{"id":7595,"date":"2024-02-13T18:12:24","date_gmt":"2024-02-13T09:12:24","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=7595"},"modified":"2024-02-13T18:14:30","modified_gmt":"2024-02-13T09:14:30","slug":"maxima-%e3%81%a7%e8%a4%87%e6%95%b0%e3%81%ae%e6%9b%b2%e7%b7%9a%e3%82%92%e4%b8%80%e6%b0%97%e3%81%ab%e3%82%b0%e3%83%a9%e3%83%95%e3%81%ab%e3%81%99%e3%82%8b%e4%be%8b%e3%81%a8%e3%82%aa%e3%83%97%e3%82%b7","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/7595\/","title":{"rendered":"Maxima \u3066\u3099\u8907\u6570\u306e\u66f2\u7dda\u3092\u4e00\u6c17\u306b\u30b0\u30e9\u30d5\u306b\u3059\u308b\u4f8b\u3068\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b"},"content":{"rendered":"
\n
<\/div>\n
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Maxima \u3092\u4f7f\u3063\u3066\uff0c\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u5909\u3048\u3066\u8907\u6570\u306e\u66f2\u7dda\u3092\u4e00\u6c17\u306b\u30b0\u30e9\u30d5\u306b\u3059\u308b\u4f8b\u3002\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u969b\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u8a2d\u5b9a\u306b\u3064\u3044\u3066\u3082\u307e\u3068\u3081\u305f\u3002<\/p>\n

\u4f8b\uff1a\u659c\u65b9\u6295\u5c04<\/h3>\n

\u7c21\u5358\u306e\u305f\u3081\u306b\uff08\u521d\u901f\u5ea6 $v_0 \\rightarrow 1$, \u91cd\u529b\u52a0\u901f\u5ea6 $g \\rightarrow 1$ \u306a\u3069\u3068\u3057\u3066\uff09\u9069\u5b9c\u7121\u6b21\u5143\u5316\u3057\u305f\u89e3\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u6642\u9593 $t$ \u3068\u6295\u5c04\u89d2\u5ea6 $\\theta$ \u306e\u95a2\u6570\u3068\u306a\u308b\u3002<\/p>\n

\\begin{eqnarray}
\nx(t, \\theta) &=& t \\cos\\theta \\\\
\ny(t, \\theta) &=& t \\sin\\theta – \\frac{1}{2} t^2
\n\\end{eqnarray}<\/p>\n

$t=0$ \u3067\u5730\u4e0a $y=0$ \u304b\u3089\u6295\u5c04\u3055\u308c\u305f\u7269\u4f53\u304c\u3075\u305f\u305f\u3073\u5730\u4e0a\u306b\u843d\u3061\u308b\u307e\u3067\u306e\u6ede\u7a7a\u6642\u9593 $t_d$ \u306f
\n$$t_d(\\theta) = 2 \\sin\\theta$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n
<\/div>\n
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\u95a2\u6570\u306e\u5b9a\u7fa9<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
\n
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In\u00a0[1]:<\/div>\n
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\n
\/* \u89d2\u5ea6 th \u306f\u5ea6\u3067 *\/<\/span>\r\n\/* [theta] \u306f block() \u5185\u3060\u3051\u3067\u4f7f\u3048\u308b\u30ed\u30fc\u30ab\u30eb\u5909\u6570 *\/<\/span>\r\nx<\/span>(<\/span>t<\/span>, th<\/span>)<\/span>:=<\/span> block<\/span>(<\/span>\r\n    [<\/span>theta<\/span>:<\/span> th<\/span> *<\/span> %pi<\/span>\/<\/span>180]<\/span>,\r\n    t<\/span>*<\/span>cos<\/span>(<\/span>theta<\/span>)<\/span>\r\n    )<\/span>$\r\n\r\ny<\/span>(<\/span>t<\/span>, th<\/span>)<\/span>:=<\/span> block<\/span>(<\/span>\r\n    [<\/span>theta<\/span>:<\/span> th<\/span> *<\/span> %pi<\/span>\/<\/span>180]<\/span>,\r\n    t<\/span>*<\/span>sin<\/span>(<\/span>theta<\/span>)<\/span> -<\/span> t<\/span>**<\/span>2\/<\/span>2<\/span>\r\n    )<\/span>$\r\n    \r\ntd<\/span>(<\/span>th<\/span>)<\/span>:=<\/span> block<\/span>(<\/span>\r\n    [<\/span>theta<\/span>:<\/span> th<\/span> *<\/span> %pi<\/span>\/<\/span>180]<\/span>,\r\n    2*<\/span>sin<\/span>(<\/span>theta<\/span>)<\/span>\r\n    )<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
