{"id":4249,"date":"2022-11-24T17:17:19","date_gmt":"2022-11-24T08:17:19","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=4249"},"modified":"2023-11-21T17:36:23","modified_gmt":"2023-11-21T08:36:23","slug":"%e4%b8%8b%e3%81%93%e3%82%99%e3%81%97%e3%82%89%e3%81%88%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%e7%a8%8b-2","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/4249\/","title":{"rendered":"\u4e0b\u3053\u3099\u3057\u3089\u3048\u3057\u305f\u4e07\u6709\u5f15\u529b\u306e2\u4f53\u554f\u984c\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092 Python \u3066\u3099\u6570\u5024\u7684\u306b\u89e3\u304d gnuplot \u3067\u30b0\u30e9\u30d5\u306b\u3059\u308b"},"content":{"rendered":"

\u300c\u4e0b\u3053\u3099\u3057\u3089\u3048\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<\/a>\u300d\u306e Python & gnuplot \u7248\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<\/a>\u300d\u306b\u307e\u3068\u3081\u305f\u3088\u3046\u306b\uff0c\u7cfb\u306b\u7279\u5fb4\u7684\u306a\u9577\u3055\u3068\u6642\u9593\u30b9\u30b1\u30fc\u30eb\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} = – \\frac{X}{\\left(X^2 + Y^2\\right)^{\\frac{3}{2}}} \\\\
\n\\frac{d^2 Y}{dT^2} = – \\frac{Y}{\\left(X^2 + Y^2\\right)^{\\frac{3}{2}}}
\n\\end{eqnarray}<\/p>\n

\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 &=& 1 \\\\
\nY &=& 0\\\\
\nV_x &=& \\frac{dX}{dT} = 0 \\\\
\nV_y &=& \\frac{dY}{dT} = \\frac{v_{y0}}{v_0} = k \\ \\ ( 0 < k < \\sqrt{2})
\n\\end{eqnarray}<\/p>\n

\u6955\u5186\u306e\u8ecc\u9053\u8981\u7d20\uff08\u9577\u534a\u5f84\uff0c\u96e2\u5fc3\u7387\uff0c\u5468\u671f\uff09<\/h3>\n

\u3053\u306e\u3068\u304d\uff0c\u6570\u5024\u8a08\u7b97\u3059\u308b\u524d\u306b\u3082\u3046\uff0c\u8ecc\u9053\u306f\u898f\u683c\u5316\u3055\u308c\u305f\u9577\u534a\u5f84\u304c<\/p>\n

$$ A \\equiv \\frac{a}{x_0} = \\frac{1}{2 – k^2} $$<\/p>\n

\u96e2\u5fc3\u7387\u304c<\/p>\n

$$e = |k^2 – 1|$$<\/p>\n

\u306e\u6955\u5186\u306b\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3057\u307e\u3046\u3002\u307e\u305f\uff0c\u898f\u683c\u5316\u3055\u308c\u305f\u5468\u671f\u304c<\/p>\n

$$P \\equiv \\frac{p}{\\tau} = 2 \\pi A^{\\frac{3}{2}} = \\frac{2 \\pi}{\\left(2 – k^2\\right)^{\\frac{3}{2}}}$$<\/p>\n

\u3068\u306a\u308b\u3053\u3068\u3082\u308f\u304b\u3063\u3066\u3057\u307e\u3063\u3066\u3044\u308b\u306e\u3067\u3042\u3063\u305f\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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\u6570\u5024\u89e3\u6cd5\u7528\u306b\u9023\u7acb1\u968e\u5fae\u5206\u65b9\u7a0b\u5f0f\u7cfb\u306b<\/h3>\n

\\begin{eqnarray}
\n\\frac{dX}{dt} &=& V \\\\
\n\\frac{dY}{dt} &=& W \\\\
\n\\frac{dV}{dt} &=&
\n-\\frac{X}{\\left(X^2 + Y^2\\right)^{\\frac{3}{2}}} \\\\
\n\\frac{dW}{dt} &=&
\n-\\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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scipy.integrate.solve_ivp()<\/code> \u3067\u89e3\u304f<\/h3>\n

\u521d\u671f\u6761\u4ef6 $k = 1$ \u3067\u5186\u8ecc\u9053\u3068\u306a\u308b\u3053\u3068\u3092\u78ba\u8a8d<\/h4>\n

