{"id":7036,"date":"2023-11-21T10:30:49","date_gmt":"2023-11-21T01:30:49","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=7036"},"modified":"2023-11-21T17:35:29","modified_gmt":"2023-11-21T08:35:29","slug":"%e4%b8%8b%e3%81%94%e3%81%97%e3%82%89%e3%81%88%ef%bc%88ver-2%ef%bc%89%e3%81%97%e3%81%9f%e4%b8%87%e6%9c%89%e5%bc%95%e5%8a%9b%e3%81%ae2%e4%bd%93%e5%95%8f%e9%a1%8c%e3%81%ae%e9%81%8b%e5%8b%95%e6%96%b9","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/7036\/","title":{"rendered":"\u4e0b\u3053\u3099\u3057\u3089\u3048\uff08ver.2\uff09\u3057\u305f\u4e07\u6709\u5f15\u529b\u306e2\u4f53\u554f\u984c\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092 Maxima \u3066\u3099\u6570\u5024\u7684\u306b\u89e3\u304f"},"content":{"rendered":"

\u300c\u4e07\u6709\u5f15\u529b\u306e2\u4f53\u554f\u984c\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u524d\u306e\u4e0b\u3054\u3057\u3089\u3048 ver. 2<\/a>\u300d\u3067\u4e0b\u3054\u3057\u3089\u3048\u3057\u305f\u5f0f\u3092 Maxima \u3067\u6570\u5024\u7684\u306b\u89e3\u304f\u3002<\/p>\n

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\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u904b\u52d5\u65b9\u7a0b\u5f0f<\/h3>\n

\u300c\u4e07\u6709\u5f15\u529b\u306e2\u4f53\u554f\u984c\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u524d\u306e\u4e0b\u3054\u3057\u3089\u3048 ver. 2<\/a>\u300d\u306b\u307e\u3068\u3081\u305f\u3088\u3046\u306b\uff0c\u8ecc\u9053\u9577\u534a\u5f84 $a$ \u3068\u5468\u671f $P$ \u3067\u7121\u6b21\u5143\u5316\u3057\u305f\u5909\u6570\u306b\u5bfe\u3059\u308b\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u306e\u3067\u3042\u3063\u305f\u3002<\/p>\n

\\begin{eqnarray}
\n\\frac{d^2 X}{dT^2} = – 4\\pi^2\\frac{X}{\\left(X^2 + Y^2\\right)^{\\frac{3}{2}}} \\\\
\n\\frac{d^2 Y}{dT^2} = – 4\\pi^2\\frac{Y}{\\left(X^2 + Y^2\\right)^{\\frac{3}{2}}}
\n\\end{eqnarray}<\/p>\n

\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u521d\u671f\u6761\u4ef6<\/h3>\n

\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u5909\u6570\u306b\u5bfe\u3059\u308b\u521d\u671f\u6761\u4ef6\u306f $T = 0$ \u3067<\/p>\n

\\begin{eqnarray}
\nX(0) &=& 1-e \\\\
\nY(0) &=& 0\\\\
\nV_x(0) &=& 0 \\\\
\nV_y(0) &=& 2\\pi\\sqrt{\\frac{1+e}{1-e}}
\n\\end{eqnarray}<\/p>\n

\u3053\u306e\u521d\u671f\u6761\u4ef6\u3067\u6570\u5024\u8a08\u7b97\u3059\u308b\u3068\uff0c\uff08\u898f\u683c\u5316\u3055\u308c\u305f\uff09\u9577\u534a\u5f84 $1$\uff0c\u96e2\u5fc3\u7387 $e$ \u306e\u6955\u5186\u306e\u8ecc\u9053\u304c\u5f97\u3089\u308c\u308b\u30cf\u30ba\u3002<\/p>\n

\u3058\u3083\u3042\uff0c\u305d\u3053\u307e\u3067\u308f\u304b\u3063\u3066\u3044\u308b\u306e\u306a\u3089\uff0c\u306a\u305c\u308f\u3056\u308f\u3056\u6570\u5024\u8a08\u7b97\u3059\u308b\u306e\u304b<\/strong><\/span>\u3068\u3044\u3046\u3068\uff0c\u305d\u308c\u306f\u6955\u5186\u8ecc\u9053\u306e\u89e3\u304c\u6642\u9593 $t$ \u306e\u967d\u95a2\u6570\u3068\u3057\u3066\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u308f\u3051\u3067\u306f\u306a\u3044\u304b\u3089<\/strong><\/span>\u3002\u6642\u523b $t$ \u306e\u3068\u304d\uff0c\u3069\u3053\u306b\u3044\u308b\u304b\u304c\u89e3\u6790\u7684\u306b\u308f\u304b\u3063\u3066\u3044\u306a\u3044\u306e\u3067\uff0c\u305d\u308c\u3092\u77e5\u308a\u305f\u3044\u304b\u3089\u6570\u5024\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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Runge-Kutta \u7528\u306b\u9023\u7acb1\u968e\u5fae\u5206\u65b9\u7a0b\u5f0f\u7cfb\u306b<\/h3>\n

