{"id":5066,"date":"2023-12-18T10:40:48","date_gmt":"2023-12-18T01:40:48","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=5066"},"modified":"2023-12-18T10:42:05","modified_gmt":"2023-12-18T01:42:05","slug":"maxima-%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\/%e5%8f%82%e8%80%83%ef%bc%9amaxima-%e7%b7%a8\/maxima-%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":"Maxima \u3067\u9ad8\u3055 h \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u5230\u9054\u8ddd\u96e2\u3092\u6c42\u3081\u308b"},"content":{"rendered":"<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>\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u89e3\u3092\u66f8\u304f\u3068<\/p>\n<p>\\begin{eqnarray}<br \/>\nX &amp;=&amp; \\cos\\theta\\cdot T \\\\<br \/>\nY &amp;=&amp; H+ \\sin\\theta\\cdot T \u2013 \\frac{1}{2} T^2 \\\\<br \/>\n\\end{eqnarray}<\/p>\n<p>\u6ede\u7a7a\u6642\u9593 $T_1$ \u306f<\/p>\n<p>$$T_1 = \\sin\\theta + \\sqrt{\\sin^2\\theta + 2 H}$$<\/p>\n<p>\u3053\u306e\u6642\u9593\u3067\u306e\u6c34\u5e73\u65b9\u5411\u306e\u5230\u9054\u8ddd\u96e2 $L$ \u306f<\/p>\n<p>$$L = X(T_1) = \\cos\\theta\\cdot T_1$$<\/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 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-maxima\">\n<pre><span class=\"cm\">\/* \u5ea6\u3092\u30e9\u30b8\u30a2\u30f3\u306b\u5909\u63db\u3059\u308b\u95a2\u6570\u3092\u6e96\u5099\u3057\u3066\u304a\u304f *\/<\/span>\r\n<span class=\"nf\">radians<\/span><span class=\"p\">(<\/span><span class=\"nv\">deg<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">deg<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span>180$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u89d2\u5ea6 th \u306f\u5ea6\u3067 *\/<\/span>\r\n<span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">T<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nf\">radians<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span><span class=\"p\">))<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">T<\/span>;\r\n<span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">T<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">H<\/span> <span class=\"o\">+<\/span> <span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nf\">radians<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span><span class=\"p\">))<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">T<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">T<\/span><span class=\"o\">**<\/span>2<span class=\"o\">\/<\/span><span class=\"mi\">2<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[2]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{2}$}X\\left({\\it th} , T\\right):=\\cos {\\it radians}\\left({\\it th}\\right)\\,T\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[2]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{3}$}Y\\left({\\it th} , T , H\\right):=H+\\sin {\\it radians}\\left({\\it th}\\right)\\,T+\\frac{-T^2}{2}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nf\">radians<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span><span class=\"p\">))<\/span> <span class=\"o\">+<\/span> <span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nf\">radians<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span><span class=\"p\">))<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">2<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">H<\/span><span class=\"p\">)<\/span>;\r\n<span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nf\">radians<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span><span class=\"p\">))<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[3]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{4}$}T_{1}\\left({\\it th} , H\\right):=\\sin {\\it radians}\\left({\\it th}\\right)+\\sqrt{\\sin ^2{\\it radians}\\left({\\it th}\\right)+2\\,H}\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[3]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{5}$}L\\left({\\it th} , H\\right):=\\cos {\\it radians}\\left({\\it th}\\right)\\,T_{1}\\left({\\it th} , H\\right)\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"$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<\/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-maxima\">\n<pre><span class=\"cm\">\/* \u03b8 = 45\u00b0 \u306e\u30b0\u30e9\u30d5\u306e\u307f *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u591a\u3081\u306b *\/<\/span>\r\n  <span class=\"nv\">nticks<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>, \r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/span>,\r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 1<span class=\"o\">.<\/span>1<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  \r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u03b8 = 45\u00b0\"<\/span>, <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>, \r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"mi\">45<\/span>,<span class=\"nv\">T<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"mi\">45<\/span>,<span class=\"nv\">T<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"mi\">45<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">))<\/span>\r\n<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-5067\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mhtosha01.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\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[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u8907\u6570\u306e\u30b0\u30e9\u30d5\u3092\u4e00\u5ea6\u306b\u63cf\u304f\u5834\u5408\u306f... *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u591a\u3081\u306b *\/<\/span>\r\n  <span class=\"nv\">nticks<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>, \r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/span>,\r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 1<span class=\"o\">.