{"id":4052,"date":"2022-10-20T11:01:27","date_gmt":"2022-10-20T02:01:27","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=4052"},"modified":"2023-03-14T16:59:19","modified_gmt":"2023-03-14T07:59:19","slug":"maxima-%e3%81%a6%e3%82%99%e3%82%b1%e3%83%95%e3%82%9a%e3%83%a9%e3%83%bc%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e9%80%90%e6%ac%a1%e8%bf%91%e4%bc%bc%e7%9a%84%e3%81%ab%e8%a7%a3%e3%81%84%e3%81%a6-draw2d","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/4052\/","title":{"rendered":"Maxima \u3066\u3099\u30b1\u30d5\u309a\u30e9\u30fc\u65b9\u7a0b\u5f0f\u3092\u9010\u6b21\u8fd1\u4f3c\u7684\u306b\u89e3\u3044\u3066 draw2d \u3067\u63cf\u3044\u3066\u30d1\u30e9\u30d1\u30e9\u30a2\u30cb\u30e1\u306b\u3059\u308b"},"content":{"rendered":"

\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\u306e\u5185\u5bb9\u3092\uff0c\u9010\u6b21\u8fd1\u4f3c\u89e3\u3092\u4f7f\u3044\uff0cdraw2d()<\/code> \u3067\u89e3\u304f\u4f8b\u3002<\/p>\n

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\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f<\/h4>\n

\u6955\u5186\u306e\u7126\u70b9\u3092\u539f\u70b9\u3068\u3057\u305f\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19 $x, y$ \u306f\u5a92\u4ecb\u5909\u6570 $u$ \uff08\u96e2\u5fc3\u8fd1\u70b9\u96e2\u89d2\uff09\u306b\u3088\u3063\u3066\uff0c\u6642\u9593 $t$ \u3068\u95a2\u4fc2\u3065\u3051\u3089\u308c\u3066\u3044\u308b\u304c\uff0c$t$ \u306e\u967d\u95a2\u6570\u3068\u3057\u3066\u306f\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u3002<\/p>\n

\\begin{eqnarray}
\nx &=& r \\cos\\varphi = a(\\cos u – e)\\\\
\ny &=& r \\sin\\varphi = a \\sqrt{1-e^2} \\sin u\\\\
\n\\frac{2\\pi}{T} t &=& u – e \\sin u
\n\\end{eqnarray}<\/p>\n

\u4e0a\u8a18\u306e3\u884c\u76ee\u306e\u5f0f\u3092 $\\omega \\equiv \\frac{2\\pi}{T}$ \u3068\u3057\u3066<\/p>\n

$$u – e \\sin u= \\omega t$$<\/p>\n

\u3068\u66f8\u3044\u305f\u5f0f\u304c\uff0c\u96e2\u5fc3\u8fd1\u70b9\u96e2\u89d2 $u$ \u3068\u6642\u9593 $t$ \u3092\u95a2\u4fc2\u4ed8\u3051\u308b \u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f<\/strong><\/span> \u3067\u3042\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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\u9010\u6b21\u8fd1\u4f3c\u6cd5\u306b\u3088\u308b\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306e\u9010\u6b21\u8fd1\u4f3c\u89e3<\/h4>\n

\u96e2\u5fc3\u7387 $e$ \u306f $0 \\leq e < 1$ \u3067\u3042\u308b\u3053\u3068\u304b\u3089\uff0c\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f
\n$$u – e \\sin u = \\omega t$$
\n\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u9010\u6b21\u8fd1\u4f3c\u7684\u306b\u89e3\u3044\u3066\u307f\u307e\u3059\u3002<\/p>\n

\\begin{eqnarray}
\nu &=& \\omega t + e \\sin u \\\\
\nu_0 &=& \\omega t\\\\
\nu_1 &=& \\omega t + e \\sin u_0 = \\omega t + e \\sin \\omega t\\\\
\nu_2 &=& \\omega t + e \\sin u_1 =\\omega t + e \\sin\\left(\\omega t + e \\sin \\omega t\\right) \\\\
\nu_3 &=& \\omega t + e \\sin u_2 =\\omega t + e \\sin\\left\\{\\omega t + e \\sin\\left(\\omega t + e \\sin \\omega t\\right)\\right\\} \\\\
\n&\\vdots&\\\\
\nu_{n} &=& \\omega t + e \\sin u_{n-1} = \\dots\\\\
\n\\end{eqnarray}<\/p>\n

$n$ \u304c\u5927\u304d\u304f\u306a\u308b\u3068\uff0c\u5165\u308c\u5b50\u306b\u306a\u3063\u3066\u3044\u308b\u9805\u304c\u3069\u3093\u3069\u3093\u5897\u6b96\u3057\u3066\u3044\u304d\u307e\u3059\u304c\uff0c$u_3$ \u306e\u3042\u305f\u308a\u307e\u3067\u306f\uff0c\u8fd1\u4f3c\u7684\u306b $u$ \u306f $t$ \u306e\u967d\u95a2\u6570\u3068\u3057\u3066\u3042\u3089\u308f\u3055\u308c\u3066\u3044\u308b\u306a\u3041… \u3068\u3044\u3046\u898b\u305f\u76ee\u304c\u3057\u307e\u3059\u3002<\/p>\n