\\begin{eqnarray}
\n\\frac{dX}{dT} &=& F_1(V_x) = V_x \\\\
\n\\frac{dY}{dT} &=& F_2(V_y) = V_y \\\\
\n\\frac{dV_x}{dT} &=& F_3(X, Y)
\n= -4\\pi^2 \\frac{X}{\\left(X^2 + Y^2\\right)^{\\frac{3}{2}}} \\\\
\n\\frac{dV_y}{dT} &=& F_4(X, Y)
\n= -4\\pi^2 \\frac{Y}{\\left(X^2 + Y^2\\right)^{\\frac{3}{2}}}
\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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In\u00a0[1]:<\/div>\n
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F1<\/span>(<\/span>Vx<\/span>)<\/span>:=<\/span> Vx<\/span>;\r\nF2<\/span>(<\/span>Vy<\/span>)<\/span>:=<\/span> Vy<\/span>;\r\nF3<\/span>(<\/span>X<\/span>, Y<\/span>)<\/span>:=<\/span> -<\/span>4*<\/span>%pi<\/span>**<\/span>2<\/span> *<\/span> X<\/span>\/<\/span>(<\/span>X<\/span>**<\/span>2<\/span> +<\/span> Y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>(<\/span>3\/<\/span>2<\/span>)<\/span>;\r\nF4<\/span>(<\/span>X<\/span>, Y<\/span>)<\/span>:=<\/span> -<\/span>4*<\/span>%pi<\/span>**<\/span>2<\/span> *<\/span> Y<\/span>\/<\/span>(<\/span>X<\/span>**<\/span>2<\/span> +<\/span> Y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>(<\/span>3\/<\/span>2<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{1}$}F_{1}\\left({\\it Vx}\\right):={\\it Vx}\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{2}$}F_{2}\\left({\\it Vy}\\right):={\\it Vy}\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{3}$}F_{3}\\left(X , Y\\right):=\\frac{\\left(-4\\right)\\,\\pi^2\\,X}{\\left(X^2+Y^2\\right)^{\\frac{3}{2}}}\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{4}$}F_{4}\\left(X , Y\\right):=\\frac{\\left(-4\\right)\\,\\pi^2\\,Y}{\\left(X^2+Y^2\\right)^{\\frac{3}{2}}}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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rk()<\/code> \u3067\u9023\u7acb\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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\/* T \u306e\u521d\u671f\u5024 *\/<\/span>\r\nT0<\/span>:<\/span> 0$\r\n\/* T \u306e\u7d42\u4e86\u5024 *\/<\/span>\r\nTend<\/span>:<\/span> 1$\r\n\/* \u5206\u5272\u6570 *\/<\/span>\r\nndiv<\/span>:<\/span> 100$\r\nNdiv<\/span>:<\/span> 36$\r\nN<\/span>:<\/span> Ndiv<\/span> *<\/span> ndiv<\/span>$\r\n\/* \u523b\u307f\u5e45 h \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066\u8a08\u7b97\u3055\u308c\u308b\u3002*\/<\/span>\r\nh<\/span>:<\/span> float<\/span>((<\/span>Tend<\/span> -<\/span> T0<\/span>)<\/span>\/<\/span>N<\/span>)<\/span>$\r\n\r\n\/* \u96e2\u5fc3\u7387 e *\/<\/span>\r\ne<\/span> :<\/span> 0.<\/span>6$\r\n\/* \u521d\u671f\u6761\u4ef6 *\/<\/span>\r\nX0<\/span>:<\/span> 1-<\/span>e<\/span>$\r\nY0<\/span>:<\/span> 0$\r\nVx0<\/span>:<\/span> 0$\r\nVy0<\/span>:<\/span> 2*<\/span>%pi<\/span>*<\/span>sqrt<\/span>((<\/span>1+<\/span>e<\/span>)<\/span>\/<\/span>(<\/span>1-<\/span>e<\/span>))<\/span>$\r\n\r\nrksol<\/span>:<\/span>\r\nrk<\/span>([<\/span>F1<\/span>(<\/span>Vx<\/span>)<\/span>, F2<\/span>(<\/span>Vy<\/span>)<\/span>, F3<\/span>(<\/span>X<\/span>, Y<\/span>)<\/span>, F4<\/span>(<\/span>X<\/span>, Y<\/span>)]<\/span>, \r\n   [<\/span>X<\/span>, Y<\/span>, Vx<\/span>, Vy<\/span>]<\/span>, [<\/span>X0<\/span>, Y0<\/span>, Vx0<\/span>, Vy0<\/span>]<\/span>, \r\n   [<\/span>T<\/span>, T0<\/span>, Tend<\/span>, h<\/span>])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u3061\u3087\u3046\u30691\u5468\u671f $T=t\/P = 1$ \u307e\u3067\u3044\u304f\u3068\uff0c$T=0$ \u306e\u6642\u306e\u521d\u671f\u5024\u306b\u306a\u3063\u3066\u3044\u308b\u306f\u305a\u3060\u304b\u3089\uff0c\u6570\u5024\u8aa4\u5dee\u3092\u78ba\u8a8d\u3059\u308b\u3002<\/p>\n