\n
\n
plot2d()<\/code> \u3067\u8ecc\u9053\u306e\u30b0\u30e9\u30d5<\/h3>\n
\u3068\u308a\u3042\u3048\u305a 1 \u672c\u306e\u8ecc\u9053\u3092\u63cf\u304f<\/h4>\n
$\\theta = 45^{\\circ}$ \u3067\u306e\u659c\u65b9\u6295\u5c04\u306e\u8ecc\u9053\u3092\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3002<\/p>\n
\u307e\u305a\u306f\uff0c\u3068\u308a\u3042\u3048\u305a\u306e\u30b0\u30e9\u30d5\uff1a<\/p>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
In\u00a0[2]:<\/div>\n
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th<\/span>:<\/span> 45$\r\n\r\nplot2d<\/span>([<\/span>parametric<\/span>, x<\/span>(<\/span>t<\/span>, th<\/span>)<\/span>, y<\/span>(<\/span>t<\/span>, th<\/span>)<\/span>, [<\/span>t<\/span>, 0<\/span>, td<\/span>(<\/span>th<\/span>)]])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n
<\/div>\n
\n
<\/p>\n
\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
\n
\n
\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b<\/h4>\n
\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3057\u3066\uff0c\u3082\u3046\u5c11\u3057\u4f53\u88c1\u3092\u6574\u3048\u307e\u3059\u3002<\/p>\n
    \n
  • $\\theta$ \u306e\u5024\u3092\u51e1\u4f8b\u306b<\/li>\n
  • \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb<\/li>\n
  • \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/li>\n
  • \u7e26\u8ef8\u6a2a\u8ef8\u306e\u30a2\u30b9\u30da\u30af\u30c8\u6bd4<\/li>\n
  • \u5ea7\u6a19\u8ef8\u306e\u76ee\u76db\u306e\u9593\u9694…<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[3]:<\/div>\n
    \n
    \n
    \n
    th<\/span>:<\/span> 45$\r\n\r\nplot2d<\/span>(<\/span>\r\n    [<\/span>parametric<\/span>, x<\/span>(<\/span>t<\/span>, th<\/span>)<\/span>, y<\/span>(<\/span>t<\/span>, th<\/span>)<\/span>, [<\/span>t<\/span>, 0<\/span>, td<\/span>(<\/span>th<\/span>)]]<\/span>, \r\n\r\n    \/* \u51e1\u4f8b *\/<\/span>\r\n    [<\/span>legend<\/span>, printf<\/span>(<\/span>false<\/span>, \"\u03b8 = ~2d\u00b0\"<\/span>, th<\/span>)]<\/span>, \r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n    [<\/span>xlabel<\/span>, \"x\"<\/span>]<\/span>, [<\/span>ylabel<\/span>, \"y\"<\/span>]<\/span>,\r\n    \/* \u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb *\/<\/span>\r\n    [<\/span>title<\/span>, \"\u659c\u65b9\u6295\u5c04\"<\/span>]<\/span>,\r\n    \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n    [<\/span>x<\/span>, 0<\/span>, 1.<\/span>1]<\/span>, [<\/span>y<\/span>, 0<\/span>, 0.<\/span>5]<\/span>, \r\n    \/* \u30a2\u30b9\u30da\u30af\u30c8\u6bd4*\/<\/span>\r\n    [<\/span>same_xy<\/span>]<\/span>, \r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u76ee\u76db *\/<\/span>\r\n    [<\/span>gnuplot_preamble<\/span>, \"set xtics 0.1\"<\/span>]<\/span>, \r\n    \/* \u30b0\u30ea\u30c3\u30c9 *\/<\/span>\r\n    grid2d<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    <\/div>\n
    \n
    <\/p>\n
    \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    2\u672c\u306e\u8ecc\u9053\u3092\u63cf\u304f<\/h4>\n
    $\\theta = 30^{\\circ}$ \u3068 $\\theta = 45^{\\circ}$ \u306e2\u672c\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u4f8b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[4]:<\/div>\n
    \n
    \n
    \n