<\/span>1<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  \r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u03b8 = 47\u00b0\"<\/span>, <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>, \r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"mi\">47<\/span>,<span class=\"nv\">T<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"mi\">47<\/span>,<span class=\"nv\">T<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"mi\">47<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">))<\/span>,\r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u03b8 = 46\u00b0\"<\/span>, <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>, \r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"mi\">46<\/span>,<span class=\"nv\">T<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"mi\">46<\/span>,<span class=\"nv\">T<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"mi\">46<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">))<\/span>,\r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u03b8 = 45\u00b0\"<\/span>, <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>, \r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"mi\">45<\/span>,<span class=\"nv\">T<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"mi\">45<\/span>,<span class=\"nv\">T<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"mi\">45<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">))<\/span>,\r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u03b8 = 44\u00b0\"<\/span>, <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">4<\/span>, \r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"mi\">44<\/span>,<span class=\"nv\">T<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"mi\">44<\/span>,<span class=\"nv\">T<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"mi\">44<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">))<\/span>,\r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u03b8 = 43\u00b0\"<\/span>, <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">5<\/span>, \r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"mi\">43<\/span>,<span class=\"nv\">T<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"mi\">43<\/span>,<span class=\"nv\">T<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"mi\">43<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">))<\/span>\r\n<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-5068\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mhtosha02.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\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-maxima\">\n<pre><span class=\"cm\">\/* \u6700\u521d\u306b makelist \u3067\u4f5c\u3063\u3066\u304a\u304f\u3068\u3044\u3044\u304b\u3082 *\/<\/span>\r\n<span class=\"nv\">lines<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">([<\/span><span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">concat<\/span><span class=\"p\">(<\/span><span class=\"s\">\"\u03b8 = \"<\/span>, 48<span class=\"o\">-<\/span><span class=\"nv\">i<\/span><span class=\"p\">)<\/span>,\r\n                 <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">i<\/span>, \r\n                 <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span>48<span class=\"o\">-<\/span><span class=\"nv\">i<\/span>,<span class=\"nv\">T<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span>48<span class=\"o\">-<\/span><span class=\"nv\">i<\/span>,<span class=\"nv\">T<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span>48<span class=\"o\">-<\/span><span class=\"nv\">i<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">))]<\/span>, \r\n                <span class=\"nv\">i<\/span>, <span class=\"mi\">1<\/span>, <span class=\"mi\">5<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u591a\u3081\u306b *\/<\/span>\r\n  <span class=\"nv\">nticks<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>, \r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/span>,\r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 1<span class=\"o\">.<\/span>1<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n\r\n  <span class=\"nv\">lines<\/span>\r\n<span class=\"p\">)<\/span>$\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-5069\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mhtosha03.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\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-maxima\">\n<pre><span class=\"cm\">\/* \u7740\u5730\u70b9\u4ed8\u8fd1\u3092\u62e1\u5927\u8868\u793a\u3057\u3066 45\u00b0 \u304c\u6700\u5927\u5230\u9054\u8ddd\u96e2\u3068\u306a\u308b\u3053\u3068\u3092\u78ba\u8a8d *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u591a\u3081\u306b *\/<\/span>\r\n  <span class=\"nv\">nticks<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1000<\/span>, \r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2\u3092\u8abf\u6574\u3059\u308b *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mf\">0.996<\/span>, 1<span class=\"o\">.<\/span>002<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>001<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n\r\n  <span class=\"nv\">lines<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-5070\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mhtosha04.