\u4e0a\u306e\u5f0f\u306b\u305d\u3063\u3066\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u95a2\u6570 $u(n, e, \\omega t)$ \u3092\u518d\u5e30\u7684\u306b\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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u<\/span>(<\/span>N<\/span>, e<\/span>, omegat<\/span>)<\/span>:=<\/span>\r\nblock<\/span>(<\/span>  \r\n  if<\/span> N<\/span> =<\/span> 0<\/span> then<\/span>\r\n    omegat<\/span>\r\n  else<\/span>\r\n    omegat<\/span> +<\/span> e<\/span>*<\/span>sin<\/span>(<\/span>u<\/span>(<\/span>N<\/span>-<\/span>1<\/span>, e<\/span>, omegat<\/span>))<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\/* \u305f\u3068\u3048\u3070 n = 3 \u306e\u3068\u304d\u306f... *\/<\/span>\r\nu3<\/span> =<\/span> u<\/span>(<\/span>3<\/span>, e<\/span>, omega<\/span> *<\/span> t<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[2]:<\/div>\n
\\[\\tag{${\\it \\%o}_{2}$}u_{3}=e\\,\\sin \\left(e\\,\\sin \\left(e\\,\\sin \\left(\\omega\\,t\\right)+\\omega\\,t\\right)+\\omega\\,t\\right)+\\omega\\,t\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$u(\\omega t)$ \u3092\u4f7f\u3048\u3070\uff0c\u5929\u4f53\u306e\u4f4d\u7f6e $x, \\ y$ \u304c $t$ \u306e\u3042\u304b\u3089\u3055\u307e\u306a\u95a2\u6570\uff08\u967d\u95a2\u6570\uff09\u3068\u3057\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002$N = 10$ \u3068\u3057\u3066\u304a\u304d\u307e\u3059\u3002\uff08$N$ \u3092\u3069\u308c\u304f\u3089\u3044\u306b\u3059\u308b\u304b\u306f\uff0c\u9010\u6b21\u8fd1\u4f3c\u306e\u7cbe\u5ea6\u3092\u3069\u306e\u7a0b\u5ea6\u306b\u3059\u308b\u304b\u306b\u3088\u308a\u307e\u3059\u3002\u5404\u81ea\u7cbe\u5ea6\u306e\u30c1\u30a7\u30c3\u30af\u3092\u3059\u308b\u3053\u3068\u3002\uff09<\/p>\n
\\begin{eqnarray}
\nx(\\omega t) &=& a (\\cos u(\\omega t) – e) \\\\
\ny(\\omega t) &=& a \\sqrt{1-e^2} \\sin u(\\omega t)
\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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x<\/span>(<\/span>a<\/span>, e<\/span>, omegat<\/span>)<\/span>:=<\/span> a<\/span>*<\/span>(<\/span>cos<\/span>(<\/span>u<\/span>(<\/span>10<\/span>, e<\/span>, omegat<\/span>))<\/span> -<\/span> e<\/span>)<\/span>;\r\ny<\/span>(<\/span>a<\/span>, e<\/span>, omegat<\/span>)<\/span>:=<\/span> a<\/span>*<\/span>sqrt<\/span>(<\/span>1-<\/span>e<\/span>**<\/span>2<\/span>)<\/span>*<\/span>sin<\/span>(<\/span>u<\/span>(<\/span>10<\/span>, e<\/span>, omegat<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{3}$}x\\left(a , e , {\\it omegat}\\right):=a\\,\\left(\\cos u\\left(10 , e , {\\it omegat}\\right)-e\\right)\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{4}$}y\\left(a , e , {\\it omegat}\\right):=a\\,\\sqrt{1-e^2}\\,\\sin u\\left(10 , e , {\\it omegat}\\right)\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\/* omega t \u306e\u7bc4\u56f2 [0, 2 \u03c0] \u3092 Ndiv \u7b49\u5206\u3057\u3066 <\/span>\r\n   \u5929\u4f53\u306e\u4f4d\u7f6e [x, y] \u306e\u30ea\u30b9\u30c8\u3092\u4f5c\u6210\u3059\u308b    *\/<\/span>\r\nNdiv<\/span>:<\/span> 36$\r\npi<\/span>:<\/span> float<\/span>(<\/span>%pi<\/span>)<\/span>$ \r\npxy<\/span>:<\/span> makelist<\/span>([<\/span>x<\/span>(<\/span>5<\/span>, 0.6<\/span>, 2*<\/span>pi<\/span>\/<\/span>Ndiv<\/span> *<\/span> i<\/span>)<\/span>, y<\/span>(<\/span>5<\/span>, 0.6<\/span>, 2*<\/span>pi<\/span>\/<\/span>Ndiv<\/span> *<\/span> i<\/span>)]<\/span>, i<\/span>, 