    plot2d<\/span>(<\/span>\r\n    [[<\/span>parametric<\/span>, x<\/span>(<\/span>t<\/span>, 45<\/span>)<\/span>, y<\/span>(<\/span>t<\/span>, 45<\/span>)<\/span>, [<\/span>t<\/span>, 0<\/span>, td<\/span>(<\/span>45<\/span>)]]<\/span>, \r\n     [<\/span>parametric<\/span>, x<\/span>(<\/span>t<\/span>, 30<\/span>)<\/span>, y<\/span>(<\/span>t<\/span>, 30<\/span>)<\/span>, [<\/span>t<\/span>, 0<\/span>, td<\/span>(<\/span>30<\/span>)]]]<\/span>, \r\n\r\n    \/* \u51e1\u4f8b *\/<\/span>\r\n    [<\/span>legend<\/span>, \"\u03b8 = 45\u00b0\"<\/span>, \"\u03b8 = 30\u00b0\"<\/span>]<\/span>, \r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n    [<\/span>xlabel<\/span>, \"x\"<\/span>]<\/span>, [<\/span>ylabel<\/span>, \"y\"<\/span>]<\/span>,\r\n    \/* \u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb *\/<\/span>\r\n    [<\/span>title<\/span>, \"\u659c\u65b9\u6295\u5c04\"<\/span>]<\/span>,\r\n    \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n    [<\/span>x<\/span>, 0<\/span>, 1.<\/span>1]<\/span>, [<\/span>y<\/span>, 0<\/span>, 0.<\/span>5]<\/span>, \r\n    \/* \u30a2\u30b9\u30da\u30af\u30c8\u6bd4*\/<\/span>\r\n    [<\/span>same_xy<\/span>]<\/span>, \r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u76ee\u76db *\/<\/span>\r\n    [<\/span>gnuplot_preamble<\/span>, \"set xtics 0.1\"<\/span>]<\/span>, \r\n    \/* \u30b0\u30ea\u30c3\u30c9 *\/<\/span>\r\n    grid2d<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    <\/div>\n
    \n
    <\/p>\n
    \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    2 \u672c\u306e\u8ecc\u9053\u3092\u63cf\u304f\u3082\u3046\u4e00\u3064\u306e\u4f8b<\/h4>\n
    makelist()<\/code> \u3092\u4f7f\u3063\u3066\uff0c\u5a92\u4ecb\u5909\u6570\u8868\u793a\u306e\u30b0\u30e9\u30d5\u90e8\u5206\u3068\u51e1\u4f8b\u90e8\u5206\u3092\u3042\u3089\u304b\u3058\u3081\u30ea\u30b9\u30c8\u3068\u3057\u3066\u3064\u304f\u3063\u3066\u304a\u304f\uff0c\u3068\u3044\u3046\u4f5c\u6226\u3002\u51e1\u4f8b\u90e8\u5206\u3092\u3069\u3046\u3059\u308b\u304b\uff0c\u3061\u3087\u3063\u3068\u82e6\u52b4\u3057\u307e\u3057\u305f\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[5]:<\/div>\n
    \n
    \n
    \n
    lines<\/span>:<\/span> makelist<\/span>(<\/span>\r\n    [<\/span>parametric<\/span>, x<\/span>(<\/span>t<\/span>, th<\/span>)<\/span>, y<\/span>(<\/span>t<\/span>, th<\/span>)<\/span>, [<\/span>t<\/span>, 0<\/span>, td<\/span>(<\/span>th<\/span>)]]<\/span>, \r\n    th<\/span>, 45<\/span>, 30<\/span>, -<\/span>15<\/span>\r\n    )<\/span>$\r\nkeys<\/span>:<\/span> makelist<\/span>(<\/span>\r\n    printf<\/span>(<\/span>false<\/span>, \"\u03b8 = ~2d\u00b0\"<\/span>, th<\/span>)<\/span>, \r\n    th<\/span>, 45<\/span>, 30<\/span>, -<\/span>15<\/span>\r\n    )<\/span>$\r\n\r\nplot2d<\/span>(<\/span>\r\n    lines<\/span>, \r\n\r\n    \/* \u51e1\u4f8b *\/<\/span>\r\n    flatten<\/span>([<\/span>legend<\/span>, keys<\/span>])<\/span>, \r\n\r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n    [<\/span>xlabel<\/span>, \"x\"<\/span>]<\/span>, [<\/span>ylabel<\/span>, \"y\"<\/span>]<\/span>,\r\n    \/* \u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb *\/<\/span>\r\n    [<\/span>title<\/span>, \"\u659c\u65b9\u6295\u5c04\"<\/span>]<\/span>,\r\n    \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n    [<\/span>x<\/span>, 0<\/span>, 1.<\/span>1]<\/span>, [<\/span>y<\/span>, 0<\/span>, 0.<\/span>5]<\/span>, \r\n    \/* \u30a2\u30b9\u30da\u30af\u30c8\u6bd4*\/<\/span>\r\n    [<\/span>same_xy<\/span>]<\/span>, \r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u76ee\u76db *\/<\/span>\r\n    [<\/span>gnuplot_preamble<\/span>, \"set xtics 0.1\"<\/span>]<\/span>, \r\n    \/* \u30b0\u30ea\u30c3\u30c9 *\/<\/span>\r\n    grid2d<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    <\/div>\n
