{"id":7447,"date":"2024-01-29T11:35:32","date_gmt":"2024-01-29T02:35:32","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=7447"},"modified":"2024-01-29T23:05:47","modified_gmt":"2024-01-29T14:05:47","slug":"%e7%a9%ba%e6%b0%97%e6%8a%b5%e6%8a%97%e3%81%8c%e3%81%82%e3%82%8b%e5%a0%b4%e5%90%88%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%81%ae%e6%9c%80%e5%a4%a7%e6%b0%b4%e5%b9%b3%e5%88%b0%e9%81%94%e8%b7%9d","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/7447\/","title":{"rendered":"\u7a7a\u6c17\u62b5\u6297\u304b\u3099\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3092\u8abf\u3078\u3099\u308b"},"content":{"rendered":"<p>\u300c<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\/%e7%a9%ba%e6%b0%97%e6%8a%b5%e6%8a%97%e3%81%8c%e3%81%82%e3%82%8b%e5%a0%b4%e5%90%88%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%82%92%e8%aa%bf%e3%81%b9%e3%82%8b%e6%ba%96%e5%82%99\/\">\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u3092\u8abf\u3079\u308b\u6e96\u5099<\/a>\u300d\u3092\u53c2\u7167\u3002<\/p>\n<p><!--more--><\/p>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"SymPy-\u3067\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3092\u8abf\u3079\u308b\">SymPy \u3067\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3092\u8abf\u3079\u308b<\/h3>\n<p>\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u8ecc\u9053\u3092\uff0cPython \u306e SymPy \u3092\u4f7f\u3063\u3066\uff08\u304b\u3064 SciPy \u3084 NumPy \u3092\u4f7f\u308f\u305a\u306b\uff09\u8abf\u3079\u308b\u3002<\/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\/%e7%a9%ba%e6%b0%97%e6%8a%b5%e6%8a%97%e3%81%8c%e3%81%82%e3%82%8b%e5%a0%b4%e5%90%88%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%82%92%e8%aa%bf%e3%81%b9%e3%82%8b%e6%ba%96%e5%82%99\/#i-5\">\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u3092\u8abf\u3079\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<h4 id=\"SymPy-\u306e-import\">SymPy \u306e import<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"kn\">from<\/span> <span class=\"nn\">sympy<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n<span class=\"c1\"># 1\u6587\u5b57\u5909\u6570\u306e Symbol \u306e\u5ba3\u8a00\u304c\u7701\u7565\u3067\u304d\u308b<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">sympy.abc<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n<span class=\"c1\"># \u5186\u5468\u7387<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">sympy<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">pi<\/span>\r\n\r\n<span class=\"n\">init_printing<\/span><span class=\"p\">()<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u89e3\">\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u89e3<\/h4>\n<p>\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u659c\u65b9\u6295\u5c04\u306e\u89e3\u306f\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\nX(T, \\theta) &amp;=&amp; \\frac{1-e^{-bT}}{b} \\cos\\theta \\\\<br \/>\nY(T, \\theta) &amp;=&amp; H+ \\frac{1-e^{-bT}}{b}\\sin\\theta + \\frac{1 &#8211; bT-e^{-bT}}{b^2}<br \/>\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"k\">def<\/span> <span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">exp<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"o\">*<\/span><span class=\"n\">T<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"n\">b<\/span> <span class=\"o\">*<\/span> <span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">)<\/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\">theta<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">H<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">exp<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"o\">*<\/span><span class=\"n\">T<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"n\">b<\/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=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"o\">*<\/span><span class=\"n\">T<\/span><span class=\"o\">-<\/span><span class=\"n\">exp<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"o\">*<\/span><span class=\"n\">T<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"n\">b<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/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[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/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\">$\\displaystyle \\frac{\\left(1 &#8211; e^{- T b}\\right) \\cos{\\left(\\theta \\right)}}{b}$<\/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[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/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[4]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle H + \\frac{\\left(1 &#8211; e^{- T b}\\right) \\sin{\\left(\\theta \\right)}}{b} + \\frac{- T b + 1 &#8211; e^{- T b}}{b^{2}}$<\/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=\"\u6ede\u7a7a\u6642\u9593-$T_1$\">\u6ede\u7a7a\u6642\u9593 $T_1$<\/h4>\n<p>\u6ede\u7a7a\u6642\u9593 $T_1\\ \\ (&gt;0)$ \u306f\u4ee5\u4e0b\u306e\u5f0f\u3092\u6e80\u305f\u3059\u3002<\/p>\n<p>$$Y(T_1, \\theta, H, b) = 0 \\quad\\Rightarrow\\quad T_1 = T_1(\\theta)$$<\/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=\"\u9670\u95a2\u6570\u5b9a\u7406\u3092\u4f7f\u3046\">\u9670\u95a2\u6570\u5b9a\u7406\u3092\u4f7f\u3046<\/h4>\n<p>\u7c21\u5358\u306a\u5834\u5408\u306b\u306f\uff0c$T_1$ \u306f $\\theta$ \u306e\u967d\u95a2\u6570\u3068\u3057\u3066\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u304c\uff0c\u4e00\u822c\u306b\u306f\u305d\u3046\u306f\u3044\u304b\u306a\u3044\u304b\u3082\u3057\u308c\u306a\u3044\u3002\u305d\u3053\u3067\uff0c$T_1$ \u306f $\\theta$ \u306e\u9670\u95a2\u6570\u3067\u3042\u308b\u3068\u3057\u3066\u8a71\u3092\u9032\u3081\u308b\u3002<\/p>\n<p>$Y(T_1(\\theta), \\theta) = 0$ \u3067\u3042\u308b\u304b\u3089\uff0c<\/p>\n<p>$$\\frac{d}{d\\theta} Y(T_1(\\theta),\\theta)=<br \/>\n\\frac{\\partial Y}{\\partial T_1} \\frac{d T_1}{d\\theta} +<br \/>\n\\frac{\\partial Y}{\\partial \\theta}<br \/>\n= 0$$<\/p>\n<p>\u3088\u308a\uff0c$\\displaystyle \\frac{d T_1}{d\\theta}$ \u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\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[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">T1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">Function<\/span><span class=\"p\">(<\/span><span class=\"s1\">'T1'<\/span><span class=\"p\">)(<\/span><span class=\"n\">theta<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">dY<\/span> <span class=\"o\">=<\/span> <span class=\"n\">diff<\/span><span class=\"p\">(<\/span><span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T1<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">theta<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">sol1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">solve<\/span><span class=\"p\">(<\/span><span class=\"n\">dY<\/span><span class=\"p\">,<\/span> <span class=\"n\">diff<\/span><span class=\"p\">(<\/span><span class=\"n\">T1<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">sol1<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[5]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle \\left[ \\frac{\\left(1 &#8211; e^{b T_{1}{\\left(\\theta \\right)}}\\right) \\cos{\\left(\\theta \\right)}}{b \\sin{\\left(\\theta \\right)} &#8211; e^{b T_{1}{\\left(\\theta \\right)}} + 1}\\right]$<\/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[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">dT1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sol1<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span>\r\n<span class=\"n\">Eq<\/span><span class=\"p\">(<\/span><span class=\"n\">Derivative<\/span><span class=\"p\">(<\/span><span class=\"n\">T1<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta<\/span><span class=\"p\">),<\/span> <span class=\"n\">dT1<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[6]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle \\frac{d}{d \\theta} T_{1}{\\left(\\theta \\right)} = \\frac{\\left(1 &#8211; e^{b T_{1}{\\left(\\theta \\right)}}\\right) \\cos{\\left(\\theta \\right)}}{b \\sin{\\left(\\theta \\right)} &#8211; e^{b T_{1}{\\left(\\theta \\right)}} + 1}$<\/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=\"\u6c34\u5e73\u5230\u9054\u8ddd\u96e2-$L$\">\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L$<\/h4>\n<p>\u6ede\u7a7a\u6642\u9593 $T_1(\\theta)$ \u306e\u9593\u306b\u6c34\u5e73\u65b9\u5411\u306b\u9032\u3080\u8ddd\u96e2\u306f<\/p>\n<p>$$L = X(T_1(\\theta), \\theta)$$<\/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=\"k\">def<\/span> <span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">theta<\/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\">theta<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[7]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle \\frac{\\left(1 &#8211; e^{- b T_{1}{\\left(\\theta \\right)}}\\right) \\cos{\\left(\\theta \\right)}}{b}$<\/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-$\\theta_{\\rm-max}$\">$L$ \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6 $\\theta_{\\rm max}$<\/h4>\n<p>$\\displaystyle \\frac{dL}{d\\theta} = 0$ \u3068\u306a\u308b\u89d2\u5ea6 $\\theta \\equiv \\theta_{\\rm max}$ \u3092\u6c42\u3081\u308b\u3002\u9670\u95a2\u6570\u5b9a\u7406\u306e\u7d50\u679c\u3092 <code>.subs()<\/code> \u3067\u4ee3\u5165\u3057\u3066&#8230;<\/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=\"n\">dL<\/span> <span class=\"o\">=<\/span> <span class=\"n\">diff<\/span><span class=\"p\">(<\/span><span class=\"n\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">),<\/span> <span class=\"n\">theta<\/span><span class=\"p\">)<\/span><span class=\"o\">.<\/span><span class=\"n\">subs<\/span><span class=\"p\">(<\/span><span class=\"n\">diff<\/span><span class=\"p\">(<\/span><span class=\"n\">T1<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta<\/span><span class=\"p\">),<\/span> <span class=\"n\">dT1<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">dL<\/span> <span class=\"o\">=<\/span> <span class=\"n\">simplify<\/span><span class=\"p\">(<\/span><span class=\"n\">dL<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">Eq<\/span><span class=\"p\">(<\/span><span class=\"n\">Derivative<\/span><span class=\"p\">(<\/span><span class=\"n\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">),<\/span> <span class=\"n\">theta<\/span><span class=\"p\">),<\/span> <span class=\"n\">dL<\/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[8]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle \\frac{\\partial}{\\partial \\theta} \\frac{\\left(1 &#8211; e^{- b T_{1}{\\left(\\theta \\right)}}\\right) \\cos{\\left(\\theta \\right)}}{b} = &#8211; \\frac{\\left(e^{b T_{1}{\\left(\\theta \\right)}} &#8211; 1\\right) \\left(b &#8211; e^{b T_{1}{\\left(\\theta \\right)}} \\sin{\\left(\\theta \\right)} + \\sin{\\left(\\theta \\right)}\\right) e^{- b T_{1}{\\left(\\theta \\right)}}}{b \\left(b \\sin{\\left(\\theta \\right)} &#8211; e^{b T_{1}{\\left(\\theta \\right)}} + 1\\right)}$<\/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<p>$L$ \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u306f\uff0c\u9023\u7acb\u65b9\u7a0b\u5f0f<\/p>\n<p>\\begin{eqnarray}<br \/>\nY(T_1(\\theta), \\theta) &amp;=&amp; 0 \\\\<br \/>\n\\frac{d}{d\\theta} L(\\theta) &amp;=&amp; 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3092\uff0c$\\sin\\theta$ \u3068 $T_1(\\theta)$ \u306b\u3064\u3044\u3066\u89e3\u3044\u3066\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\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=\"n\">Eq<\/span><span class=\"p\">(<\/span><span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T1<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"mi\">0<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[9]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle H + \\frac{\\left(1 &#8211; e^{- b T_{1}{\\left(\\theta \\right)}}\\right) \\sin{\\left(\\theta \\right)}}{b} + \\frac{- b T_{1}{\\left(\\theta \\right)} + 1 &#8211; e^{- b T_{1}{\\left(\\theta \\right)}}}{b^{2}} = 0$<\/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[10]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">Eq<\/span><span class=\"p\">(<\/span><span class=\"n\">dL<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[10]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle &#8211; \\frac{\\left(e^{b T_{1}{\\left(\\theta \\right)}} &#8211; 1\\right) \\left(b &#8211; e^{b T_{1}{\\left(\\theta \\right)}} \\sin{\\left(\\theta \\right)} + \\sin{\\left(\\theta \\right)}\\right) e^{- b T_{1}{\\left(\\theta \\right)}}}{b \\left(b \\sin{\\left(\\theta \\right)} &#8211; e^{b T_{1}{\\left(\\theta \\right)}} + 1\\right)} = 0$<\/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\u9023\u7acb\u65b9\u7a0b\u5f0f\u306f\uff0c$T_1$ \u306b\u3064\u3044\u3066\u8d85\u8d8a\u65b9\u7a0b\u5f0f\u3067\u3042\u308a\uff0c<code>solve()<\/code> \u3067\u89e3\u304f\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002<\/p>\n<p>\u305d\u3053\u3067\u307e\u305a\uff0c$Y(T_1(\\theta), \\theta) = 0$ \u306e\u5f0f\u304b\u3089 $\\sin\\theta$ \u3092 $T_1$ \u3067\u8868\u3057\uff0c$\\sin\\theta$ \u3092\u6d88\u53bb\u3057\u30661\u5909\u6570 $T_1$ \u306b\u95a2\u3059\u308b\u65b9\u7a0b\u5f0f\u306b\u3059\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-ipython3\">\n<pre><span class=\"n\">eqsin<\/span> <span class=\"o\">=<\/span> <span class=\"n\">solve<\/span><span class=\"p\">(<\/span><span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T1<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">Eq<\/span><span class=\"p\">(<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">),<\/span> <span class=\"n\">eqsin<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">])<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[11]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle \\sin{\\left(\\theta \\right)} = &#8211; \\frac{H b^{2} e^{b T_{1}{\\left(\\theta \\right)}} &#8211; b T_{1}{\\left(\\theta \\right)} e^{b T_{1}{\\left(\\theta \\right)}} + e^{b T_{1}{\\left(\\theta \\right)}} &#8211; 1}{b \\left(e^{b T_{1}{\\left(\\theta \\right)}} &#8211; 1\\right)}$<\/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<p>\u3053\u308c\u3092 $\\displaystyle \\frac{d}{d\\theta} L(\\theta) = 0$ \u306e\u5f0f\u306b\u4ee3\u5165\u3057\u3066\uff0c$T_1(\\theta)$ \u306b\u95a2\u3059\u308b1\u672c\u306e\u65b9\u7a0b\u5f0f\u306b\u3059\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[12]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">eq<\/span> <span class=\"o\">=<\/span> <span class=\"n\">factor<\/span><span class=\"p\">(<\/span><span class=\"n\">dL<\/span><span class=\"o\">.<\/span><span class=\"n\">subs<\/span><span class=\"p\">(<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">),<\/span> <span class=\"n\">eqsin<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]))<\/span>\r\n<span class=\"n\">Eq<\/span><span class=\"p\">(<\/span><span class=\"n\">eq<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[12]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle \\frac{\\left(e^{b T_{1}{\\left(\\theta \\right)}} &#8211; 1\\right)^{2} \\left(H b^{2} e^{b T_{1}{\\left(\\theta \\right)}} + b^{2} &#8211; b T_{1}{\\left(\\theta \\right)} e^{b T_{1}{\\left(\\theta \\right)}} + e^{b T_{1}{\\left(\\theta \\right)}} &#8211; 1\\right) e^{- 2 b T_{1}{\\left(\\theta \\right)}}}{b^{2} \\left(H b^{2} &#8211; b T_{1}{\\left(\\theta \\right)} + e^{b T_{1}{\\left(\\theta \\right)}} &#8211; 1\\right)} = 0$<\/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-ipython3\">\n<pre><span class=\"k\">def<\/span> <span class=\"nf\">eqT1<\/span><span class=\"p\">(<\/span><span class=\"n\">Ti<\/span><span class=\"p\">,<\/span> <span class=\"n\">Hi<\/span><span class=\"p\">,<\/span> <span class=\"n\">bi<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">tmp<\/span> <span class=\"o\">=<\/span> <span class=\"n\">eq<\/span><span class=\"o\">.<\/span><span class=\"n\">subs<\/span><span class=\"p\">(<\/span><span class=\"n\">T1<\/span><span class=\"p\">,<\/span> <span class=\"n\">Ti<\/span><span class=\"p\">)<\/span><span class=\"o\">.<\/span><span class=\"n\">subs<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">Hi<\/span><span class=\"p\">)<\/span><span class=\"o\">.