rksol[length(rksol)]<\/code> \u306f\u30ea\u30b9\u30c8 rksol<\/code> \u306e\u6700\u5f8c\u306e\u9805\uff0crksol[1]<\/code> \u306f\u6700\u521d\u306e\u9805\u3002<\/p>\n
rksol<\/code> \u306f\u9806\u756a\u306b [T, x, y, v, w]<\/code> \u306e5\u3064\u306e\u9805\u304b\u3089\u306a\u308b\u304b\u3089\uff0crksol[1]<\/code> \u306e x<\/code> \u306e\u5024\u306f rksol[1][2]<\/code> \u306a\u3069\u3068\u3057\u3066\u53c2\u7167\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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\/* X \u306e\u8aa4\u5dee *\/<\/span>\r\nrksol<\/span>[<\/span>length<\/span>(<\/span>rksol<\/span>)][<\/span>2]<\/span> -<\/span> rksol<\/span>[<\/span>1][<\/span>2]<\/span>;\r\n\/* Y \u306e\u8aa4\u5dee *\/<\/span>\r\nrksol<\/span>[<\/span>length<\/span>(<\/span>rksol<\/span>)][<\/span>3]<\/span> -<\/span> rksol<\/span>[<\/span>1][<\/span>3]<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{17}$}5.745404152435185 \\times 10^{-14}\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{18}$}1.152249439959063 \\times 10^{-9}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4e00\u5b9a\u6642\u9593\u9593\u9694\u3054\u3068\u306e\u4f4d\u7f6e\u3092\u30b0\u30e9\u30d5\u306b<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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\/* Runge-Kutta \u6cd5\u3067\u6c42\u3081\u305f\u89e3\u306e (X, Y) \u3092\u9593\u5f15\u304f *\/<\/span>\r\nXY_rk<\/span>:<\/span> \r\n  makelist<\/span>([<\/span>rksol<\/span>[<\/span>i<\/span>][<\/span>2]<\/span>, rksol<\/span>[<\/span>i<\/span>][<\/span>3]]<\/span>, i<\/span>, 1<\/span>, length<\/span>(<\/span>rksol<\/span>)<\/span>, ndiv<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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plot2d()<\/code> \u3067\u30b0\u30e9\u30d5\u4f5c\u6210<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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plot2d<\/span>([<\/span>discrete<\/span>, XY_rk<\/span>]<\/span>, [<\/span>style<\/span>, [<\/span>points<\/span>,1]]<\/span>, \r\n       [<\/span>same_xy<\/span>]<\/span>, [<\/span>x<\/span>, -<\/span>2<\/span>, 1]<\/span>, [<\/span>y<\/span>, -<\/span>1.5<\/span>, 1.<\/span>5])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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draw2d()<\/code> \u3067\u30b0\u30e9\u30d5\u4f5c\u6210<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[6]:<\/div>\n
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draw2d<\/span>(<\/span>\r\n  \/* \u70b9\u3092\u5857\u308a\u3064\u3076\u3057\u305f\u4e38\u306b *\/<\/span>\r\n  point_type<\/span> =<\/span> 7<\/span>, \r\n  \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  xrange<\/span> =<\/span> [<\/span>-<\/span>2<\/span>, 1]<\/span>, yrange<\/span> =<\/span> [<\/span>-<\/span>1.5<\/span>, 1.<\/span>5]<\/span>,\r\n  \/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  proportional_axes<\/span>=<\/span>xy<\/span>,\r\n  \/* x \u8ef8 y \u8ef8 *\/<\/span>\r\n  xaxis<\/span> =<\/span> true<\/span>, yaxis<\/span> =<\/span> true<\/span>,   \r\n  \r\n  \/* \u70b9\u306e\u5927\u304d\u3055 *\/<\/span>\r\n  point_size<\/span> =<\/span> 0.5<\/span>, \r\n  points<\/span>(<\/span>XY_rk<\/span>)<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u305f\u5834\u5408\u306e\u89e3\u3068\u306e\u6bd4\u8f03<\/h3>\n