    \n
    <\/p>\n
    \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u8907\u6570\u306e\u8ecc\u9053\u3092\u4e00\u5ea6\u306b\u63cf\u304f<\/h4>\n
    $\\theta$ \u306e\u5024\u3092 $30^{\\circ}$ \u304b\u3089 $60^{\\circ}$ \u307e\u3067 $5^{\\circ}$ \u523b\u307f\u3067\u5909\u3048\u3066\uff0c\u8907\u6570\u306e\u66f2\u7dda\u3092\u4e00\u5ea6\u306b\u63cf\u304f\u4f8b\u3002<\/p>\n
    2\u672c\u306e\u8ecc\u9053\u304c makelist()<\/code> \u3067\u63cf\u3051\u308c\u3070\uff0c\u8907\u6570\u306e\u8ecc\u9053\u3092\u4e00\u5ea6\u306b\u63cf\u304f\u306e\u3082\u7c21\u5358\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[6]:<\/div>\n
    \n
    \n
    \n
    lines<\/span>:<\/span> makelist<\/span>(<\/span>\r\n    [<\/span>parametric<\/span>, x<\/span>(<\/span>t<\/span>, th<\/span>)<\/span>, y<\/span>(<\/span>t<\/span>, th<\/span>)<\/span>, [<\/span>t<\/span>, 0<\/span>, td<\/span>(<\/span>th<\/span>)]]<\/span>, \r\n    th<\/span>, 60<\/span>, 30<\/span>, -<\/span>5<\/span>\r\n    )<\/span>$\r\nkeys<\/span>:<\/span> makelist<\/span>(<\/span>\r\n    printf<\/span>(<\/span>false<\/span>, \"\u03b8 = ~2d\u00b0\"<\/span>, th<\/span>)<\/span>, \r\n    th<\/span>, 60<\/span>, 30<\/span>, -<\/span>5<\/span>\r\n    )<\/span>$\r\n\r\nplot2d<\/span>(<\/span>\r\n    lines<\/span>, \r\n\r\n    \/* \u51e1\u4f8b *\/<\/span>\r\n    flatten<\/span>([<\/span>legend<\/span>, keys<\/span>])<\/span>, \r\n\r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n    [<\/span>xlabel<\/span>, \"x\"<\/span>]<\/span>, [<\/span>ylabel<\/span>, \"y\"<\/span>]<\/span>,\r\n    \/* \u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb *\/<\/span>\r\n    [<\/span>title<\/span>, \"\u659c\u65b9\u6295\u5c04\"<\/span>]<\/span>,\r\n    \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n    [<\/span>x<\/span>, 0<\/span>, 1.<\/span>1]<\/span>, [<\/span>y<\/span>, 0<\/span>, 0.<\/span>5]<\/span>, \r\n    \/* \u30a2\u30b9\u30da\u30af\u30c8\u6bd4*\/<\/span>\r\n    [<\/span>same_xy<\/span>]<\/span>, \r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u76ee\u76db *\/<\/span>\r\n    [<\/span>gnuplot_preamble<\/span>, \"set xtics 0.1\"<\/span>]<\/span>, \r\n    \/* \u30b0\u30ea\u30c3\u30c9 *\/<\/span>\r\n    grid2d<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    <\/div>\n
    \n
    <\/p>\n
    \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    draw2d()<\/code> \u3067\u8ecc\u9053\u306e\u30b0\u30e9\u30d5<\/h3>\n
    \u3068\u308a\u3042\u3048\u305a 1 \u672c\u306e\u8ecc\u9053\u3092\u63cf\u304f<\/h4>\n
    $\\theta = 45^{\\circ}$ \u3067\u306e\u659c\u65b9\u6295\u5c04\u306e\u8ecc\u9053\u3092\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3002<\/p>\n
    \u307e\u305a\u306f\uff0c\u3068\u308a\u3042\u3048\u305a\u306e\u30b0\u30e9\u30d5\uff1a<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[7]:<\/div>\n
    \n
    \n
    \n