0<\/span>, Ndiv<\/span>+<\/span>1<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\/* draw2d() \u3067\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3057\u3066\u30b0\u30e9\u30d5\u3092\u63cf\u304f *\/<\/span>\r\ndraw2d<\/span>(<\/span>\r\n  \/* \u6ed1\u3089\u304b\u306b\u66f2\u7dda\u3092\u63cf\u304f\u3088\u3046\u306b *\/<\/span>\r\n  nticks<\/span> =<\/span> 300<\/span>, \r\n  \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  xrange<\/span> =<\/span> [<\/span>-<\/span>9<\/span>, 3]<\/span>, yrange<\/span> =<\/span> [<\/span>-<\/span>6<\/span>, 6]<\/span>,\r\n  \/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  proportional_axes<\/span> =<\/span> xy<\/span>,\r\n  \/* x \u8ef8 y \u8ef8\u306e\u8868\u793a *\/<\/span>\r\n  xaxis<\/span> =<\/span> true<\/span>, yaxis<\/span> =<\/span> true<\/span>, \r\n  \/* \u8ef8\u306e\u304d\u3056\u307f\u76ee\u76db\u306e\u975e\u8868\u793a *\/<\/span>\r\n  xtics<\/span> =<\/span> false<\/span>, ytics<\/span> =<\/span> false<\/span>, \r\n  \/* \u6a2a\u8ef8\u7e26\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n  xlabel<\/span> =<\/span> \"x\"<\/span>, ylabel<\/span> =<\/span> \"y\"<\/span>,\r\n  \r\n  \/* \u6955\u5186\u8ecc\u9053 *\/<\/span>\r\n  line_width<\/span> =<\/span> 1<\/span>, \r\n  color<\/span> =<\/span> red<\/span>, \r\n  parametric<\/span>(<\/span>x<\/span>(<\/span>5<\/span>, 0.6<\/span>, omegat<\/span>)<\/span>, y<\/span>(<\/span>5<\/span>, 0.6<\/span>, omegat<\/span>)<\/span>, omegat<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>)<\/span>,\r\n  \r\n  \/* 2\u70b9\u3092\u3080\u3059\u3076\u76f4\u7dda\u3092\u63cf\u304f\u4f8b *\/<\/span>\r\n  point_type<\/span> =<\/span> none<\/span>, \r\n  line_type<\/span> =<\/span> dots<\/span>,\r\n  color<\/span> =<\/span> black<\/span>,\r\n  points_joined<\/span> =<\/span> true<\/span>, \r\n  points<\/span>([[<\/span>0<\/span>, 0]<\/span>,pxy<\/span>[<\/span>2]])<\/span>, \r\n  points<\/span>([[<\/span>0<\/span>, 0]<\/span>,pxy<\/span>[<\/span>18]])<\/span>, \r\n  points<\/span>([[<\/span>0<\/span>, 0]<\/span>,pxy<\/span>[<\/span>20]])<\/span>, \r\n  points<\/span>([[<\/span>0<\/span>, 0]<\/span>,pxy<\/span>[<\/span>36]])<\/span>, \r\n  points_joined<\/span> =<\/span> false<\/span>,\r\n  \r\n  \/* \u70b9\u3092\u6253\u3064\u4f8b *\/<\/span>\r\n  point_type<\/span> =<\/span> 7<\/span>, \r\n  point_size<\/span> =<\/span> 1<\/span>, \r\n  color<\/span> =<\/span> blue<\/span>,\r\n  points<\/span>(<\/span>pxy<\/span>)<\/span>, \r\n  \r\n  \/* \u539f\u70b9 *\/<\/span>\r\n  point_type<\/span> =<\/span> 7<\/span>, \r\n  point_size<\/span> =<\/span> 1<\/span>, \r\n  color<\/span> =<\/span> black<\/span>,\r\n  points<\/span>([[<\/span>0<\/span>, 0]])<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4e0a\u306e\u56f3\u304b\u3089\uff0c\u4e00\u5b9a\u6642\u9593\u9593\u9694\u3054\u3068\u306e\u4f4d\u7f6e\u306e\u30d7\u30ed\u30c3\u30c8\u306a\u306e\u306b\uff0c\u539f\u70b9\uff08\u7126\u70b9\uff09\u306b\u8fd1\u3044\u3068\u304d\u306f\u9593\u9694\u304c\u5e83\u3044\uff0c\u3064\u307e\u308a\u3059\u3070\u3084\u304f\u52d5\u304d\uff0c\u539f\u70b9\u304b\u3089\u96e2\u308c\u3066\u3044\u308b\u3068\u304d\u306f\u611f\u899a\u304c\u72ed\u3044\uff0c\u3064\u307e\u308a\u3086\u3063\u304f\u308a\u52d5\u3044\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n
\u539f\u70b9\u306e\u53f3\u5074\uff0c\u8fd1\u70b9\u4ed8\u8fd1\u306e\u6247\u5f62\u306e\u9762\u7a4d\u3068\uff0c\u539f\u70b9\u306e\u5de6\u5074\uff0c\u9060\u70b9\u4ed8\u8fd1\u306e\u6247\u5f62\u306e\u9762\u7a4d\u306f\u7b49\u3057\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[6]:<\/div>\n
