span class=\"p\">))<\/span><span class=\"o\">.<\/span><span class=\"n\">root<\/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>40.20296588835251\r\n40.2029658845539\r\n40.20296588569512\r\n40.20296588835251\r\n40.20296588448801\r\n40.20296551268753\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>\u4e0a\u306e\u7d50\u679c\u304b\u3089\uff0c<code>delta = 1.e-5<\/code> \u306b\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u95a2\u6570\u3092\u5b9a\u7fa9\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[12]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"k\">def<\/span> <span class=\"nf\">thm<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"sd\">\"\"\" \u9ad8\u3055 H \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u3067\u6700\u5927\u5230\u9054\u8ddd\u96e2\u306b\u306a\u308b\u89d2\u5ea6\uff08\u00b0\uff09<\/span>\r\n<span class=\"sd\">    \"\"\"<\/span>\r\n    <span class=\"n\">ans<\/span> <span class=\"o\">=<\/span> <span class=\"n\">root_scalar<\/span><span class=\"p\">(<\/span><span class=\"n\">dL<\/span><span class=\"p\">,<\/span> <span class=\"n\">bracket<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">89<\/span><span class=\"p\">],<\/span> <span class=\"n\">args<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">))<\/span><span class=\"o\">.<\/span><span class=\"n\">root<\/span>    \r\n    <span class=\"k\">return<\/span> <span class=\"n\">ans<\/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>\u5b9a\u7fa9\u3057\u305f <code>thm(H)<\/code> \u3092\u4f7f\u3063\u3066\uff0c<code>H = 0.2<\/code> \u306e\u3068\u304d\u306e\u6700\u5927\u5230\u9054\u8ddd\u96e2\u3068\u306a\u308b\u8ecc\u9053\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304d\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[13]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u4e0a\u306e\u7d50\u679c\u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u3092\u63cf\u304f<\/span>\r\n<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\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.2<\/span>\r\n\r\n<span class=\"c1\"># \u6642\u9593 T \u306e\u7bc4\u56f2\u3002\u6ede\u7a7a\u6642\u9593 T1 \u307e\u3067\u3002<\/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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">thm<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">),<\/span> <span class=\"n\">H<\/span><span class=\"p\">),<\/span> <span class=\"mi\">100<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u306e\u6570\u5024\u306e\u6841\u6570\u3092\u63c3\u3048\u308b<\/span>\r\n<span class=\"n\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'H=<\/span><span class=\"si\">%3.1f<\/span><span class=\"s1\">, \u03b8=<\/span><span class=\"si\">%6.3f<\/span><span class=\"s1\">\u00b0, Lmax=<\/span><span class=\"si\">%6.3f<\/span><span class=\"s1\">'<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">thm<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">),<\/span> <span class=\"n\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">thm<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">),<\/span> <span class=\"n\">H<\/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\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">thm<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">)),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">thm<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">),<\/span> <span class=\"n\">H<\/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\"># \u30b0\u30e9\u30d5\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b<\/span>\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\u30c9\u30c3\u30c8\u3067<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/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\">\"X\"<\/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=\"s2\">\"Y\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u9ad8\u3055 H \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u7e26\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=\"mf\">1.2<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylim<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.3<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_aspect<\/span><span class=\"p\">(<\/span><span class=\"s1\">'equal'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\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-10048\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/axNhtosha08.