    th<\/span>:<\/span> 45$\r\n\r\ndraw2d<\/span>(<\/span>parametric<\/span>(<\/span>x<\/span>(<\/span>t<\/span>, th<\/span>)<\/span>, y<\/span>(<\/span>t<\/span>, th<\/span>)<\/span>, t<\/span>, 0<\/span>, td<\/span>(<\/span>th<\/span>)))<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    <\/div>\n
    \n
    <\/p>\n
    \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b<\/h4>\n
    \u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3057\u3066\uff0c\u3082\u3046\u5c11\u3057\u4f53\u88c1\u3092\u6574\u3048\u307e\u3059\u3002<\/p>\n
      \n
    • $\\theta$ \u306e\u5024\u3092\u51e1\u4f8b\u306b<\/li>\n
    • \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb<\/li>\n
    • \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/li>\n
    • \u7e26\u8ef8\u6a2a\u8ef8\u306e\u30a2\u30b9\u30da\u30af\u30c8\u6bd4<\/li>\n
    • \u5ea7\u6a19\u8ef8\u306e\u76ee\u76db\u306e\u9593\u9694…<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[8]:<\/div>\n
      \n
      \n
      \n
      th<\/span>:<\/span> 45$\r\n\r\ndraw2d<\/span>(<\/span>\r\n    \/* \u51e1\u4f8b *\/<\/span>\r\n    key<\/span> =<\/span> printf<\/span>(<\/span>false<\/span>, \"\u03b8 = ~2d\u00b0\"<\/span>, th<\/span>)<\/span>,\r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n    xlabel<\/span> =<\/span> \"x\"<\/span>, ylabel<\/span> =<\/span> \"y\"<\/span>,\r\n    \/* \u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb *\/<\/span>\r\n    title<\/span> =<\/span> \"\u659c\u65b9\u6295\u5c04\"<\/span>, \r\n    \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n    xrange<\/span> =<\/span> [<\/span>0<\/span>, 1.<\/span>1]<\/span>, yrange<\/span> =<\/span> [<\/span>0<\/span>, 0.<\/span>5]<\/span>,\r\n    \/* \u30a2\u30b9\u30da\u30af\u30c8\u6bd4 *\/<\/span>\r\n    proportional_axes<\/span> =<\/span> xy<\/span>,\r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u76ee\u76db *\/<\/span>\r\n    user_preamble<\/span> =<\/span> \"set xtics 0.1\"<\/span>,\r\n    \/* \u30b0\u30ea\u30c3\u30c9 *\/<\/span>\r\n    grid<\/span> =<\/span> true<\/span>,\r\n    \r\n    parametric<\/span>(<\/span>x<\/span>(<\/span>t<\/span>, th<\/span>)<\/span>, y<\/span>(<\/span>t<\/span>, th<\/span>)<\/span>, t<\/span>, 0<\/span>, td<\/span>(<\/span>th<\/span>))<\/span>\r\n    )<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      <\/div>\n
      \n
      <\/p>\n
      \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      2\u672c\u306e\u8ecc\u9053\u3092\u63cf\u304f<\/h4>\n
      $\\theta = 30^{\\circ}$ \u3068 $\\theta = 45^{\\circ}$ \u306e2\u672c\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u4f8b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[9]:<\/div>\n
      \n
      \n
      \n
      draw2d<\/span>(<\/span>\r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n    xlabel<\/span> =<\/span> \"x\"<\/span>, ylabel<\/span> =<\/span> \"y\"<\/span>,\r\n    \/* \u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb *\/<\/span>\r\n    title<\/span> =<\/span> \"\u659c\u65b9\u6295\u5c04\"<\/span>, \r\n    \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n    xrange<\/span> =<\/span> [<\/span>0<\/span>, 1.<\/span>1]<\/span>, yrange<\/span> =<\/span> [<\/span>0<\/span>, 0.