\u300c\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u3066\u30b1\u30d7\u30e9\u30fc\u306e\u7b2c2\u6cd5\u5247\u3092\u8996\u899a\u7684\u306b\u78ba\u8a8d\u3059\u308b<\/a>\u300d\u306b\u307e\u3068\u3081\u3066\u3044\u308b\u3088\u3046\u306b\uff0c<\/p>\n
\\begin{eqnarray}
\nx &=& r \\cos\\varphi = a(\\cos u \u2013 e)\\\\
\ny &=& r \\sin\\varphi = a \\sqrt{1-e^2} \\sin u\\\\
\n\\frac{2\\pi}{P} t &=& u \u2013 e \\sin u
\n\\end{eqnarray}<\/p>\n
\u3060\u304b\u3089\uff0c\u7121\u6b21\u5143\u5316\u3057\u305f\u5909\u6570\u3067\u306f<\/p>\n
\\begin{eqnarray}
\nX_u(u) &=& \\frac{x}{a} = \\cos u \u2013 e\\\\
\nY_u(u) &=& \\frac{y}{a} = \\sqrt{1-e^2} \\sin u\\\\
\n2\\pi T &=& u \u2013 e \\sin u, \\quad T = \\frac{t}{P}
\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3<\/h4>\n
$$g(u) \\equiv u – e \\sin u$$<\/p>\n
\u3068\u3057\u3066 $T_i = \\frac{i}{N_{\\rm div}}$ \u306e\u3068\u304d\u306b\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f $g(u_i) = 2\\pi T_i $ \u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u3066 $u_i$ \u3092\u6c42\u3081\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[7]:<\/div>\n
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\/* \u96e2\u5fc3\u7387 *\/<\/span>\r\ne<\/span>$\r\n\r\n\/* \u5206\u5272\u6570 *\/<\/span>\r\nNdiv<\/span>$\r\n\r\n\/* \u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u3092 find_root \u3067\u6570\u5024\u7684\u306b\u89e3\u304f *\/<\/span>\r\ng<\/span>(<\/span>u<\/span>)<\/span>:=<\/span> u<\/span> -<\/span> e<\/span>*<\/span>sin<\/span>(<\/span>u<\/span>)<\/span>$\r\nfor<\/span> i<\/span>:<\/span>0<\/span> thru<\/span> Ndiv<\/span> do<\/span> \r\n    u<\/span>[<\/span>i<\/span>]<\/span>:<\/span> find_root<\/span>(<\/span>g<\/span>(<\/span>u<\/span>)<\/span> =<\/span> 2*<\/span>%pi<\/span>\/<\/span>Ndiv<\/span> *<\/span> i<\/span>, u<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4e00\u5b9a\u6642\u9593\u9593\u9694\u3054\u3068\u306e\u4f4d\u7f6e<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[8]:<\/div>\n
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Xu<\/span>(<\/span>u<\/span>)<\/span>:=<\/span> (<\/span>cos<\/span>(<\/span>u<\/span>)<\/span> -<\/span> e<\/span>)<\/span>;\r\nYu<\/span>(<\/span>u<\/span>)<\/span>:=<\/span> sqrt<\/span>(<\/span>1-<\/span>e<\/span>**<\/span>2<\/span>)<\/span>*<\/span>sin<\/span>(<\/span>u<\/span>)<\/span>;\r\n\r\nXY_kep<\/span>:<\/span> makelist<\/span>([<\/span>Xu<\/span>(<\/span>u<\/span>[<\/span>i<\/span>])<\/span>, Yu<\/span>(<\/span>u<\/span>[<\/span>i<\/span>])]<\/span>, i<\/span>, 0<\/span>, Ndiv<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[8]:<\/div>\n
\\[\\tag{${\\it \\%o}_{28}$}{\\it Xu}\\left(u\\right):=\\cos u-e\\]<\/div>\n<\/div>\n
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Out[8]:<\/div>\n
\\[\\tag{${\\it \\%o}_{29}$}{\\it Yu}\\left(u\\right):=\\sqrt{1-e^2}\\,\\sin u\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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2\u3064\u306e\u89e3\u306e\u6bd4\u8f03<\/h4>\n
\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u305f\u89e3\u3067\u3042\u308b xy_rk<\/code> \u3068\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u305f\u89e3\u3067\u3042\u308b xy_kep<\/code> \u306f\uff0c\u5f53\u7136\u306a\u304c\u3089\u6570\u5024\u8aa4\u5dee\u306e\u7bc4\u56f2\u5185\u3067\u4e00\u81f4\u3057\u3066\u3044\u308b\u306f\u305a\u3067\u3042\u308b\u3002<\/p>\n
2\u3064\u306e\u30ea\u30b9\u30c8\u306e\u5f15\u304d\u7b97\u3092\u3057\u3066\u5dee\u3092\u8abf\u3079\u308b\u300237\u7d44\u5168\u3066\u8868\u793a\u3059\u308b\u3068\u5197\u9577\u306a\u306e\u3067\uff0c\u4ee3\u8868\u3057\u30663\u7d44\u307b\u3069\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[9]:<\/div>\n