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<h3 id=\"\u25cb\u7df4\u7fd2\uff1a$H$-\u3092\u5909\u3048\u3066\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3092\u6c42\u3081\u308b\">\u25cb\u7df4\u7fd2\uff1a$H$ \u3092\u5909\u3048\u3066\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3092\u6c42\u3081\u308b<\/h3>\n<p>\u9ad8\u3055 $H$ \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u6253\u3061\u51fa\u3057\u89d2\u5ea6\u3068\uff0c\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u308f\u304b\u308b\u3088\u3046\u306a\u30b0\u30e9\u30d5\u3092\u6b21\u306e $H$ \u306b\u3064\u3044\u3066\u307e\u3068\u3081\u3066\u63cf\u3051\u3002<\/p>\n<p>$H = 0.2, 0.4, 0.6, 0.8, 1.0$<\/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[14]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">Hs<\/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=\"mf\">0.2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">Hs<\/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[14]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>array([0.2, 0.4, 0.6, 0.8, 1. ])<\/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[15]:<\/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<span class=\"c1\"># \u30b0\u30e9\u30d5\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b<\/span>\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\u30c9\u30c3\u30c8\u3067<\/span>\r\n...\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/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\">\"X\"<\/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=\"s2\">\"Y\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u9ad8\u3055 H \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u7e26\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=\"mf\">2.4<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylim<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.5<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_aspect<\/span><span class=\"p\">(<\/span><span class=\"s1\">'equal'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\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-10049\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/axNhtosha09.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<h3 id=\"\u25cb\u7df4\u7fd2\uff1a\u9ad8\u3055-$H$--\u3068\u6253\u3061\u51fa\u3057\u89d2\u5ea6-$\\theta_{\\rm-m}$-\u306e\u30b0\u30e9\u30d5\">\u25cb\u7df4\u7fd2\uff1a\u9ad8\u3055 $H$ \u3068\u6253\u3061\u51fa\u3057\u89d2\u5ea6 $\\theta_{\\rm m}$ \u306e\u30b0\u30e9\u30d5<\/h3>\n<p>\u9ad8\u3055 $H$ \u3092\u6a2a\u8ef8\u306b\uff0c\u305d\u306e\u3068\u304d\u306e\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u6253\u3061\u51fa\u3057\u89d2\u5ea6 $\\theta_{\\rm m}$ \u3092\u7e26\u8ef8\u306b\u3057\u305f\u30b0\u30e9\u30d5\u3092\u63cf\u3051\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[16]:<\/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\"># \u6a2a\u8ef8\u306f H<\/span>\r\n<span class=\"c1\"># (0, 1) \u533a\u9593<\/span>\r\n<span class=\"n\">...<\/span>\r\n\r\n<span class=\"c1\"># \u7e26\u8ef8\u306f thm(H)<\/span>\r\n...\r\n...\r\n\r\n<span class=\"c1\"># \u30b0\u30e9\u30d5\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b<\/span>\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\u30c9\u30c3\u30c8\u3067<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u6253\u3061\u51fa\u3057\u89d2\u5ea6\"<\/span><span class=\"p\">);<\/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\u9ad8\u3055 H\"<\/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=\"s2\">\"\u6253\u3061\u51fa\u3057\u89d2\u5ea6 (\u00b0)\"<\/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-10050\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/axNhtosha10.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<h3 id=\"\u25cb\u7df4\u7fd2\uff1a\u9ad8\u3055-$H$-\u3068\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2-$L_{\\rm-m}$-\u306e\u30b0\u30e9\u30d5\">\u25cb\u7df4\u7fd2\uff1a\u9ad8\u3055 $H$ \u3068\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L_{\\rm m}$ \u306e\u30b0\u30e9\u30d5<\/h3>\n<p>\u9ad8\u3055 $H$ \u3092\u6a2a\u8ef8\u306b\uff0c\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L_{\\rm m} = L(\\theta_{\\rm m}, H)$ \u3092\u7e26\u8ef8\u306b\u3057\u305f\u30b0\u30e9\u30d5\u3092\u63cf\u3051\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[17]:<\/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\">...\r\n...\r\n...\r\n\r\n\r\n# \u30b0\u30e9\u30d5\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b<\/span>\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\u30c9\u30c3\u30c8\u3067<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span><span class=\"p\">);<\/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\u9ad8\u3055 H\"<\/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=\"s2\">\"\u898f\u683c\u5316\u3055\u308c\u305f\u9ad8\u3055\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/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-10051\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/axNhtosha11.