<\/span>5]<\/span>,\r\n    \/* \u30a2\u30b9\u30da\u30af\u30c8\u6bd4 *\/<\/span>\r\n    proportional_axes<\/span> =<\/span> xy<\/span>,\r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u76ee\u76db *\/<\/span>\r\n    user_preamble<\/span> =<\/span> \"set xtics 0.1\"<\/span>,\r\n    \/* \u30b0\u30ea\u30c3\u30c9 *\/<\/span>\r\n    grid<\/span> =<\/span> true<\/span>,\r\n\r\n    color<\/span> =<\/span> 1<\/span>,\r\n    key<\/span> =<\/span> printf<\/span>(<\/span>false<\/span>, \"\u03b8 = ~2d\u00b0\"<\/span>, 45<\/span>)<\/span>,\r\n    parametric<\/span>(<\/span>x<\/span>(<\/span>t<\/span>, 45<\/span>)<\/span>, y<\/span>(<\/span>t<\/span>, 45<\/span>)<\/span>, t<\/span>, 0<\/span>, td<\/span>(<\/span>45<\/span>))<\/span>,   \r\n\r\n    color<\/span> =<\/span> 2<\/span>,\r\n    key<\/span> =<\/span> printf<\/span>(<\/span>false<\/span>, \"\u03b8 = ~2d\u00b0\"<\/span>, 30<\/span>)<\/span>,\r\n    parametric<\/span>(<\/span>x<\/span>(<\/span>t<\/span>, 30<\/span>)<\/span>, y<\/span>(<\/span>t<\/span>, 30<\/span>)<\/span>, t<\/span>, 0<\/span>, td<\/span>(<\/span>30<\/span>))<\/span>\r\n    )<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      <\/div>\n
      \n
      <\/p>\n
      \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      2 \u672c\u306e\u8ecc\u9053\u3092\u63cf\u304f\u3082\u3046\u4e00\u3064\u306e\u4f8b<\/h4>\n
      makelist()<\/code> \u3092\u4f7f\u3063\u3066\uff0c\u5a92\u4ecb\u5909\u6570\u8868\u793a\u306e\u30b0\u30e9\u30d5\u90e8\u5206\u3068\u51e1\u4f8b\u90e8\u5206\u3092\u3042\u3089\u304b\u3058\u3081\u30ea\u30b9\u30c8\u3068\u3057\u3066\u3064\u304f\u3063\u3066\u304a\u304f\uff0c\u3068\u3044\u3046\u4f5c\u6226\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[10]:<\/div>\n
      \n
      \n
      \n
      th<\/span>:<\/span> [<\/span>45<\/span>, 30]<\/span>$\r\n\r\nlines<\/span>:<\/span> makelist<\/span>(<\/span>\r\n    [<\/span>color<\/span> =<\/span> i<\/span>,\r\n     key<\/span> =<\/span> printf<\/span>(<\/span>false<\/span>, \"\u03b8 = ~2d\u00b0\"<\/span>, th<\/span>[<\/span>i<\/span>])<\/span>,\r\n     parametric<\/span>(<\/span>x<\/span>(<\/span>t<\/span>, th<\/span>[<\/span>i<\/span>])<\/span>, y<\/span>(<\/span>t<\/span>, th<\/span>[<\/span>i<\/span>])<\/span>, t<\/span>, 0<\/span>, td<\/span>(<\/span>th<\/span>[<\/span>i<\/span>]))]<\/span>, \r\n    i<\/span>, 1<\/span>, length<\/span>(<\/span>th<\/span>)<\/span>\r\n    )<\/span>$\r\n\r\ndraw2d<\/span>(<\/span>\r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n    xlabel<\/span> =<\/span> \"x\"<\/span>, ylabel<\/span> =<\/span> \"y\"<\/span>,\r\n    \/* \u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb *\/<\/span>\r\n    title<\/span> =<\/span> \"\u659c\u65b9\u6295\u5c04\"<\/span>, \r\n    \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n    xrange<\/span> =<\/span> [<\/span>0<\/span>, 1.<\/span>1]<\/span>, yrange<\/span> =<\/span> [<\/span>0<\/span>, 0.<\/span>5]<\/span>,\r\n    \/* \u30a2\u30b9\u30da\u30af\u30c8\u6bd4 *\/<\/span>\r\n    proportional_axes<\/span> =<\/span> xy<\/span>,\r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u76ee\u76db *\/<\/span>\r\n    user_preamble<\/span> =<\/span> \"set xtics 0.1\"<\/span>,\r\n    \/* \u30b0\u30ea\u30c3\u30c9 *\/<\/span>\r\n    grid<\/span> =<\/span> true<\/span>,\r\n\r\n    lines<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      <\/div>\n
      \n
      <\/p>\n
      \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      \u8907\u6570\u306e\u8ecc\u9053\u3092\u4e00\u5ea6\u306b\u63cf\u304f<\/h4>\n