\u307e\u305a\u306f\uff0c$k = 1$ \u3068\u3044\u3046\u521d\u671f\u6761\u4ef6\u3067\u5186\u8ecc\u9053\u306b\u306a\u308b\u3053\u3068\u3092\u78ba\u8a8d\u30021\u5468\u671f\u3092 $N$ \u7b49\u5206\u3057\uff0c$t = P(1) = 2 \\pi$ \u307e\u3067\u8a08\u7b97\u3057\u305f\u3068\u304d\u306e\u7b54\u3048\u304c $x_0 = 1, y_0 = 0$ \u306b\u306a\u3063\u3066\u3044\u308b\u304b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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import<\/span> scipy.integrate<\/span>\r\nimport<\/span> numpy<\/span> as<\/span> np<\/span>\r\nimport<\/span> matplotlib.pyplot<\/span> as<\/span> plt<\/span>\r\n\r\nfrom<\/span> IPython.display<\/span> import<\/span> set_matplotlib_formats<\/span>\r\n%<\/span>matplotlib<\/span> inline\r\nset_matplotlib_formats<\/span>(<\/span>'svg'<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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# scipy.integrate.solve_ivp() \u306f<\/span>\r\n# dy\/dt = F(t, y) \u306e\u5f62\u3092\u89e3\u304f<\/span>\r\n\r\ndef<\/span> F<\/span>(<\/span>t<\/span>,<\/span> y<\/span>):<\/span>\r\n    X<\/span> =<\/span> y<\/span>[<\/span>0<\/span>]<\/span>\r\n    Y<\/span> =<\/span> y<\/span>[<\/span>1<\/span>]<\/span>\r\n    V<\/span> =<\/span> y<\/span>[<\/span>2<\/span>]<\/span>\r\n    W<\/span> =<\/span> y<\/span>[<\/span>3<\/span>]<\/span>\r\n    return<\/span> [<\/span>V<\/span>,<\/span> W<\/span>,<\/span> -<\/span>X<\/span>\/<\/span>np<\/span>.<\/span>sqrt<\/span>(<\/span>X<\/span>**<\/span>2<\/span>+<\/span>Y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>3<\/span>,<\/span> -<\/span>Y<\/span>\/<\/span>np<\/span>.<\/span>sqrt<\/span>(<\/span>X<\/span>**<\/span>2<\/span>+<\/span>Y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>3<\/span>]<\/span>\r\n\r\n# \u5468\u671f<\/span>\r\ndef<\/span> P<\/span>(<\/span>k<\/span>):<\/span>\r\n    return<\/span> 2<\/span>*<\/span>np<\/span>.<\/span>pi<\/span>\/<\/span>(<\/span>np<\/span>.<\/span>sqrt<\/span>(<\/span>2<\/span> -<\/span> k<\/span>**<\/span>2<\/span>)<\/span>**<\/span>3<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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N<\/span> =<\/span> 36<\/span>\r\ny_ini<\/span> =<\/span> [<\/span>1<\/span>,<\/span> 0<\/span>,<\/span> 0<\/span>,<\/span> 1<\/span>]<\/span>\r\nt_span<\/span> =<\/span> [<\/span>0<\/span>,<\/span> P<\/span>(<\/span>1<\/span>)]<\/span>\r\n\r\nt_list<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>0<\/span>,<\/span> P<\/span>(<\/span>1<\/span>),<\/span> N<\/span>+<\/span>1<\/span>)<\/span>\r\n\r\n# scipy.integrate.solve_ivp() \u306f<\/span>\r\n# dy\/dt = F(t, y) \u306e\u5f62\u3092\u89e3\u304f<\/span>\r\n\r\nivp_c<\/span> =<\/span> scipy<\/span>.<\/span>integrate<\/span>.<\/span>solve_ivp<\/span>(<\/span>F<\/span>,<\/span> t_span<\/span>,<\/span> y_ini<\/span>,<\/span> \r\n                    t_eval<\/span> =<\/span> t_list<\/span>,<\/span> \r\n                    rtol<\/span> =<\/span> 1.e-12<\/span>,<\/span> \r\n                    atol<\/span> =<\/span> 1.e-15<\/span>)<\/span>\r\n\r\nprint<\/span>(<\/span>\"X \u306e\u8aa4\u5dee \"<\/span>,<\/span> 1<\/span> -<\/span> ivp_c<\/span>.<\/span>y<\/span>[<\/span>0<\/span>,<\/span> -<\/span>1<\/span>])<\/span>\r\nprint<\/span>(<\/span>\"Y \u306e\u8aa4\u5dee \"<\/span>,<\/span> 0<\/span> -<\/span> ivp_c<\/span>.<\/span>y<\/span>[<\/span>1<\/span>,<\/span> -<\/span>1<\/span>])<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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X \u306e\u8aa4\u5dee  -1.8822721159494904e-12\r\nY \u306e\u8aa4\u5dee  7.521387158926363e-12\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$e = 0.6$ \u3068\u306a\u308b\u521d\u671f\u6761\u4ef6\u3067\u6570\u5024\u8a08\u7b97<\/h4>\n