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\/* 2\u3064\u306e\u6570\u5024\u89e3\u306e\u5dee *\/<\/span>\r\n(<\/span>XY_rk<\/span> -<\/span> XY_kep<\/span>)[<\/span>10]<\/span>;\r\n(<\/span>XY_rk<\/span> -<\/span> XY_kep<\/span>)[<\/span>20]<\/span>;\r\n(<\/span>XY_rk<\/span> -<\/span> XY_kep<\/span>)[<\/span>30]<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[9]:<\/div>\n
\\[\\tag{${\\it \\%o}_{31}$}\\left[ -2.297673162843239 \\times 10^{-11} , -1.414408590250105 \\times 10^{-10} \\right] \\]<\/div>\n<\/div>\n
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Out[9]:<\/div>\n
\\[\\tag{${\\it \\%o}_{32}$}\\left[ 1.573587926628761 \\times 10^{-10} , -2.727420372883316 \\times 10^{-10} \\right] \\]<\/div>\n<\/div>\n
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Out[9]:<\/div>\n
\\[\\tag{${\\it \\%o}_{33}$}\\left[ 5.570213179595385 \\times 10^{-10} , -1.223591228338705 \\times 10^{-10} \\right] \\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u5ff5\u306e\u305f\u3081\u306b2\u3064\u306e\u6570\u5024\u89e3\u3092\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3068\uff0c\u5f53\u7136\u306a\u304c\u3089\u91cd\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[10]:<\/div>\n
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draw2d<\/span>(<\/span>\r\n  \/* \u70b9\u3092\u5857\u308a\u3064\u3076\u3057\u305f\u4e38\u306b *\/<\/span>\r\n  point_type<\/span> =<\/span> 7<\/span>, \r\n  \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  xrange<\/span> =<\/span> [<\/span>-<\/span>2<\/span>, 1]<\/span>, yrange<\/span> =<\/span> [<\/span>-<\/span>1.5<\/span>, 1.<\/span>5]<\/span>,\r\n  \/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  proportional_axes<\/span>=<\/span>xy<\/span>,\r\n  \/* x \u8ef8 y \u8ef8 *\/<\/span>\r\n  xaxis<\/span> =<\/span> true<\/span>, yaxis<\/span> =<\/span> true<\/span>,   \r\n\r\n  point_size<\/span> =<\/span> 0.5<\/span>, color<\/span> =<\/span> red<\/span>, key<\/span> =<\/span> \"\u904b\u52d5\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\"<\/span>,\r\n  points<\/span>(<\/span>XY_rk<\/span>)<\/span>, \r\n  \r\n  point_size<\/span> =<\/span> 0.2<\/span>, color<\/span> =<\/span> blue<\/span>, key<\/span> =<\/span> \"\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\"<\/span>,\r\n  points<\/span>(<\/span>XY_kep<\/span>)<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
\u300c\u4e07\u6709\u5f15\u529b\u306e2\u4f53\u554f\u984c\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u524d\u306e\u4e0b\u3054\u3057\u3089\u3048 ver. 2\u300d\u3067\u4e0b\u3054\u3057\u3089\u3048\u3057\u305f\u5f0f\u3092 Maxima \u3067\u6570\u5024\u7684\u306b\u89e3\u304f\u3002<\/p>
\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":[14,22],"tags":[],"class_list":["post-7036","post","type-post","status-publish","format-standard","hentry","category-maxima","category-22","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7036","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=7036"}],"version-history":[{"count":4,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7036\/revisions"}],"predecessor-version":[{"id":7051,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7036\/revisions\/7051"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=7036"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=7036"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=7036"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}