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<h3 id=\"\u25cb\u7df4\u7fd2\uff1a\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3092\u6c42\u3081\u308b\">\u25cb\u7df4\u7fd2\uff1a\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3092\u6c42\u3081\u308b<\/h3>\n<p>$h = 5\\,\\mbox{(m)}$ \u306e\u9ad8\u3055\u304b\u3089\u901f\u3055 $v_0 = 10\\,\\mbox{(m\/s)}$ \u3067\u659c\u65b9\u6295\u5c04\u3057\u305f\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u306f\u4f55 $\\mbox{m}$ \u304b\u3002\u307e\u305f\u305d\u306e\u3068\u304d\u306e\u6253\u51fa\u3057\u89d2\u5ea6\u306f\u4f55\u5ea6\u304b\u3002<\/p>\n<p>\u30d2\u30f3\u30c8\uff1a<\/p>\n<p>$h = 5\\,\\mbox{(m)}$ \u306f\u898f\u683c\u5316\u3055\u308c\u305f\u9ad8\u3055 $H$ \u3067\u306f\u3044\u304f\u3089\u304b\uff0c\u307e\u305f\u898f\u683c\u5316\u3055\u308c\u305f\u6700\u5927\u5230\u9054\u8ddd\u96e2 $L_{\\rm max}(H)$ \u3092\u6b21\u5143\u3092\u3082\u3063\u305f\u91cf\u306b\u76f4\u3059\u3068\u3044\u304f\u3089\u304b\uff0c\u3068\u3044\u3046\u3053\u3068\u3002<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\ell &amp;=&amp; \\frac{v_0^2}{g} \\\\<br \/>\nH &amp;=&amp; \\frac{h}{\\ell} = \\frac{g h}{v_0^2} \\\\<br \/>\nx &amp;=&amp; \\ell X = \\frac{v_0^2}{g} X \\\\<br \/>\nx_{\\rm max} &amp;=&amp; \\frac{v_0^2}{g} L_{\\rm max}(H)<br \/>\n\\end{eqnarray}<\/p>\n<p>\u91cd\u529b\u52a0\u901f\u5ea6 $g = 9.80665 \\,(\\mbox{m}\/\\mbox{s}^2)$<\/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[18]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">h<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">5<\/span>\r\n<span class=\"n\">v0<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">10<\/span>\r\n<span class=\"n\">g<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">9.80665<\/span>\r\n\r\n...\r\n...\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_subarea output_stream output_stdout output_text\">\n<pre>\u9ad8\u3055 h =  5 m \u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u306f **.****** m\r\n\u305d\u306e\u3068\u304d\u306e\u6253\u3061\u51fa\u3057\u89d2\u5ea6\u306f **.******\u00b0\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5730\u9762\u304b\u3089\u9ad8\u3055 $h$ \u306e\u5730\u70b9\u304b\u3089\u7a7a\u6c17\u62b5\u6297\u306a\u3057\u306e\u659c\u65b9\u6295\u5c04\u3092\u884c\u3046\u3068\uff0c\u521d\u901f\u5ea6\u306e\u5927\u304d\u3055\u3092\u4e00\u5b9a\u3068\u3057\u305f\u5834\u5408\uff0c\u6c34\u5e73\u65b9\u5411\u306e\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f\u6253\u3061\u4e0a\u3052\u89d2\u5ea6\uff08\u4ef0\u89d2\uff09\u304c\u4f55\u5ea6\u306e\u3068\u304d\u304b\u3092 Python \u306e SciPy \u3068 NumPy \u3092\u4f7f\u3063\u3066\uff08\u304b\u3064 SymPy \u3092\u4f7f\u308f\u305a\u306b\uff09\u6c42\u3081\u308b\u3002<\/p>\n<p>Python \u306e Matplotlib \u306b\u3088\u308b\u30b0\u30e9\u30d5\u4f5c\u6210\u306b\u306f\uff0cplt.*** \u3068\u3044\u3046\u95a2\u6570\u306e\u307f\u3092\u4f7f\u3063\u305f plt (pyplot) \u6d41\uff08pyplot \u30a4\u30f3\u30bf\u30fc\u30d5\u30a7\u30fc\u30b9\u3068\u3082\uff09\u3068\uff0cax.*** \u3068\u3044\u3046\u95a2\u6570\u306e\u307f\u3092\u4f7f\u3063\u305f ax \u6d41\uff08\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u6307\u5411\u30a4\u30f3\u30bf\u30fc\u30d5\u30a7\u30fc\u30b9\u3068\u3082\uff09\u306e2\u3064\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u306f ax.*** \u306e\u307f\u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n<p>ax.*** \u306e\u307f\u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u3092\u4f5c\u6210\u3059\u308b\u65b9\u6cd5\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u306b\u307e\u3068\u3081\u3066\u3044\u307e\u3059\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\/%e9%ab%98%e3%81%95-h-%e3%81%8b%e3%82%89%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%81%ae%e6%9c%80%e5%a4%a7%e5%88%b0%e9%81%94%e8%b7%9d%e9%9b%a2%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e6%ba%96\/scipy-%e3%81%a7%e9%ab%98%e3%81%95-h-%e3%81%8b%e3%82%89%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%81%ae%e6%9c%80%e5%a4%a7%e5%88%b0%e9%81%94%e8%b7%9d%e9%9b%a2%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b\/\">\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":5052,"menu_order":30,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-5093","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\/5093","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=5093"}],"version-history":[{"count":14,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/5093\/revisions"}],"predecessor-version":[{"id":10053,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/5093\/revisions\/10053"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/5052"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=5093"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}