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"$H-=-0.1$-\u306e\u5834\u5408\u306e\u8ecc\u9053\">$H = 0.1$ \u306e\u5834\u5408\u306e\u8ecc\u9053<\/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[8]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">H<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>1$\r\n<span class=\"nv\">lines1<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">([<\/span><span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">concat<\/span><span class=\"p\">(<\/span><span class=\"s\">\"\u03b8 = \"<\/span>, 48<span class=\"o\">-<\/span><span class=\"nv\">i<\/span><span class=\"p\">)<\/span>,\r\n                 <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">i<\/span>, \r\n                 <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span>48<span class=\"o\">-<\/span><span class=\"nv\">i<\/span>,<span class=\"nv\">T<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span>48<span class=\"o\">-<\/span><span class=\"nv\">i<\/span>,<span class=\"nv\">T<\/span>,<span class=\"nv\">H<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span>48<span class=\"o\">-<\/span><span class=\"nv\">i<\/span>,<span class=\"nv\">H<\/span><span class=\"p\">))]<\/span>, \r\n                <span class=\"nv\">i<\/span>, <span class=\"mi\">1<\/span>, <span class=\"mi\">10<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u591a\u3081\u306b *\/<\/span>\r\n  <span class=\"nv\">nticks<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>, \r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/span>,\r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 1<span class=\"o\">.<\/span>2<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>6<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n\r\n  <span class=\"nv\">lines1<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-5071\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mhtosha05.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u7740\u5730\u70b9\u4ed8\u8fd1\u3092\u62e1\u5927\u8868\u793a *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u591a\u3081\u306b *\/<\/span>\r\n  <span class=\"nv\">nticks<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1000<\/span>, \r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2\u3092\u8abf\u6574\u3059\u308b *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mf\">1.08<\/span>, 1<span class=\"o\">.<\/span>1<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>001<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n\r\n  <span class=\"nv\">lines1<\/span>\r\n<span class=\"p\">)<\/span>$\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-5072\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mhtosha06.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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[10]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">H<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>1$\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">font<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Arial\"<\/span>, <span class=\"nv\">font_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">14<\/span>, \r\n  <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>, \r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u6253\u3061\u51fa\u3057\u89d2\u5ea6 (\u00b0)\"<\/span>, <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u898f\u683c\u5316\u3055\u308c\u305f\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span>,\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">concat<\/span><span class=\"p\">(<\/span><span class=\"s\">\"H = \"<\/span>, <span class=\"nv\">H<\/span>, <span class=\"s\">\"\u306e\u5834\u5408\u306e\u6253\u3061\u51fa\u3057\u89d2\u5ea6\u3068\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span><span class=\"p\">)<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">th<\/span>, <span class=\"mi\">38<\/span>, <span class=\"mi\">48<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\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-5084\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mhtosha07a.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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=\"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<\/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-maxima\">\n<pre><span class=\"cm\">\/* \u6570\u5024\u5fae\u5206: h \u306f\u5c0f\u3055\u3044\u307b\u3069\u3088\u3044\uff0c\u3068\u3044\u3046\u308f\u3051\u3067\u306f\u306a\u3044 *\/<\/span>\r\n<span class=\"nf\">dL<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">h<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"p\">(<\/span><span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span><span class=\"o\">+<\/span><span class=\"nv\">h<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">)<\/span> <span class=\"o\">-<\/span> <span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span><span class=\"o\">-<\/span><span class=\"nv\">h<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span>2<span class=\"o\">*<\/span><span class=\"nv\">h<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[12]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3 *\/<\/span>\r\n<span class=\"nv\">fpprintprec<\/span><span class=\"o\">:<\/span> 0$\r\n<span class=\"nv\">H<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>1$\r\n<span class=\"cm\">\/* h \u3092\u5909\u3048\u3066\u307f\u308b *\/<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"nv\">h<\/span> <span class=\"nv\">in<\/span> <span class=\"p\">[<\/span><span class=\"mf\">1.e-3<\/span>, <span class=\"mf\">1.e-4<\/span>, <span class=\"mf\">1.e-5<\/span>, <span class=\"mf\">1.e-6<\/span>, 1<span class=\"o\">.