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\/* \u73fe\u5728\u306e\u30b0\u30e9\u30d5\u3092\u30d5\u30a1\u30a4\u30eb\u306b\u4fdd\u5b58\u3002*\/<\/span>\r\n\/* \u5f18\u5927 JupyterHub \u3067\u306f <\/span>\r\n   set_draw_defaults(file_name=\"~\/.maxplot\",terminal='svg)$<\/span>\r\n   \u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3002*\/<\/span>\r\nsystem<\/span>(<\/span>\"cp ~\/.maxplot.svg .\/draw-kep.svg\"<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30d1\u30e9\u30d1\u30e9\u30a2\u30cb\u30e1\u3092\u3064\u304f\u308b<\/h4>\n
\u5404\u6642\u523b\u3054\u3068\u306e\u753b\u50cf\u3092 %03d.png<\/code> \u306e\u3088\u3046\u306b\u30d5\u30a1\u30a4\u30eb\u3068\u3057\u3066\u4fdd\u5b58\u3057\uff0c\uff08\u5f18\u5927 JupyterHub \u306b\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3055\u308c\u3066\u3044\u308b ffmpeg<\/code> \u3092\u4f7f\u3063\u3066\uff09\u30d5\u30a1\u30a4\u30eb\u540d out.mp4<\/code> \u306e\u52d5\u753b\u30d5\u30a1\u30a4\u30eb\u3092\u4f5c\u6210\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\/* \u30d0\u30ea\u30a8\u30fc\u30b7\u30e7\u30f3 1 *\/<\/span>\r\nfor<\/span> i<\/span>:<\/span>1<\/span> thru<\/span> Ndiv<\/span> do<\/span>(<\/span>\r\n  \/* %03d.png \u306e\u3088\u3046\u306a filename \u306b\u3057\u305f\u3044\u3002*\/<\/span>\r\n  tmpname<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \"~4d\"<\/span>,1000+<\/span>i<\/span>)<\/span>,\r\n  filename<\/span>:<\/span> substring<\/span>(<\/span>tmpname<\/span>, 2<\/span>)<\/span>, \r\n  draw2d<\/span>(<\/span>\r\n  \/* \u6ed1\u3089\u304b\u306b\u66f2\u7dda\u3092\u63cf\u304f\u3088\u3046\u306b *\/<\/span>\r\n  nticks<\/span> =<\/span> 300<\/span>, \r\n  \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  xrange<\/span> =<\/span> [<\/span>-<\/span>9<\/span>, 3]<\/span>, yrange<\/span> =<\/span> [<\/span>-<\/span>6<\/span>, 6]<\/span>,\r\n  \/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  proportional_axes<\/span> =<\/span> xy<\/span>,\r\n  \/* x \u8ef8 y \u8ef8\u306e\u8868\u793a *\/<\/span>\r\n  xaxis<\/span> =<\/span> true<\/span>, yaxis<\/span> =<\/span> true<\/span>, \r\n  \/* \u8ef8\u306e\u304d\u3056\u307f\u76ee\u76db\u306e\u975e\u8868\u793a *\/<\/span>\r\n  xtics<\/span> =<\/span> false<\/span>, ytics<\/span> =<\/span> false<\/span>, \r\n  \/* \u6a2a\u8ef8\u7e26\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n  xlabel<\/span> =<\/span> \"x\"<\/span>, ylabel<\/span> =<\/span> \"y\"<\/span>,\r\n  \r\n  \/* \u6955\u5186\u8ecc\u9053 *\/<\/span>\r\n  line_width<\/span> =<\/span> 1<\/span>, \r\n  color<\/span> =<\/span> red<\/span>, \r\n  parametric<\/span>(<\/span>x<\/span>(<\/span>5<\/span>, 0.6<\/span>, omegat<\/span>)<\/span>, y<\/span>(<\/span>5<\/span>, 0.6<\/span>, omegat<\/span>)<\/span>, omegat<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>)<\/span>,\r\n    \r\n  \/* \u70b9\u3092\u6253\u3064\u4f8b *\/<\/span>\r\n  point_type<\/span> =<\/span> 7<\/span>, \r\n  point_size<\/span> =<\/span> 3<\/span>, \r\n  color<\/span> =<\/span> blue<\/span>,\r\n  points<\/span>([<\/span>pxy<\/span>[<\/span>i<\/span>]])<\/span>, \r\n  \r\n  \/* \u539f\u70b9 *\/<\/span>\r\n  point_type<\/span> =<\/span> 7<\/span>, \r\n  point_size<\/span> =<\/span> 3<\/span>, \r\n  color<\/span> =<\/span> black<\/span>,\r\n  points<\/span>([[<\/span>0<\/span>, 0]])<\/span>, \r\n  \r\n  \/* \u5404 i \u3054\u3068\u306b png \u30d5\u30a1\u30a4\u30eb\u306b\u4fdd\u5b58\u3059\u308b\u3002*\/<\/span> \r\n  file_name<\/span> =<\/span> filename<\/span>, \r\n  dimensions<\/span> =<\/span> 120*<\/span>[<\/span>12.0<\/span>,9.<\/span>0]<\/span>,\r\n  terminal<\/span> =<\/span> png<\/span> \r\n  )<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In [8 ]:<\/div>\n