      $\\theta$ \u306e\u5024\u3092 $30^{\\circ}$ \u304b\u3089 $60^{\\circ}$ \u307e\u3067 $5^{\\circ}$ \u523b\u307f\u3067\u5909\u3048\u3066\uff0c\u8907\u6570\u306e\u66f2\u7dda\u3092\u4e00\u5ea6\u306b\u63cf\u304f\u4f8b\u3002<\/p>\n
      2\u672c\u306e\u8ecc\u9053\u304c makelist()<\/code> \u3067\u63cf\u3051\u308c\u3070\uff0c\u8907\u6570\u306e\u8ecc\u9053\u3092\u4e00\u5ea6\u306b\u63cf\u304f\u306e\u3082\u7c21\u5358\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[11]:<\/div>\n
      \n
      \n
      \n
      th<\/span>:<\/span> makelist<\/span>(<\/span>i<\/span>, i<\/span>, 60<\/span>, 30<\/span>, -<\/span>5<\/span>)<\/span>$\r\n\r\nlines<\/span>:<\/span> makelist<\/span>(<\/span>\r\n    [<\/span>color<\/span> =<\/span> i<\/span>,\r\n     key<\/span> =<\/span> printf<\/span>(<\/span>false<\/span>, \"\u03b8 = ~2d\u00b0\"<\/span>, th<\/span>[<\/span>i<\/span>])<\/span>,\r\n     parametric<\/span>(<\/span>x<\/span>(<\/span>t<\/span>, th<\/span>[<\/span>i<\/span>])<\/span>, y<\/span>(<\/span>t<\/span>, th<\/span>[<\/span>i<\/span>])<\/span>, t<\/span>, 0<\/span>, td<\/span>(<\/span>th<\/span>[<\/span>i<\/span>]))]<\/span>, \r\n    i<\/span>, 1<\/span>, length<\/span>(<\/span>th<\/span>)<\/span>\r\n    )<\/span>$\r\n\r\ndraw2d<\/span>(<\/span>\r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n    xlabel<\/span> =<\/span> \"x\"<\/span>, ylabel<\/span> =<\/span> \"y\"<\/span>,\r\n    \/* \u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb *\/<\/span>\r\n    title<\/span> =<\/span> \"\u659c\u65b9\u6295\u5c04\"<\/span>, \r\n    \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n    xrange<\/span> =<\/span> [<\/span>0<\/span>, 1.<\/span>1]<\/span>, yrange<\/span> =<\/span> [<\/span>0<\/span>, 0.<\/span>5]<\/span>,\r\n    \/* \u30a2\u30b9\u30da\u30af\u30c8\u6bd4 *\/<\/span>\r\n    proportional_axes<\/span> =<\/span> xy<\/span>,\r\n    \/* \u5ea7\u6a19\u8ef8\u306e\u76ee\u76db *\/<\/span>\r\n    user_preamble<\/span> =<\/span> \"set xtics 0.1\"<\/span>,\r\n    \/* \u30b0\u30ea\u30c3\u30c9 *\/<\/span>\r\n    grid<\/span> =<\/span> true<\/span>,\r\n\r\n    lines<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      <\/div>\n
      \n
      <\/p>\n
      \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
      Maxima \u3092\u4f7f\u3063\u3066\uff0c\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u5909\u3048\u3066\u8907\u6570\u306e\u66f2\u7dda\u3092\u4e00\u6c17\u306b\u30b0\u30e9\u30d5\u306b\u3059\u308b\u4f8b\u3002\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u969b\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u8a2d\u5b9a\u306b\u3064\u3044\u3066\u3082\u307e\u3068\u3081\u305f\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],"tags":[],"class_list":["post-7595","post","type-post","status-publish","format-standard","hentry","category-maxima","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7595","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=7595"}],"version-history":[{"count":2,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7595\/revisions"}],"predecessor-version":[{"id":7607,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7595\/revisions\/7607"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=7595"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=7595"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=7595"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}