<\/span><span class=\"nv\">e<\/span><span class=\"o\">-<\/span>7<span class=\"p\">]<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nf\">print<\/span><span class=\"p\">(<\/span><span class=\"nf\">find_root<\/span><span class=\"p\">(<\/span><span class=\"nf\">dL<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">h<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"nv\">th<\/span>, <span class=\"mi\">38<\/span>, <span class=\"mi\">48<\/span><span class=\"p\">))<\/span>\r\n<span class=\"p\">)<\/span>$\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_latex output_subarea \">\\(42.39204571350186\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(42.39204571469371\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(42.39204572066672\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(42.39204581678321\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(42.39204550128903\\)<\/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[13]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3 *\/<\/span>\r\n<span class=\"nv\">H<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>1$\r\n<span class=\"nv\">thmax<\/span><span class=\"o\">:<\/span> \r\n<span class=\"nf\">find_root<\/span><span class=\"p\">(<\/span><span class=\"nf\">dL<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H<\/span>, <span class=\"mf\">1e-5<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"nv\">th<\/span>, <span class=\"mi\">38<\/span>, <span class=\"mi\">48<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>,<span class=\"s\">\"H = ~3,1f \u306e\u3068\u304d\uff0cL \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u306f ~9,6f \u00b0~%\"<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">thmax<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>,<span class=\"s\">\"    \u6700\u5927\u5230\u9054\u8ddd\u96e2\u306f ~9,6f\"<\/span>, <span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"nv\">thmax<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">))<\/span>$\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_subarea output_stream output_stdout output_text\">\n<pre>H = 0.1 \u306e\u3068\u304d\uff0cL \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u306f 42.392046 \u00b0\r\n    \u6700\u5927\u5230\u9054\u8ddd\u96e2\u306f  1.095445<\/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=\"L-\u304c\u6700\u5927\u5024\u3068\u306a\u308b\u89d2\u5ea6\u3092\u89e3\u6790\u7684\u5fae\u5206\u3067\u6c42\u3081\u308b\">L \u304c\u6700\u5927\u5024\u3068\u306a\u308b\u89d2\u5ea6\u3092\u89e3\u6790\u7684\u5fae\u5206\u3067\u6c42\u3081\u308b<\/h4>\n<p>$u \\equiv \\tan\\theta$ \u3068\u3057\u3066\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L$ \u3092 $u$ \u3067\u8868\u3059\u3068<\/p>\n<p>\\begin{eqnarray}<br \/>\nL(u, H)<br \/>\n&amp;=&amp; \\frac{1}{1+u^2} \\left\\{u + \\sqrt{(1+2H) u^2 + 2H} \\right\\}<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[14]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">kill<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">Lu<\/span><span class=\"p\">(<\/span><span class=\"nv\">u<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> 1<span class=\"o\">\/<\/span><span class=\"p\">(<\/span>1<span class=\"o\">+<\/span><span class=\"nv\">u<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"p\">(<\/span><span class=\"nv\">u<\/span><span class=\"o\">+<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">((<\/span>1<span class=\"o\">+<\/span>2<span class=\"o\">*<\/span><span class=\"nv\">H<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"nv\">u<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> 2<span class=\"o\">*<\/span><span class=\"nv\">H<\/span><span class=\"p\">))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[14]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{26}$}{\\it Lu}\\left(u , H\\right):=\\frac{1}{1+u^2}\\,\\left(u+\\sqrt{\\left(1+2\\,H\\right)\\,u^2+2\\,H}\\right)\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[15]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* u \u306b\u95a2\u3059\u308b\u5fae\u5206\u3092\u89e3\u6790\u7684\u306b *\/<\/span>\r\n<span class=\"nf\">define<\/span><span class=\"p\">(<\/span><span class=\"nf\">dLu<\/span><span class=\"p\">(<\/span><span class=\"nv\">u<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">diff<\/span><span class=\"p\">(<\/span><span class=\"nf\">Lu<\/span><span class=\"p\">(<\/span><span class=\"nv\">u<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">u<\/span><span class=\"p\">))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[15]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{27}$}{\\it dLu}\\left(u , H\\right):=\\frac{\\frac{\\left(2\\,H+1\\right)\\,u}{\\sqrt{\\left(2\\,H+1\\right)\\,u^2+2\\,H}}+1}{u^2+1}-\\frac{2\\,u\\,\\left(\\sqrt{\\left(2\\,H+1\\right)\\,u^2+2\\,H}+u\\right)}{\\left(u^2+1\\right)^2}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[16]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u30e9\u30b8\u30a2\u30f3\u3092\u5ea6\u306b\u5909\u63db\u3059\u308b\u95a2\u6570\u3082\u6e96\u5099\u3057\u3066\u304a\u304f *\/<\/span>\r\n<span class=\"nf\">degrees<\/span><span class=\"p\">(<\/span><span class=\"nv\">theta<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">theta<\/span><span class=\"o\">*<\/span>180<span class=\"o\">\/<\/span><span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* \u5fae\u5206\u304c\u30bc\u30ed\u3068\u306a\u308b u \u306f\u6570\u5024\u7684\u306b\u6c42\u3081\u308b *\/<\/span>\r\n<span class=\"nv\">H<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>1$\r\n<span class=\"nv\">ans<\/span><span class=\"o\">:<\/span> <span class=\"nf\">find_root<\/span><span class=\"p\">(<\/span><span class=\"nf\">dLu<\/span><span class=\"p\">(<\/span><span