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\/* \u30d0\u30ea\u30a8\u30fc\u30b7\u30e7\u30f3 2 *\/<\/span>\r\nfor<\/span> i<\/span>:<\/span>1<\/span> thru<\/span> Ndiv<\/span> do<\/span>(<\/span>\r\n  \/* %03d.png \u306e\u3088\u3046\u306a filename \u306b\u3057\u305f\u3044\u3002*\/<\/span>\r\n  tmpname<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \"~4d\"<\/span>,1000+<\/span>Ndiv<\/span>+<\/span>i<\/span>)<\/span>,\r\n  filename<\/span>:<\/span> substring<\/span>(<\/span>tmpname<\/span>, 2<\/span>)<\/span>, \r\n  draw2d<\/span>(<\/span>\r\n  \/* \u6ed1\u3089\u304b\u306b\u66f2\u7dda\u3092\u63cf\u304f\u3088\u3046\u306b *\/<\/span>\r\n  nticks<\/span> =<\/span> 300<\/span>, \r\n  \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  xrange<\/span> =<\/span> [<\/span>-<\/span>9<\/span>, 3]<\/span>, yrange<\/span> =<\/span> [<\/span>-<\/span>6<\/span>, 6]<\/span>,\r\n  \/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  proportional_axes<\/span> =<\/span> xy<\/span>,\r\n  \/* x \u8ef8 y \u8ef8\u306e\u8868\u793a *\/<\/span>\r\n  xaxis<\/span> =<\/span> true<\/span>, yaxis<\/span> =<\/span> true<\/span>, \r\n  \/* \u8ef8\u306e\u304d\u3056\u307f\u76ee\u76db\u306e\u975e\u8868\u793a *\/<\/span>\r\n  xtics<\/span> =<\/span> false<\/span>, ytics<\/span> =<\/span> false<\/span>, \r\n  \/* \u6a2a\u8ef8\u7e26\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n  xlabel<\/span> =<\/span> \"x\"<\/span>, ylabel<\/span> =<\/span> \"y\"<\/span>,\r\n  \r\n  \/* \u6955\u5186\u8ecc\u9053 *\/<\/span>\r\n  line_width<\/span> =<\/span> 1<\/span>, \r\n  color<\/span> =<\/span> red<\/span>, \r\n  parametric<\/span>(<\/span>x<\/span>(<\/span>5<\/span>, 0.6<\/span>, omegat<\/span>)<\/span>, y<\/span>(<\/span>5<\/span>, 0.6<\/span>, omegat<\/span>)<\/span>, omegat<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>)<\/span>,\r\n    \r\n  \/* \u70b9\u3092\u6253\u3064\u4f8b *\/<\/span>\r\n  point_type<\/span> =<\/span> 7<\/span>, \r\n  point_size<\/span> =<\/span> 3<\/span>, \r\n  color<\/span> =<\/span> blue<\/span>,\r\n  points<\/span>(<\/span>firstn<\/span>(<\/span>pxy<\/span>, i<\/span>))<\/span>, \r\n  \r\n  \/* \u539f\u70b9 *\/<\/span>\r\n  point_type<\/span> =<\/span> 7<\/span>, \r\n  point_size<\/span> =<\/span> 3<\/span>, \r\n  color<\/span> =<\/span> black<\/span>,\r\n  points<\/span>([[<\/span>0<\/span>, 0]])<\/span>, \r\n  \r\n  \/* \u5404 i \u3054\u3068\u306b png \u30d5\u30a1\u30a4\u30eb\u306b\u4fdd\u5b58\u3059\u308b\u3002*\/<\/span> \r\n  file_name<\/span> =<\/span> filename<\/span>, \r\n  dimensions<\/span> =<\/span> 120*<\/span>[<\/span>12.0<\/span>,9.<\/span>0]<\/span>,\r\n  terminal<\/span> =<\/span> png<\/span> \r\n  )<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In [9 ]:<\/div>\n