\u521d\u671f\u6761\u4ef6 $k$ \u3068\u6955\u5186\u306e\u96e2\u5fc3\u7387 $e$ \u3068\u306e\u95a2\u4fc2\u306f $e = |k^2 – 1|$ \u3067\u3042\u3063\u305f\u304b\u3089…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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k<\/span> =<\/span> np<\/span>.<\/span>sqrt<\/span>(<\/span>1<\/span> +<\/span> 0.6<\/span>)<\/span>\r\n\r\ny_ini<\/span> =<\/span> [<\/span>1<\/span>,<\/span> 0<\/span>,<\/span> 0<\/span>,<\/span> k<\/span>]<\/span>\r\nt_span<\/span> =<\/span> [<\/span>0<\/span>,<\/span> P<\/span>(<\/span>k<\/span>)]<\/span>\r\n\r\nt_list<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>0<\/span>,<\/span> P<\/span>(<\/span>k<\/span>),<\/span> N<\/span>+<\/span>1<\/span>)<\/span>\r\n\r\n# scipy.integrate.solve_ivp() \u306f<\/span>\r\n# dy\/dt = Fun(t, y) \u306e\u5f62\u3092\u89e3\u304f<\/span>\r\n\r\nivp_e<\/span> =<\/span> scipy<\/span>.<\/span>integrate<\/span>.<\/span>solve_ivp<\/span>(<\/span>F<\/span>,<\/span> t_span<\/span>,<\/span> y_ini<\/span>,<\/span> \r\n                    t_eval<\/span> =<\/span> t_list<\/span>,<\/span> \r\n                    rtol<\/span> =<\/span> 1.e-12<\/span>,<\/span> \r\n                    atol<\/span> =<\/span> 1.e-15<\/span>)<\/span>\r\n\r\nprint<\/span>(<\/span>\"X \u306e\u8aa4\u5dee \"<\/span>,<\/span> 1<\/span> -<\/span> ivp_e<\/span>.<\/span>y<\/span>[<\/span>0<\/span>,<\/span> -<\/span>1<\/span>])<\/span>\r\nprint<\/span>(<\/span>\"Y \u306e\u8aa4\u5dee \"<\/span>,<\/span> 0<\/span> -<\/span> ivp_e<\/span>.<\/span>y<\/span>[<\/span>1<\/span>,<\/span> -<\/span>1<\/span>])<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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X \u306e\u8aa4\u5dee  -9.197087535994797e-13\r\nY \u306e\u8aa4\u5dee  6.560043740860833e-11\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\u3092\u30b0\u30e9\u30d5\u306b<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>(<\/span>6<\/span>,<\/span>6<\/span>))<\/span>\r\ng<\/span> =<\/span> plt<\/span>.<\/span>subplot<\/span>()<\/span>\r\n\r\ng<\/span>.<\/span>set_xlim<\/span> (<\/span>-<\/span>4.5<\/span>,<\/span> 1.5<\/span>)<\/span>\r\ng<\/span>.<\/span>set_ylim<\/span> (<\/span>-<\/span>3<\/span>,<\/span> 3<\/span>)<\/span>\r\n\r\ng<\/span>.<\/span>set_aspect<\/span>(<\/span>'equal'<\/span>)<\/span>\r\ng<\/span>.<\/span>plot<\/span>(<\/span>ivp_e<\/span>.<\/span>y<\/span>[<\/span>0<\/span>],<\/span> ivp_e<\/span>.<\/span>y<\/span>[<\/span>1<\/span>],<\/span> 'o'<\/span>,<\/span> color<\/span> =<\/span> \"blue\"<\/span>,<\/span> markersize<\/span> =<\/span> 4<\/span>)<\/span>\r\ng<\/span>.<\/span>plot<\/span>(<\/span>0<\/span>,<\/span> 0<\/span>,<\/span> 'o'<\/span>,<\/span> color<\/span> =<\/span> \"black\"<\/span>,<\/span> markersize<\/span> =<\/span> 6<\/span>)<\/span>\r\n\r\n# \u8ef8\u76ee\u76db\u3092\u975e\u8868\u793a<\/span>\r\nplt<\/span>.<\/span>xticks<\/span>([])<\/span>\r\nplt<\/span>.<\/span>yticks<\/span>([])<\/span>\r\n\r\nplt<\/span>.<\/span>savefig<\/span>(<\/span>\".\/ivp_e_fig1.svg\"<\/span>)<\/span>\r\n# \u30b0\u30e9\u30d5\u3092\u8868\u793a<\/span>\r\nplt<\/span>.<\/span>show<\/span>()<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6570\u5024\u8a08\u7b97\u306e\u7d50\u679c\u3092\u30d5\u30a1\u30a4\u30eb\u3078\u66f8\u304d\u51fa\u3059<\/h3>\n