class=\"nv\">u<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"nv\">u<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mf\">1.2<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nv\">thmax<\/span><span class=\"o\">:<\/span> <span class=\"nf\">degrees<\/span><span class=\"p\">(<\/span><span class=\"nf\">atan<\/span><span class=\"p\">(<\/span><span class=\"nv\">ans<\/span><span class=\"p\">))<\/span>$\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>,<span class=\"s\">\"H = ~3,1f \u306e\u3068\u304d\uff0cL \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u306f ~15,12f \u00b0~%\"<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">thmax<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>,<span class=\"s\">\"    \u6700\u5927\u5230\u9054\u8ddd\u96e2\u306f ~15,12f\"<\/span>, <span class=\"nf\">Lu<\/span><span class=\"p\">(<\/span><span class=\"nv\">ans<\/span>, <span class=\"nv\">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_subarea output_stream output_stdout output_text\">\n<pre>H = 0.1 \u306e\u3068\u304d\uff0cL \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u306f 42.392045714773 \u00b0\r\n    \u6700\u5927\u5230\u9054\u8ddd\u96e2\u306f  1.095445115010<\/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[17]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u4e0a\u306e\u7d50\u679c\u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u3092\u63cf\u304f *\/<\/span>\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">font<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Arial\"<\/span>, <span class=\"nv\">font_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">14<\/span>, \r\n  <span class=\"cm\">\/* \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u591a\u3081\u306b *\/<\/span>\r\n  <span class=\"nv\">nticks<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>, \r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/span>,\r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 1<span class=\"o\">.<\/span>2<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"X\"<\/span>, <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Y\"<\/span>,\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u9ad8\u3055 H \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span>,\r\n  \r\n  <span class=\"cm\">\/* \u6570\u5024\u3092\u53d6\u308a\u8fbc\u3093\u3060\u51e1\u4f8b\u306e\u8a2d\u5b9a\u4f8b *\/<\/span>\r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> \r\n    <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">false<\/span>,<span class=\"s\">\"H = ~3,1f, \u03b8 = ~5,2f\u00b0, Lmax = ~5,3f\"<\/span>,<span class=\"nv\">H<\/span>,<span class=\"nv\">thmax<\/span>,<span class=\"nf\">Lu<\/span><span class=\"p\">(<\/span><span class=\"nv\">ans<\/span>,<span class=\"nv\">H<\/span><span class=\"p\">))<\/span>,\r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"nv\">thmax<\/span>, <span class=\"nv\">T<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">thmax<\/span>, <span class=\"nv\">T<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"nv\">thmax<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">))<\/span>\r\n<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-5074\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mhtosha08.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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=\"\u554f\u984c-1\">\u554f\u984c 1<\/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[18]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">Hl<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span><span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nv\">i<\/span><span class=\"o\">\/<\/span><span class=\"mi\">10<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">i<\/span>, <span class=\"mi\">2<\/span>, <span class=\"mi\">10<\/span>, <span class=\"mi\">2<\/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[18]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{35}$}\\left[ 0.2 , 0.4 , 0.6 , 0.8 , 1.0 \\right] \\]<\/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=\"\u89e3\u7b54\u4f8b\">\u89e3\u7b54\u4f8b<\/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[19]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5ff5\u306e\u305f\u3081 *\/<\/span> <span class=\"nf\">kill<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* \u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u3092\u8ffd\u52a0\u3059\u308b\u30ea\u30b9\u30c8 *\/<\/span>\r\n<span class=\"nv\">thml<\/span><span class=\"o\">:<\/span><span class=\"p\">[]<\/span>$\r\n<span class=\"nv\">ansl<\/span><span class=\"o\">:<\/span><span class=\"p\">[]<\/span>$\r\n\r\n<span class=\"k\">for<\/span> <span class=\"nv\">H<\/span> <span class=\"nv\">in<\/span> <span class=\"nv\">Hl<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">ans<\/span><span class=\"o\">:<\/span> <span class=\"nf\">find_root<\/span><span class=\"p\">(<\/span><span class=\"nf\">dLu<\/span><span class=\"p\">(<\/span><span class=\"nv\">u<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"nv\">u<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mf\">1.2<\/span><span class=\"p\">)<\/span>, \r\n  <span class=\"nv\">thmax<\/span><span class=\"o\">:<\/span> <span class=\"nf\">degrees<\/span><span class=\"p\">(<\/span><span class=\"nf\">atan<\/span><span class=\"p\">(<\/span><span class=\"nv\">ans<\/span><span class=\"p\">))<\/span>, \r\n  <span class=\"nv\">thml<\/span><span class=\"o\">:<\/span> <span class=\"nf\">append<\/span><span class=\"p\">(<\/span><span class=\"nv\">thml<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">thmax<\/span><span class=\"p\">])<\/span>, \r\n  <span class=\"nv\">ansl<\/span><span class=\"o\">:<\/span> <span class=\"nf\">append<\/span><span