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\/* \u30d0\u30ea\u30a8\u30fc\u30b7\u30e7\u30f3 3 *\/<\/span>\r\nfor<\/span> i<\/span>:<\/span>2<\/span> thru<\/span> Ndiv<\/span>+<\/span>1<\/span> do<\/span>(<\/span>\r\n  \/* %03d.png \u306e\u3088\u3046\u306a filename \u306b\u3057\u305f\u3044\u3002*\/<\/span>\r\n  tmpname<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \"~4d\"<\/span>,1000+<\/span>2*<\/span>Ndiv<\/span>+<\/span>i<\/span>-<\/span>1<\/span>)<\/span>,\r\n  filename<\/span>:<\/span> substring<\/span>(<\/span>tmpname<\/span>, 2<\/span>)<\/span>, \r\n  draw2d<\/span>(<\/span>\r\n  \/* \u6ed1\u3089\u304b\u306b\u66f2\u7dda\u3092\u63cf\u304f\u3088\u3046\u306b *\/<\/span>\r\n  nticks<\/span> =<\/span> 300<\/span>, \r\n  \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  xrange<\/span> =<\/span> [<\/span>-<\/span>9<\/span>, 3]<\/span>, yrange<\/span> =<\/span> [<\/span>-<\/span>6<\/span>, 6]<\/span>,\r\n  \/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  proportional_axes<\/span> =<\/span> xy<\/span>,\r\n  \/* x \u8ef8 y \u8ef8\u306e\u8868\u793a *\/<\/span>\r\n  xaxis<\/span> =<\/span> true<\/span>, yaxis<\/span> =<\/span> true<\/span>, \r\n  \/* \u8ef8\u306e\u304d\u3056\u307f\u76ee\u76db\u306e\u975e\u8868\u793a *\/<\/span>\r\n  xtics<\/span> =<\/span> false<\/span>, ytics<\/span> =<\/span> false<\/span>, \r\n  \/* \u6a2a\u8ef8\u7e26\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n  xlabel<\/span> =<\/span> \"x\"<\/span>, ylabel<\/span> =<\/span> \"y\"<\/span>,\r\n  \r\n  \/* \u6955\u5186\u8ecc\u9053 *\/<\/span>\r\n  line_width<\/span> =<\/span> 1<\/span>, \r\n  color<\/span> =<\/span> red<\/span>, \r\n  parametric<\/span>(<\/span>x<\/span>(<\/span>5<\/span>, 0.6<\/span>, omegat<\/span>)<\/span>, y<\/span>(<\/span>5<\/span>, 0.6<\/span>, omegat<\/span>)<\/span>, omegat<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>)<\/span>,\r\n\r\n  \/* 2\u70b9\u3092\u3080\u3059\u3076\u76f4\u7dda\u3092\u63cf\u304f\u4f8b *\/<\/span>\r\n  point_type<\/span> =<\/span> none<\/span>, \r\n  color<\/span> =<\/span> red<\/span>,\r\n  points_joined<\/span> =<\/span> true<\/span>, \r\n  points<\/span>([[<\/span>0<\/span>, 0]<\/span>,pxy<\/span>[<\/span>i<\/span>-<\/span>1]])<\/span>, \r\n  points<\/span>([[<\/span>0<\/span>, 0]<\/span>,pxy<\/span>[<\/span>i<\/span>]])<\/span>, \r\n  points_joined<\/span> =<\/span> false<\/span>,\r\n\r\n  \/* \u70b9\u3092\u6253\u3064\u4f8b *\/<\/span>\r\n  point_type<\/span> =<\/span> 7<\/span>, \r\n  point_size<\/span> =<\/span> 3<\/span>, \r\n  color<\/span> =<\/span> blue<\/span>,\r\n  points<\/span>(<\/span>pxy<\/span>)<\/span>, \r\n  \r\n  \/* \u539f\u70b9 *\/<\/span>\r\n  point_type<\/span> =<\/span> 7<\/span>, \r\n  point_size<\/span> =<\/span> 3<\/span>, \r\n  color<\/span> =<\/span> black<\/span>,\r\n  points<\/span>([[<\/span>0<\/span>, 0]])<\/span>, \r\n  \r\n  \/* \u5404 i \u3054\u3068\u306b png \u30d5\u30a1\u30a4\u30eb\u306b\u4fdd\u5b58\u3059\u308b\u3002*\/<\/span> \r\n  file_name<\/span> =<\/span> filename<\/span>, \r\n  dimensions<\/span> =<\/span> 120*<\/span>[<\/span>12.0<\/span>,9.<\/span>0]<\/span>,\r\n  terminal<\/span> =<\/span> png<\/span> \r\n  )<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6955\u5186\u306e\u5f0f<\/p>\n
$$\\frac{(x + a e)^2}{a^2} + \\frac{y^2}{b^2} = 1$$<\/p>\n
\u3088\u308a\uff0c$y$ \u3092 $x$ \u306e\u967d\u95a2\u6570\u3068\u3057\u3066\u8868\u3057\u3066<\/p>\n
\\begin{eqnarray}
\ny = \\pm b \\sqrt{1 – \\frac{(x + a e)^2}{a^2}} = \\pm a \\sqrt{1-e^2} \\sqrt{1 – \\frac{(x + a e)^2}{a^2}}
\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In [10]:<\/div>\n
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yp<\/span>(<\/span>a<\/span>, e<\/span>, x<\/span>)<\/span>:=<\/span> a<\/span>*<\/span>sqrt<\/span>(<\/span>1-<\/span>e<\/span>**<\/span>2<\/span>)<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span> -<\/span> (<\/span>x<\/span>+<\/span>a<\/span>*<\/span>e<\/span>)<\/span>**<\/span>2\/<\/span>a<\/span>**<\/span>2<\/span>)<\/span>;\r\nym<\/span>(<\/span>a<\/span>, e<\/span>, x<\/span>)<\/span>:=<\/span> -<\/span>yp<\/span>(<\/span>a<\/span>, e<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In [11]:<\/div>\n