<\/span><span class=\"n\">subs<\/span><span class=\"p\">(<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">bi<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">tmp<\/span>\r\n\r\n<span class=\"k\">def<\/span> <span class=\"nf\">T1max<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">sol<\/span> <span class=\"o\">=<\/span> <span class=\"n\">nsolve<\/span><span class=\"p\">(<\/span><span class=\"n\">eqT1<\/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\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"p\">[<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">3<\/span><span class=\"p\">],<\/span> <span class=\"n\">prec<\/span><span class=\"o\">=<\/span><span class=\"mi\">14<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">sol<\/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>$T_{1 \\rm max}$ \u304c\u6570\u5024\u7684\u306b\u6c42\u307e\u3063\u305f\u3089\uff0c\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L$ \u3092\u6700\u5927\u306b\u3059\u308b\u89d2\u5ea6 $\\theta_{\\rm max}$ \u306f&#8230;<\/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\">var<\/span><span class=\"p\">(<\/span><span class=\"s1\">'T1_max theta_max'<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">Eq<\/span><span class=\"p\">(<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">theta_max<\/span><span class=\"p\">),<\/span> <span class=\"n\">eqsin<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">subs<\/span><span class=\"p\">(<\/span><span class=\"n\">T1<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1_max<\/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\">$\\displaystyle \\sin{\\left(\\theta_{max} \\right)} = &#8211; \\frac{H b^{2} e^{T_{1 max} b} &#8211; T_{1 max} b e^{T_{1 max} b} + e^{T_{1 max} b} &#8211; 1}{b \\left(e^{T_{1 max} b} &#8211; 1\\right)}$<\/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<p>\u304b\u3089&#8230;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[15]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">Eq<\/span><span class=\"p\">(<\/span><span class=\"n\">theta_max<\/span><span class=\"p\">,<\/span> <span class=\"n\">asin<\/span><span class=\"p\">(<\/span><span class=\"n\">eqsin<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">])<\/span><span class=\"o\">.<\/span><span class=\"n\">subs<\/span><span class=\"p\">(<\/span><span class=\"n\">T1<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1_max<\/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\">$\\displaystyle \\theta_{max} = &#8211; \\operatorname{asin}{\\left(\\frac{H b^{2} e^{T_{1 max} b} &#8211; T_{1 max} b e^{T_{1 max} b} + e^{T_{1 max} b} &#8211; 1}{b \\left(e^{T_{1 max} b} &#8211; 1\\right)} \\right)}$<\/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[16]:<\/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\">thetamax<\/span><span class=\"p\">(<\/span><span class=\"n\">Hi<\/span><span class=\"p\">,<\/span> <span class=\"n\">bi<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">tmp<\/span> <span class=\"o\">=<\/span> <span class=\"n\">eqsin<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">subs<\/span><span class=\"p\">(<\/span><span class=\"n\">T1<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1max<\/span><span class=\"p\">(<\/span><span class=\"n\">Hi<\/span><span class=\"p\">,<\/span> <span class=\"n\">bi<\/span><span class=\"p\">))<\/span><span class=\"o\">.<\/span><span class=\"n\">subs<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">Hi<\/span><span class=\"p\">)<\/span><span class=\"o\">.<\/span><span class=\"n\">subs<\/span><span class=\"p\">(<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">bi<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">asin<\/span><span class=\"p\">(<\/span><span class=\"n\">tmp<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"k\">def<\/span> <span class=\"nf\">degrees<\/span><span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"kn\">from<\/span> <span class=\"nn\">sympy<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">pi<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">theta<\/span><span class=\"o\">*<\/span><span class=\"mi\">180<\/span><span class=\"o\">\/<\/span><span class=\"nb\">float<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"p\">)<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">thmax<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">ans<\/span> <span class=\"o\">=<\/span> <span class=\"n\">thetamax<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">degrees<\/span><span class=\"p\">(<\/span><span class=\"n\">ans<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2-$L_{\\rm-max}$\">\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L_{\\rm max}$<\/h4>\n<p>\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2<br \/>\n$$L_{\\rm max} = X(T_1(\\theta_{\\rm max}), \\theta_{\\rm max}, b)$$<\/p>\n<p>\u306f\uff0c$\\theta_{\\rm max}(H, b)$ \u3067\u3042\u308b\u3053\u3068\u304b\u3089\u6700\u7d42\u7684\u306b\uff0c$L_{\\rm max}(H, b)$ \u3068\u306a\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[17]:<\/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\">Lmax<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T1max<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">thetamax<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">b<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"$H=0,-b-=-0.5$-\u306e\u5834\u5408\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3068\u8ecc\u9053\">$H=0, b = 0.5$ \u306e\u5834\u5408\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3068\u8ecc\u9053<\/h4>\n<p>\u4f8b\u3068\u3057\u3066\uff0c$H=0, b=0.5$ \u306e\u5834\u5408\u306b\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L$ \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6 $\\theta_{\\rm max}$ \u3068\uff0c\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L_{\\rm max}$ \u3092\u8868\u793a\u3055\u305b\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[18]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">Htmp<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"n\">btmp<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.5<\/span>\r\n\r\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"H = <\/span><span class=\"si\">%.1f<\/span><span class=\"s2\">, b = <\/span><span class=\"si\">%.1f<\/span><span class=\"s2\">\u306e\u3068\u304d\uff0c\"<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">Htmp<\/span><span class=\"p\">,<\/span> <span class=\"n\">btmp<\/span><span class=\"p\">))<\/span>\r\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"L \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u306f \u03b8max=<\/span><span class=\"si\">%.14f<\/span><span class=\"s2\">\u00b0\"<\/span> <span class=\"o\">%<\/span> <span class=\"n\">thmax<\/span><span class=\"p\">(<\/span><span class=\"n\">Htmp<\/span><span class=\"p\">,<\/span> <span class=\"n\">btmp<\/span><span class=\"p\">))<\/span>\r\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u306f Lmax=<\/span><span class=\"si\">%.14f<\/span><span class=\"s2\">\"<\/span> <span class=\"o\">%<\/span> <span class=\"n\">Lmax<\/span><span class=\"p\">(<\/span><span class=\"n\">Htmp<\/span><span class=\"p\">,<\/span> <span class=\"n\">btmp<\/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 = 0.0, b = 0.5\u306e\u3068\u304d\uff0c\r\nL \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u306f \u03b8max=39.48760970478555\u00b0\r\n\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u306f Lmax=0.67942108743974\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=\"Maxima-\u3067\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3092\u8abf\u3079\u308b\">Maxima \u3067\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3092\u8abf\u3079\u308b<\/h3>\n<p>\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u8ecc\u9053\u3092\uff0cMaxima \u3092\u4f7f\u3063\u3066\u8abf\u3079\u308b\u3002<\/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\/%e7%a9%ba%e6%b0%97%e6%8a%b5%e6%8a%97%e3%81%8c%e3%81%82%e3%82%8b%e5%a0%b4%e5%90%88%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%82%92%e8%aa%bf%e3%81%b9%e3%82%8b%e6%ba%96%e5%82%99\/#i-5\">\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u3092\u8abf\u3079\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<h4 id=\"\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u89e3\">\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u89e3<\/h4>\n<p>\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u659c\u65b9\u6295\u5c04\u306e\u89e3\u306f\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\nX(T, \\theta) &amp;=&amp; \\frac{1-e^{-bT}}{b} \\cos\\theta \\\\<br \/>\nY(T, \\theta) &amp;=&amp; H+ \\frac{1-e^{-bT}}{b}\\sin\\theta + \\frac{1 &#8211; bT-e^{-bT}}{b^2}<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[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">theta<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"p\">(<\/span>1<span class=\"o\">-<\/span><span class=\"nf\">exp<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"nv\">b<\/span><span class=\"o\">*<\/span><span class=\"nv\">T<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"nv\">b<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">theta<\/span><span class=\"p\">)<\/span>;\r\n<span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">theta<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">H<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span>1<span class=\"o\">-<\/span><span class=\"nf\">exp<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"nv\">b<\/span><span class=\"o\">*<\/span><span class=\"nv\">T<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"nv\">b<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">theta<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span>1<span class=\"o\">-<\/span><span class=\"nv\">b<\/span><span class=\"o\">*<\/span><span class=\"nv\">T<\/span> <span class=\"o\">-<\/span> <span class=\"nf\">exp<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"nv\">b<\/span><span class=\"o\">*<\/span><span class=\"nv\">T<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"nv\">b<\/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[1]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{1}$}X\\left(T , \\vartheta , b\\right):=\\frac{1-\\exp \\left(\\left(-b\\right)\\,T\\right)}{b}\\,\\cos \\vartheta\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[1]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{2}$}Y\\left(T , \\vartheta , H , b\\right):=H+\\frac{1-\\exp \\left(\\left(-b\\right)\\,T\\right)}{b}\\,\\sin \\vartheta+\\frac{1-b\\,T-\\exp \\left(\\left(-b\\right)\\,T\\right)}{b^2}\\]<\/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=\"\u6ede\u7a7a\u6642\u9593-$T_1$\">\u6ede\u7a7a\u6642\u9593 $T_1$<\/h4>\n<p>\u6ede\u7a7a\u6642\u9593 $T_1\\ \\ (&gt;0)$ \u306f\u4ee5\u4e0b\u306e\u5f0f\u3092\u6e80\u305f\u3059\u3002<\/p>\n<p>$$Y(T_1, \\theta, H, b) = 0 \\quad\\Rightarrow\\quad T_1 = T_1(\\theta)$$<\/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=\"\u9670\u95a2\u6570\u5b9a\u7406\u3092\u4f7f\u3046\">\u9670\u95a2\u6570\u5b9a\u7406\u3092\u4f7f\u3046<\/h4>\n<p>\u7c21\u5358\u306a\u5834\u5408\u306b\u306f\uff0c$T_1$ \u306f $\\theta$ \u306e\u967d\u95a2\u6570\u3068\u3057\u3066\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u304c\uff0c\u4e00\u822c\u306b\u306f\u305d\u3046\u306f\u3044\u304b\u306a\u3044\u304b\u3082\u3057\u308c\u306a\u3044\u3002\u305d\u3053\u3067\uff0c$T_1$ \u306f $\\theta$ \u306e\u9670\u95a2\u6570\u3067\u3042\u308b\u3068\u3057\u3066\u8a71\u3092\u9032\u3081\u308b\u3002<\/p>\n<p>$Y(T_1(\\theta), \\theta) = 0$ \u3067\u3042\u308b\u304b\u3089\uff0c<\/p>\n<p>$$\\frac{d }{d\\theta} Y(T_1(\\theta), \\theta)=<br \/>\n\\frac{\\partial Y}{\\partial T_1} \\frac{d T_1}{d\\theta} +<br \/>\n\\frac{\\partial Y}{\\partial \\theta}<br \/>\n= 0$$<\/p>\n<p>\u3088\u308a\uff0c$\\displaystyle \\frac{d T_1}{d\\theta}$ \u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\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[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">depends<\/span><span class=\"p\">(<\/span><span class=\"nv\">T1<\/span>, <span class=\"nv\">theta<\/span><span class=\"p\">)<\/span>;\r\n\r\n<span class=\"nv\">dY<\/span><span class=\"o\">:<\/span> <span class=\"nf\">diff<\/span><span class=\"p\">(<\/span><span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">T1<\/span>, <span class=\"nv\">theta<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">=<\/span><span class=\"mi\">0<\/span>, <span class=\"nv\">theta<\/span><span class=\"p\">)<\/span>;\r\n<span class=\"nv\">eqdT1<\/span><span class=\"o\">:<\/span> <span class=\"nf\">solve<\/span><span class=\"p\">(<\/span><span class=\"nv\">dY<\/span>, <span class=\"nf\">diff<\/span><span class=\"p\">(<\/span><span class=\"nv\">T1<\/span>, <span class=\"nv\">theta<\/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[2]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{3}$}\\left[ T_{1}\\left(\\vartheta\\right) \\right] \\]<\/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{${\\it \\%o}_{4}$}\\frac{d}{d\\,\\vartheta}\\,T_{1}\\,e^ {- T_{1}\\,b }\\,\\sin \\vartheta+\\frac{\\left(1-e^ {- T_{1}\\,b }\\right)\\,\\cos \\vartheta}{b}+\\frac{\\frac{d}{d\\,\\vartheta}\\,T_{1}\\,b\\,e^ {- T_{1}\\,b }-\\frac{d}{d\\,\\vartheta}\\,T_{1}\\,b}{b^2}=0\\]<\/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{${\\it \\%o}_{5}$}\\left[ \\frac{d}{d\\,\\vartheta}\\,T_{1}=-\\frac{\\left(e^{T_{1}\\,b}-1\\right)\\,\\cos \\vartheta}{b\\,\\sin \\vartheta-e^{T_{1}\\,b}+1} \\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=\"\u6c34\u5e73\u5230\u9054\u8ddd\u96e2-$L$\">\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L$<\/h4>\n<p>\u6ede\u7a7a\u6642\u9593 $T_1(\\theta)$ \u306e\u9593\u306b\u6c34\u5e73\u65b9\u5411\u306b\u9032\u3080\u8ddd\u96e2\u306f<\/p>\n<p>$$L = X(T_1(\\theta), \\theta)$$<\/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-maxima\">\n<pre><span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"nv\">theta<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"nv\">T1<\/span>, <span class=\"nv\">theta<\/span>, <span class=\"nv\">b<\/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{${\\it \\%o}_{6}$}L\\left(\\vartheta , b\\right):=X\\left(T_{1} , \\vartheta , b\\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=\"$L$-\u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6-$\\theta_{\\rm-max}$\">$L$ \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6 $\\theta_{\\rm max}$<\/h4>\n<p>$\\displaystyle \\frac{dL}{d\\theta} = 0$ \u3068\u306a\u308b\u89d2\u5ea6 $\\theta \\equiv \\theta_{\\rm max}$ \u3092\u6c42\u3081\u308b\u3002\u9670\u95a2\u6570\u5b9a\u7406\u306e\u7d50\u679c\u3092 <code>ev()<\/code> \u3067\u4ee3\u5165\u3057\u3066&#8230;<\/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=\"nv\">dL<\/span><span class=\"o\">:<\/span> <span class=\"nf\">diff<\/span><span class=\"p\">(<\/span><span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"nv\">theta<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">theta<\/span><span class=\"p\">)<\/span>;\r\n<span class=\"nv\">dL<\/span><span class=\"o\">:<\/span> <span class=\"nf\">trigsimp<\/span><span class=\"p\">(<\/span><span class=\"nf\">ev<\/span><span class=\"p\">(<\/span><span class=\"nv\">dL<\/span>, <span class=\"nv\">eqdT1<\/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[4]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{7}$}\\frac{d}{d\\,\\vartheta}\\,T_{1}\\,e^ {- T_{1}\\,b }\\,\\cos \\vartheta-\\frac{\\left(1-e^ {- T_{1}\\,b }\\right)\\,\\sin \\vartheta}{b}\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[4]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{8}$}\\frac{\\left(e^{2\\,T_{1}\\,b}-2\\,e^{T_{1}\\,b}+1\\right)\\,\\sin \\vartheta-b\\,e^{T_{1}\\,b}+b}{b^2\\,e^{T_{1}\\,b}\\,\\sin \\vartheta-b\\,e^{2\\,T_{1}\\,b}+b\\,e^{T_{1}\\,b}}\\]<\/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>$L$ \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u306f\uff0c\u9023\u7acb\u65b9\u7a0b\u5f0f<\/p>\n<p>\\begin{eqnarray}<br \/>\nY(T_1(\\theta), \\theta) &amp;=&amp; 0 \\\\<br \/>\n\\frac{d}{d\\theta} L(\\theta) &amp;=&amp; 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3092\uff0c$\\sin\\theta$ \u3068 $T_1(\\theta)$ \u306b\u3064\u3044\u3066\u89e3\u3044\u3066\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\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[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">T1<\/span>, <span class=\"nv\">theta<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>;\r\n<span class=\"nv\">dL<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[5]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{9}$}\\frac{\\left(1-e^ {- T_{1}\\,b }\\right)\\,\\sin \\vartheta}{b}+\\frac{-e^ {- T_{1}\\,b }-T_{1}\\,b+1}{b^2}+H=0\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[5]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{10}$}\\frac{\\left(e^{2\\,T_{1}\\,b}-2\\,e^{T_{1}\\,b}+1\\right)\\,\\sin \\vartheta-b\\,e^{T_{1}\\,b}+b}{b^2\\,e^{T_{1}\\,b}\\,\\sin \\vartheta-b\\,e^{2\\,T_{1}\\,b}+b\\,e^{T_{1}\\,b}}=0\\]<\/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\u9023\u7acb\u65b9\u7a0b\u5f0f\u306f\uff0c$T_1$ \u306b\u3064\u3044\u3066\u8d85\u8d8a\u65b9\u7a0b\u5f0f\u3067\u3042\u308a\uff0c<code>solve()<\/code> \u3067\u89e3\u304f\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002<\/p>\n<p>\u305d\u3053\u3067\u307e\u305a\uff0c$Y(T_1(\\theta), \\theta) = 0$ \u306e\u5f0f\u304b\u3089 $\\sin\\theta$ \u3092 $T_1$ \u3067\u8868\u3057\uff0c$\\sin\\theta$ \u3092\u6d88\u53bb\u3057\u30661\u5909\u6570 $T_1$ \u306b\u95a2\u3059\u308b\u65b9\u7a0b\u5f0f\u306b\u3059\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[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">eqsin<\/span><span class=\"o\">:<\/span> <span class=\"nf\">solve<\/span><span class=\"p\">(<\/span><span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">T1<\/span>, <span class=\"nv\">theta<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">theta<\/span><span class=\"p\">))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[6]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{11}$}\\left[ \\sin \\vartheta=-\\frac{\\left(H\\,b^2-T_{1}\\,b+1\\right)\\,e^{T_{1}\\,b}-1}{b\\,e^{T_{1}\\,b}-b} \\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<p>\u3053\u308c\u3092 $\\displaystyle \\frac{d}{d\\theta} L(\\theta) = 0$ \u306e\u5f0f\u306b\u4ee3\u5165\u3057\u3066\uff0c$T_1(\\theta)$ \u306b\u95a2\u3059\u308b1\u672c\u306e\u65b9\u7a0b\u5f0f\u306b\u3059\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[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">ev<\/span><span class=\"p\">(<\/span><span class=\"nv\">dL<\/span><span class=\"o\">=<\/span><span class=\"mi\">0<\/span>, <span class=\"nv\">eqsin<\/span><span class=\"p\">[<\/span>1<span class=\"p\">])<\/span>, <span class=\"nv\">factor<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[7]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{12}$}\\frac{e^ {- 2\\,T_{1}\\,b }\\,\\left(e^{T_{1}\\,b}-1\\right)^2\\,\\left(H\\,b^2\\,e^{T_{1}\\,b}-T_{1}\\,b\\,e^{T_{1}\\,b}+e^{T_{1}\\,b}+b^2-1\\right)}{b^2\\,\\left(e^{T_{1}\\,b}+H\\,b^2-T_{1}\\,b-1\\right)}=0\\]<\/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\u5f0f\u3082\u307e\u305f $T_1$ \u306b\u95a2\u3059\u308b\u8d85\u8d8a\u65b9\u7a0b\u5f0f\u3067\u3042\u308a\uff0c<code>solve()<\/code> \u3067\u306f\u89e3\u3051\u306a\u3044\u3002\u5de6\u8fba\u306e\u5206\u5b50 <code>num()<\/code> \u306e\u5fc5\u8981\u306a\u90e8\u5206\u306e\u307f\u3092\u53d6\u308a\u51fa\u3057&#8230;<\/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-maxima\">\n<pre><span class=\"nf\">define<\/span><span class=\"p\">(<\/span><span class=\"nf\">eqT1<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span>, \r\n  <span class=\"nf\">num<\/span><span class=\"p\">(<\/span><span class=\"nf\">factor<\/span><span class=\"p\">(<\/span><span class=\"nf\">ev<\/span><span class=\"p\">(<\/span><span class=\"nv\">dL<\/span>, <span class=\"nv\">eqsin<\/span><span class=\"p\">[<\/span>1<span class=\"p\">])<\/span><span class=\"o\">*<\/span><span class=\"nf\">exp<\/span><span class=\"p\">(<\/span>2<span class=\"o\">*<\/span><span class=\"nv\">b<\/span><span class=\"o\">*<\/span><span class=\"nv\">T1<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span>1<span class=\"o\">-<\/span><span class=\"nf\">exp<\/span><span class=\"p\">(<\/span><span class=\"nv\">b<\/span><span class=\"o\">*<\/span><span class=\"nv\">T1<\/span><span class=\"p\">))<\/span><span class=\"o\">**<\/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[8]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{13}$}{\\it eqT}_{1}\\left(H , b\\right):=H\\,b^2\\,e^{T_{1}\\,b}-T_{1}\\,b\\,e^{T_{1}\\,b}+e^{T_{1}\\,b}+b^2-1\\]<\/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>$T_1$ \u306b\u3064\u3044\u3066 <code>find_root()<\/code> \u3067\u6570\u5024\u7684\u306b\u89e3\u304f\u3053\u3068\u306b\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$H b^2 e^{b T_1}-T_1 b e^{b T_1}+e^{b T_1}+b^2-1 = 0$$\u3092 $T_1$ \u306b\u3064\u3044\u3066\u89e3\u3044\u305f\u89e3\u3092 $T_{1 \\rm{max}}$ \u3068\u3059\u308b\u3068&#8230;<\/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-maxima\">\n<pre><span class=\"nf\">T1max<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">find_root<\/span><span class=\"p\">(<\/span><span class=\"nf\">eqT1<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">=<\/span><span class=\"mi\">0<\/span>, <span class=\"nv\">T1<\/span>, <span class=\"mf\">0.1<\/span>, <span class=\"mi\">3<\/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[9]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{14}$}{\\it T1max}\\left(H , b\\right):={\\it find\\_root}\\left({\\it eqT}_{1}\\left(H , b\\right)=0 , T_{1} , 0.1 , 3\\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<p>$T_{1 \\rm max}$ \u304c\u6570\u5024\u7684\u306b\u6c42\u307e\u3063\u305f\u3089\uff0c\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L$ \u3092\u6700\u5927\u306b\u3059\u308b\u89d2\u5ea6 $\\theta_{\\rm max}$ \u306f&#8230;<\/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\">eqsin<\/span><span class=\"p\">[<\/span>1<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[10]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{15}$}\\sin \\vartheta=-\\frac{\\left(H\\,b^2-T_{1}\\,b+1\\right)\\,e^{T_{1}\\,b}-1}{b\\,e^{T_{1}\\,b}-b}\\]<\/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\u8a18\u306e\u5f0f\u304b\u3089<\/p>\n<p>$$\\theta_{\\rm max} = \\arcsin\\left(-\\frac{\\left(H\\,b^2-T_{1 \\rm{max}}\\,b+1\\right)\\,e^{<br \/>\nT_{1 \\rm{max}}\\,b}-1}{b\\,e^{T_{1 \\rm{max}}\\,b}-b}\\right)$$<\/p>\n<p>\u3088\u308a\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\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=\"nf\">thetamax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">asin<\/span><span class=\"p\">(<\/span><span class=\"nf\">ev<\/span><span class=\"p\">(<\/span><span class=\"nf\">rhs<\/span><span class=\"p\">(<\/span><span class=\"nv\">eqsin<\/span><span class=\"p\">[<\/span>1<span class=\"p\">])<\/span>, <span class=\"nv\">T1<\/span><span class=\"o\">=<\/span><span class=\"nf\">T1max<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)))<\/span>;\r\n<span class=\"cm\">\/* \u5ea6\u3068\u30e9\u30b8\u30a2\u30f3\u306e\u5909\u63db\u95a2\u6570\u3092\u4f5c\u3063\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=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nv\">theta<\/span><span class=\"o\">*<\/span>180<span class=\"o\">\/<\/span><span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span>;\r\n<span class=\"nf\">thmax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">degrees<\/span><span class=\"p\">(<\/span><span class=\"nf\">thetamax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/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[11]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{16}$}{\\it thetamax}\\left(H , b\\right):=\\arcsin {\\it ev}\\left({\\it rhs}\\left({\\it eqsin}_{1}\\right) , T_{1}={\\it T1max}\\left(H , b\\right)\\right)\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[11]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{17}$}{\\it degrees}\\left(\\vartheta\\right):={\\it float}\\left(\\frac{\\vartheta\\,180}{\\pi}\\right)\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[11]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{18}$}{\\it thmax}\\left(H , b\\right):={\\it degrees}\\left({\\it thetamax}\\left(H , b\\right)\\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=\"\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2-$L_{\\rm-max}$\">\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L_{\\rm max}$<\/h4>\n<p>\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2<br \/>\n$$L_{\\rm max} = X(T_1(\\theta_{\\rm max}), \\theta_{\\rm max}, b)$$<\/p>\n<p>\u306f\uff0c$\\theta_{\\rm max}(H, b)$ \u3067\u3042\u308b\u3053\u3068\u304b\u3089\u6700\u7d42\u7684\u306b\uff0c$L_{\\rm max}(H, b)$ \u3068\u306a\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[12]:<\/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=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"nf\">T1max<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">thetamax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">b<\/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[12]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{19}$}{\\it Lmax}\\left(H , b\\right):=X\\left({\\it T1max}\\left(H , b\\right) , {\\it thetamax}\\left(H , b\\right) , b\\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=\"$H=0,-b-=-0.5$-\u306e\u5834\u5408\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3068\u8ecc\u9053\">$H=0, b = 0.5$ \u306e\u5834\u5408\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3068\u8ecc\u9053<\/h4>\n<p>\u4f8b\u3068\u3057\u3066\uff0c$H=0, b=0.5$ \u306e\u5834\u5408\u306b\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L$ \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6 $\\theta_{\\rm max}$ \u3068\uff0c\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L_{\\rm max}$ \u3092\u8868\u793a\u3055\u305b\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[13]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">H<\/span><span class=\"o\">:<\/span> 0$\r\n<span class=\"nv\">b<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>5$\r\n\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>, <span class=\"s\">\"H = ~,f, b = ~,1f\u306e\u3068\u304d\uff0c~%\"<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>, <span class=\"s\">\"L \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u306f \u03b8max=~,14f\u00b0~%\"<\/span>, <span class=\"nf\">thmax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">))<\/span>$\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>, <span class=\"s\">\"\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u306f Lmax=~,14f~%\"<\/span>, <span class=\"nf\">Lmax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/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 = 0.0, b = 0.5\u306e\u3068\u304d\uff0c\r\nL \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6\u306f \u03b8max=39.48760970478557\u00b0\r\n\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u306f Lmax=0.67942108743974\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u300c\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u3092\u8abf\u3079\u308b\u6e96\u5099\u300d\u3092\u53c2\u7167\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/7447\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[14,12],"tags":[],"class_list":["post-7447","post","type-post","status-publish","format-standard","hentry","category-maxima","category-sympy","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7447","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/post"}],"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=7447"}],"version-history":[{"count":6,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7447\/revisions"}],"predecessor-version":[{"id":7456,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7447\/revisions\/7456"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=7447"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=7447"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=7447"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}