class=\"p\">(<\/span><span class=\"nv\">ansl<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">ans<\/span><span class=\"p\">])<\/span>\r\n<span class=\"p\">)<\/span>$\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[20]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5148\u306b\u63cf\u304f\u7dda\u3092\u30ea\u30b9\u30c8\u306b\u3057\u3066\u304a\u304f *\/<\/span>\r\n<span class=\"nv\">lines<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"p\">[<\/span><span class=\"nv\">color<\/span><span class=\"o\">=<\/span><span class=\"nv\">i<\/span>, \r\n   <span class=\"nv\">key<\/span><span class=\"o\">=<\/span><span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">false<\/span>, \r\n     <span class=\"s\">\"H = ~3,1f, \u03b8 = ~6,3f\u00b0, Lmax = ~5,3f\"<\/span>, <span class=\"nv\">Hl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>,<span class=\"nv\">thml<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nf\">Lu<\/span><span class=\"p\">(<\/span><span class=\"nv\">ansl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">Hl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]))<\/span>,\r\n   <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"nv\">thml<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">T<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">thml<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">T<\/span>, <span class=\"nv\">Hl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">])<\/span>, <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"nv\">thml<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">Hl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]))]<\/span>, \r\n  <span class=\"nv\">i<\/span>, <span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">Hl<\/span><span class=\"p\">)<\/span>, <span class=\"mi\">1<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">1<\/span>\r\n<span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">font<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Arial\"<\/span>, <span class=\"nv\">font_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">14<\/span>, \r\n  <span class=\"nv\">user_preamble<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"set key samplen 1;\"<\/span>,\r\n  <span class=\"cm\">\/* \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u591a\u3081\u306b *\/<\/span>\r\n  <span class=\"nv\">nticks<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>, \r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/span>,\r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 2<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 1<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"X\"<\/span>, <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Y\"<\/span>,\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u9ad8\u3055 H \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span>,\r\n  \r\n  <span class=\"nv\">lines<\/span>\r\n<span class=\"p\">)<\/span>$\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-5075\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mhtosha09.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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=\"\u554f\u984c-2\">\u554f\u984c 2<\/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 $\\theta$ \u3092\u7e26\u8ef8\u306b\u3057\u305f\u30b0\u30e9\u30d5\u3092\u63cf\u3051\u3002<\/p>\n<h4 id=\"\u89e3\u7b54\u4f8b\">\u89e3\u7b54\u4f8b<\/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[21]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u30ea\u30b9\u30c8 Hl \u3092\u6a2a\u8ef8\uff0cthml \u3092\u7e26\u8ef8\u306b *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nf\">points<\/span><span class=\"p\">(<\/span><span class=\"nv\">Hl<\/span>, <span class=\"nv\">thml<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-5076\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mhtosha10.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e\u307e\u307e\u3060\u3068\uff0c\u3042\u307e\u308a\u306b\u30b7\u30e7\u30dc\u3044\u306e\u3067\uff0c$H$ \u3092\u4e0e\u3048\u308b\u3068\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u6253\u3061\u51fa\u3057\u89d2\u5ea6 $\\theta$ \u3092\u4e0e\u3048\u308b\u95a2\u6570\u3092\u4f5c\u6210\u3057\uff0c\u967d\u95a2\u6570\u3068\u3057\u3066\u66f2\u7dda\u306e\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[22]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5ff5\u306e\u305f\u3081 *\/<\/span> <span class=\"nf\">kill<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">thetamax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">block<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nf\">assume<\/span><span class=\"p\">(<\/span><span class=\"nv\">u<\/span> <span class=\"o\">&gt;<\/span> <span class=\"mi\">0<\/span><span class=\"p\">)<\/span>, <span class=\"cm\">\/* H=0 \u306e\u5834\u5408\u3092\u89e3\u304f\u969b\u306b\u5fc5\u8981 *\/<\/span>\r\n  <span class=\"nv\">ans<\/span><span class=\"o\">:<\/span> <span class=\"nf\">find_root<\/span><span class=\"p\">(<\/span><span class=\"nf\">dLu<\/span><span class=\"p\">(<\/span><span class=\"nv\">u<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"nv\">u<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mf\">1.2<\/span><span class=\"p\">)<\/span>,\r\n  <span class=\"nf\">return<\/span><span class=\"p\">(<\/span><span class=\"nf\">degrees<\/span><span class=\"p\">(<\/span><span class=\"nf\">atan<\/span><span class=\"p\">(<\/span><span class=\"nv\">ans<\/span><span class=\"p\">)))<\/span>\r\n<span class=\"p\">)<\/span>$\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[23]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">font<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Arial\"<\/span>, <span