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\/* \u6247\u5f62\u3092\u5857\u308a\u3064\u3076\u3057 *\/<\/span>\r\n  \/* %03d.png \u306e\u3088\u3046\u306a filename \u306b\u3057\u305f\u3044\u3002*\/<\/span>\r\n  tmpname<\/span>:<\/span> printf<\/span>(<\/span>false<\/span>, \"~4d\"<\/span>,1000+<\/span>3*<\/span>Ndiv<\/span>+<\/span>1<\/span>)<\/span>$\r\n  filename<\/span>:<\/span> substring<\/span>(<\/span>tmpname<\/span>, 2<\/span>)<\/span>$\r\n \r\n  draw2d<\/span>(<\/span>\r\n  \/* \u30b0\u30ea\u30c3\u30c9\u3084\u5ea7\u6a19\u8ef8\u304c\u5857\u308a\u3064\u3076\u3055\u308c\u306a\u3044\u3088\u3046\u306b *\/<\/span>\r\n  user_preamble<\/span> =<\/span> \"set grid front;\"<\/span>,\r\n  \/* \u6ed1\u3089\u304b\u306b\u66f2\u7dda\u3092\u63cf\u304f\u3088\u3046\u306b *\/<\/span>\r\n  nticks<\/span> =<\/span> 300<\/span>, \r\n  \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  xrange<\/span> =<\/span> [<\/span>-<\/span>9<\/span>, 3]<\/span>, yrange<\/span> =<\/span> [<\/span>-<\/span>6<\/span>, 6]<\/span>,\r\n  \/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  proportional_axes<\/span> =<\/span> xy<\/span>,\r\n  \/* x \u8ef8 y \u8ef8\u306e\u8868\u793a *\/<\/span>\r\n  xaxis<\/span> =<\/span> true<\/span>, yaxis<\/span> =<\/span> true<\/span>, \r\n  \/* \u8ef8\u306e\u304d\u3056\u307f\u76ee\u76db\u306e\u975e\u8868\u793a *\/<\/span>\r\n  xtics<\/span> =<\/span> false<\/span>, ytics<\/span> =<\/span> false<\/span>, \r\n  \/* \u6a2a\u8ef8\u7e26\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n  xlabel<\/span> =<\/span> \"x\"<\/span>, ylabel<\/span> =<\/span> \"y\"<\/span>,\r\n  \r\n  \/* \u5857\u308a\u3064\u3076\u3059\u8272\u306e\u6307\u5b9a\u3002*\/<\/span>\r\n  fill_color<\/span> =<\/span> yellow<\/span>,    \r\n  \/* \u8fd1\u70b9\u5074 *\/<\/span>\r\n  \/* \u4e0a\u306e\u7dda\u3002y = f(x) \u3092 filled_func \u306b\u4ee3\u5165\u3002*\/<\/span>\r\n  filled_func<\/span> =<\/span> pxy<\/span>[<\/span>2][<\/span>2]<\/span>\/<\/span>pxy<\/span>[<\/span>2][<\/span>1]<\/span>*<\/span>x<\/span>,        \r\n  \/* \u4e0b\u306e\u7dda\u3002y = g(x) \u3092 0 < x < 2 \u306e\u7bc4\u56f2\u3067\u63cf\u304f\u3002*\/<\/span>\r\n  explicit<\/span>(<\/span>-<\/span>pxy<\/span>[<\/span>2][<\/span>2]<\/span>\/<\/span>pxy<\/span>[<\/span>2][<\/span>1]<\/span>*<\/span>x<\/span>, x<\/span>, 0<\/span>, pxy<\/span>[<\/span>2][<\/span>1])<\/span>,  \r\n  \/* \u4e0a\u306e\u7dda\u3002y = f(x) \u3092 filled_func \u306b\u4ee3\u5165\u3002*\/<\/span>\r\n  filled_func<\/span> =<\/span> yp<\/span>(<\/span>5<\/span>, 0.6<\/span>, x<\/span>)<\/span>,        \r\n  \/* \u4e0b\u306e\u7dda\u3002y = g(x) \u3092 0 < x < 2 \u306e\u7bc4\u56f2\u3067\u63cf\u304f\u3002*\/<\/span>\r\n  explicit<\/span>(<\/span>ym<\/span>(<\/span>5<\/span>, 0.6<\/span>, x<\/span>)<\/span>, x<\/span>, pxy<\/span>[<\/span>2][<\/span>1]<\/span>, pxy<\/span>[<\/span>1][<\/span>1])<\/span>,  \r\n\r\n  \/* \u9060\u70b9\u5074 *\/<\/span>\r\n  \/* \u4e0a\u306e\u7dda\u3002y = f(x) \u3092 filled_func \u306b\u4ee3\u5165\u3002*\/<\/span>\r\n  filled_func<\/span> =<\/span> pxy<\/span>[<\/span>18][<\/span>2]<\/span>\/<\/span>pxy<\/span>[<\/span>18][<\/span>1]<\/span>*<\/span>x<\/span>,        \r\n  \/* \u4e0b\u306e\u7dda\u3002y = g(x) \u3092 0 < x < 2 \u306e\u7bc4\u56f2\u3067\u63cf\u304f\u3002*\/<\/span>\r\n  explicit<\/span>(<\/span>-<\/span>pxy<\/span>[<\/span>18][<\/span>2]<\/span>\/<\/span>pxy<\/span>[<\/span>18][<\/span>1]<\/span>*<\/span>x<\/span>, x<\/span>, pxy<\/span>[<\/span>18][<\/span>1]<\/span>, 0<\/span>)<\/span>,  \r\n  \/* \u4e0a\u306e\u7dda\u3002y = f(x) \u3092 filled_func \u306b\u4ee3\u5165\u3002*\/<\/span>\r\n  filled_func<\/span> =<\/span> yp<\/span>(<\/span>5<\/span>, 0.6<\/span>, x<\/span>)<\/span>,        \r\n  \/* \u4e0b\u306e\u7dda\u3002y = g(x) \u3092 0 < x < 2 \u306e\u7bc4\u56f2\u3067\u63cf\u304f\u3002*\/<\/span>\r\n  explicit<\/span>(<\/span>ym<\/span>(<\/span>5<\/span>, 0.6<\/span>, x<\/span>)<\/span>, x<\/span>, pxy<\/span>[<\/span>19][<\/span>1]<\/span>, pxy<\/span>[<\/span>18][<\/span>1])<\/span>,  \r\n\r\n  \/* \u5857\u308a\u3064\u3076\u3057\u7d42\u4e86\u3002*\/<\/span>\r\n  filled_func<\/span> =<\/span> false<\/span>,\r\n  \r\n  \/* \u6955\u5186\u8ecc\u9053 *\/<\/span>\r\n  line_width<\/span> =<\/span> 1<\/span>, \r\n  color<\/span> =<\/span> red<\/span>, \r\n  parametric<\/span>(<\/span>x<\/span>(<\/span>5<\/span>, 0.6<\/span>, omegat<\/span>)<\/span>, y<\/span>(<\/span>5<\/span>, 0.6<\/span>, omegat<\/span>)<\/span>, omegat<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>)<\/span>,\r\n  \r\n  \/* 2\u70b9\u3092\u3080\u3059\u3076\u76f4\u7dda\u3092\u63cf\u304f\u4f8b *\/<\/span>\r\n  point_type<\/span> =<\/span> none<\/span>, \r\n  color<\/span> =<\/span> red<\/span>,\r\n  points_joined<\/span> =<\/span> true<\/span>, \r\n  points<\/span>([[<\/span>0<\/span>, 0]<\/span>,pxy<\/span>[<\/span>2]])<\/span>, \r\n  points<\/span>([[<\/span>0<\/span>, 0]<\/span>,pxy<\/span>[<\/span>36]])<\/span>, \r\n  points<\/span>([[<\/span>0<\/span>, 0]<\/span>,pxy<\/span>[<\/span>18]])<\/span>, \r\n  points<\/span>([[<\/span>0<\/span>, 0]<\/span>,pxy<\/span>[<\/span>20]])<\/span>, \r\n  points_joined<\/span> =<\/span> false<\/span>,\r\n\r\n  \/* \u70b9\u3092\u6253\u3064\u4f8b *\/<\/span>\r\n  point_type<\/span> =<\/span> 7<\/span>, \r\n  point_size<\/span> =<\/span> 3<\/span>, \r\n  color<\/span> =<\/span> blue<\/span>,\r\n  points<\/span>(<\/span>pxy<\/span>)<\/span>, \r\n  \r\n  \/* \u539f\u70b9 *\/<\/span>\r\n  point_type<\/span> =<\/span> 7<\/span>, \r\n  point_size<\/span> =<\/span> 3<\/span>, \r\n  color<\/span> =<\/span> black<\/span>,\r\n  points<\/span>([[<\/span>0<\/span>, 0]])<\/span>, \r\n  \r\n  \/* png \u30d5\u30a1\u30a4\u30eb\u306b\u4fdd\u5b58\u3059\u308b\u3002*\/<\/span> \r\n  file_name<\/span> =<\/span> filename<\/span>, \r\n  dimensions<\/span> =<\/span> 120*<\/span>[<\/span>12.0<\/span>,9.<\/span>0]<\/span>,\r\n  terminal<\/span> =<\/span> png<\/span> \r\n  )<\/span>$<\/pre>\n<\/div>\n<\/div>\n
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\/* \u53e4\u3044 out.mp4 \u306f\u524a\u9664\u3057\u3066\u304b\u3089\u3002*\/<\/span>\r\nsystem<\/span>(<\/span>\"rm -f out.mp4\"<\/span>)<\/span>$\r\n\r\n\/* framerate \u3092\u5909\u3048\u308b\u3068\u30d1\u30e9\u30d1\u30e9\u30a2\u30cb\u30e1\u306e\u901f\u3055\u304c\u304b\u308f\u308b\u3002*\/<\/span>\r\n\/* stream_loop \u306f\u3055\u3089\u306b\u4f55\u56de\u7e70\u308a\u8fd4\u3059\u304b\u3092\u6307\u5b9a\u3059\u308b\u3002*\/<\/span>\r\nsystem<\/span>(<\/span>\"ffmpeg -hide_banner -loglevel error -stream_loop 0 -framerate 10 -i %03d.png -vcodec libx264 -pix_fmt yuv420p out.mp4\"<\/span>)<\/span>$\r\nsystem<\/span>(<\/span>\"rm -f ???.png\"<\/span>)<\/span>$<\/pre>\n
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