class=\"nv\">font_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">14<\/span>, \r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 1<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">25<\/span>, 45<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u898f\u683c\u5316\u3055\u308c\u305f\u9ad8\u3055 H\"<\/span>, <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u89d2\u5ea6 (\u00b0)\"<\/span>,\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u9ad8\u3055 H \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3092\u6700\u5927\u306b\u3059\u308b\u6253\u51fa\u3057\u89d2\u5ea6\"<\/span>,\r\n  \r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">thetamax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">H<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>\r\n<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-5077\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mhtosha11.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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=\"\u53c2\u8003\uff1a\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u306b\u306a\u308b\u89d2\u5ea6\">\u53c2\u8003\uff1a\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u306b\u306a\u308b\u89d2\u5ea6<\/h4>\n<p>\u5b9f\u306f<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/4109\/#i-5\">\u5225\u30da\u30fc\u30b8<\/a>\u3067\u66f8\u3044\u3066\u3044\u308b\u3088\u3046\u306b\uff0c\u898f\u683c\u5316\u3055\u308c\u305f\u9ad8\u3055 $H$ \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\uff0c\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6 $\\theta_{\\rm max}$ \u306f\uff0c\u4ee5\u4e0b\u306e\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u3002<\/p>\n<p>$$\\theta_{\\rm max} = \\arctan \\frac{1}{\\sqrt{1+2H}}$$<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/4109\/\">\u9ad8\u3055 h \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u5230\u9054\u8ddd\u96e2\u306f\u89d2\u5ea645\u00b0\u306e\u3068\u304d\u3067\u306f\u306a\u3044<\/a>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/4109\/#i-5\">\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u306b\u306a\u308b\u89d2\u5ea6<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u3042\u3048\u30662\u3064\u306e\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3068\uff0c\u5b8c\u5168\u306b\u91cd\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3067\u3042\u308d\u3046\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=\"\u554f\u984c-3\">\u554f\u984c 3<\/h3>\n<p>\u9ad8\u3055 $H$ \u3092\u6a2a\u8ef8\u306b\uff0c\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3092\u7e26\u8ef8\u306b\u3057\u305f\u30b0\u30e9\u30d5\u3092\u63cf\u3051\u3002<\/p>\n<h4 id=\"\u89e3\u7b54\u4f8b\">\u89e3\u7b54\u4f8b<\/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[24]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5c0f\u6570\u70b9\u8868\u793a\u30924\u6841\u306b *\/<\/span>\r\n<span class=\"nv\">fpprintprec<\/span><span class=\"o\">:<\/span> 4$\r\n<span class=\"nv\">Lumaxl<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span><span class=\"nf\">Lu<\/span><span class=\"p\">(<\/span><span class=\"nv\">ansl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">Hl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">])<\/span>, <span class=\"nv\">i<\/span>, <span class=\"mi\">1<\/span>, <span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">Hl<\/span><span class=\"p\">))<\/span>$\r\n\r\n<span class=\"cm\">\/* \u30ea\u30b9\u30c8 Lumax \u306e\u8981\u7d20\u30921\u3064\u305a\u3064\u8868\u793a *\/<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"nv\">Lumax<\/span> <span class=\"nv\">in<\/span> <span class=\"nv\">Lumaxl<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nf\">print<\/span><span class=\"p\">(<\/span><span class=\"nv\">Lumax<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(1.183\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(1.342\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(1.483\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(1.612\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(1.732\\)<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[25]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u30ea\u30b9\u30c8 Hl \u3092\u6a2a\u8ef8\uff0cLumaxl \u3092\u7e26\u8ef8\u306b *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nf\">points<\/span><span class=\"p\">(<\/span><span class=\"nv\">Hl<\/span>, <span class=\"nv\">Lumaxl<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\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-5078\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mhtosha12.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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>\u3053\u306e\u307e\u307e\u3060\u3068\uff0c\u3042\u307e\u308a\u306b\u30b7\u30e7\u30dc\u3044\u306e\u3067\uff0c$H$ \u3092\u4e0e\u3048\u308b\u3068\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3092\u4e0e\u3048\u308b\u95a2\u6570\u3092\u4f5c\u6210\u3057\uff0c\u967d\u95a2\u6570\u3068\u3057\u3066\u66f2\u7dda\u306e\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[26]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">Lmax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">block<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nf\">assume<\/span><span class=\"p\">(<\/span><span class=\"nv\">u<\/span> <span class=\"o\">&gt;<\/span> <span class=\"mi\">0<\/span><span class=\"p\">)<\/span>, <span class=\"cm\">\/* H=0 \u306e\u5834\u5408\u3092\u89e3\u304f\u969b\u306b\u5fc5\u8981 *\/<\/span>\r\n  <span class=\"nv\">ans<\/span><span class=\"o\">:<\/span> <span class=\"nf\">find_root<\/span><span class=\"p\">(<\/span><span class=\"nf\">dLu<\/span><span class=\"p\">(<\/span><span class=\"nv\">u<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"nv\">u<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mf\">1.2<\/span><span class=\"p\">)<\/span>,\r\n  <span class=\"nf\">return<\/span><span class=\"p\">(<\/span><span class=\"nf\">Lu<\/span><span class=\"p\">(<\/span><span class=\"nv\">ans<\/span>, <span class=\"nv\">H<\/span><span class=\"p\">))<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[27]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">font<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Arial\"<\/span>, <span class=\"nv\">font_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">14<\/span>, \r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 1<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">1<\/span>, 2<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u898f\u683c\u5316\u3055\u308c\u305f\u9ad8\u3055 H\"<\/span>, <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u898f\u683c\u5316\u3055\u308c\u305f\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span>,\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u9ad8\u3055 H \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span>,\r\n  \r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">Lmax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">H<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\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-5079\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mhtosha13.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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=\"\u53c2\u8003\uff1a\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\">\u53c2\u8003\uff1a\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2<\/h4>\n<p>\u5b9f\u306f<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/4109\/#i-6\">\u5225\u30da\u30fc\u30b8<\/a>\u3067\u66f8\u3044\u3066\u3044\u308b\u3088\u3046\u306b\uff0c\u898f\u683c\u5316\u3055\u308c\u305f\u9ad8\u3055 $H$ \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u306f\uff0c\u898f\u683c\u5316\u3055\u308c\u305f\u91cf $L_{\\rm m}$ \u3067\u4ee5\u4e0b\u306e\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u3002<\/p>\n<p>$$L_{\\rm m} = \\sqrt{1+2H}$$<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/4109\/\">\u9ad8\u3055 h \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u5230\u9054\u8ddd\u96e2\u306f\u89d2\u5ea645\u00b0\u306e\u3068\u304d\u3067\u306f\u306a\u3044<\/a>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/4109\/#i-6\">\u6700\u5927\u5230\u9054\u8ddd\u96e2\u3068\u6ede\u7a7a\u6642\u9593<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u3042\u3048\u30662\u3064\u306e\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3068\uff0c\u5b8c\u5168\u306b\u91cd\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3067\u3042\u308d\u3046\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=\"\u554f\u984c-4\">\u554f\u984c 4<\/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 \/>\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<h4 id=\"\u89e3\u7b54\u4f8b\">\u89e3\u7b54\u4f8b<\/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[28]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">h<\/span><span class=\"o\">:<\/span> 5$\r\n<span class=\"nv\">v0<\/span><span class=\"o\">:<\/span> 10$\r\n<span class=\"nv\">g<\/span><span class=\"o\">:<\/span> 9<span class=\"o\">.<\/span>80665$\r\n\r\n<span class=\"nv\">H<\/span><span class=\"o\">:<\/span> <span class=\"nv\">h<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">g<\/span><span class=\"o\">\/<\/span><span class=\"nv\">v0<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[28]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{55}$}0.4903\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[29]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>, \r\n  <span class=\"s\">\"\u6700\u5927\u5230\u9054\u8ddd\u96e2\u306f ~9,6f m~%\"<\/span>,<span class=\"nv\">v0<\/span><span class=\"o\">**<\/span>2<span class=\"o\">\/<\/span><span class=\"nv\">g<\/span><span class=\"o\">*<\/span><span class=\"nf\">Lmax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span><span class=\"p\">))<\/span>$\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_subarea output_stream output_stdout output_text\">\n<pre>\u6700\u5927\u5230\u9054\u8ddd\u96e2\u306f 14.351088 m\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[30]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>, \r\n  <span class=\"s\">\"\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u306f ~9,6f \u00b0~%\"<\/span>,<span class=\"nf\">thetamax<\/span><span class=\"p\">(<\/span><span class=\"nv\">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_subarea output_stream output_stdout output_text\">\n<pre>\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u306f 35.395688 \u00b0\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":33,"featured_media":0,"parent":7137,"menu_order":60,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-5066","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\/5066","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=5066"}],"version-history":[{"count":9,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/5066\/revisions"}],"predecessor-version":[{"id":5163,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/5066\/revisions\/5163"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/7137"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=5066"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}