matplotlib \u306b\u4e0d\u6163\u308c\u306a\u5834\u5408\uff08\u79c1\u3067\u3059\uff09\uff0c\u6570\u5024\u8a08\u7b97\u306e\u7d50\u679c\u3092\u30d5\u30a1\u30a4\u30eb\u306b\u66f8\u304d\u51fa\u3057\u3066\uff0cgnuplot \u306a\u3069\u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n
\u307e\u305a\uff0c$e=0.6$ \u3068\u306a\u308b\u521d\u671f\u6761\u4ef6\u3067\u6570\u5024\u8a08\u7b97\u3057\u305f\u7d50\u679c\u306e $x, y$ \u3092\u30d5\u30a1\u30a4\u30eb xy_e.txt<\/code> \u306b\u66f8\u304d\u51fa\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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# \u30d5\u30a1\u30a4\u30eb\u3078\u306e\u66f8\u304d\u51fa\u3057<\/span>\r\n\r\nxy_e<\/span> =<\/span> []<\/span>\r\nfor<\/span> i<\/span> in<\/span> range<\/span>(<\/span>0<\/span>,<\/span> N<\/span>+<\/span>1<\/span>):<\/span>\r\n    xy_e<\/span>.<\/span>append<\/span>([<\/span>ivp_e<\/span>.<\/span>y<\/span>[<\/span>0<\/span>,<\/span> i<\/span>],<\/span> ivp_e<\/span>.<\/span>y<\/span>[<\/span>1<\/span>,<\/span> i<\/span>]])<\/span>\r\n\r\n# \u914d\u5217 xy_e \u3092\u30d5\u30a1\u30a4\u30eb xy_e.txt \u306b\u66f8\u304d\u8fbc\u307f\u307e\u3059\u3002<\/span>\r\nnp<\/span>.<\/span>savetxt<\/span>(<\/span>'xy_e.txt'<\/span>,<\/span> xy_e<\/span>)<\/span>\r\n\r\n# \u30d5\u30a1\u30a4\u30eb\u306e\u4e2d\u8eab\u3092\u78ba\u8a8d\u3059\u308b\u3068\u304d\u306f... <\/span>\r\n# ! cat xy_e.txt<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Gnuplot \u3092 Python Notebook \u3067\u4f7f\u3046<\/h3>\n
\u5f18\u5927 JupyterHub \u306b\u306f gnuplot kernel<\/a> \u3082\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3055\u308c\u3066\u3044\u308b\u3002\u5225\u9014 gnuplot kernel \u306e Notebook \u3092\u958b\u304f\u307e\u3067\u3082\u306a\u304f\uff0c\u3053\u306e Python \u306e Notebook \u306e\u4e2d\u3067 gnuplot kernel \u3092\u4f7f\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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# Python Notebook \u306e\u4e2d\u304b\u3089 gnuplot_kernel \u3092\u4f7f\u3046\u5834\u5408\uff0c<\/span>\r\n# \u307e\u305a\u6700\u521d\u306b1\u56de\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b %load_ext \u3057\u307e\u3059\u3002<\/span>\r\n%<\/span>load_ext<\/span> gnuplot_kernel\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4e00\u65e6 %load_ext<\/code> \u3059\u308c\u3070\uff0c%%gnuplot<\/code> \u304b\u3089\u59cb\u307e\u308b\u30bb\u30eb\u306e\u4e2d\u3067\u306f gnuplot \u306e\u30b3\u30de\u30f3\u30c9\u304c\u305d\u306e\u307e\u307e\u4f7f\u3048\u308b\u3002<\/p>\n
inline \u306e plot \u30aa\u30d7\u30b7\u30e7\u30f3\uff08\u753b\u50cf\u30d5\u30a9\u30fc\u30de\u30c3\u30c8\uff0c\u753b\u50cf\u30b5\u30a4\u30ba\uff0c\u30d5\u30a9\u30f3\u30c8\u30b5\u30a4\u30ba\u7b49\uff09\u3092\u5909\u66f4\u3059\u308b\u306b\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b %gnuplot<\/code> line magic \u3092\u4f7f\u3046\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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%<\/span>gnuplot<\/span> inline svg size 600,600 fixed enhanced font ',16'\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u8a08\u7b97\u7d50\u679c\u306e $x, y$ \u5ea7\u6a19\u5024\u306f\u30d5\u30a1\u30a4\u30eb xy_e.txt<\/code> \u306b\u4fdd\u5b58\u3055\u308c\u3066\u3044\u308b\u3002
\ngnuplot \u3067\u3053\u306e\u30d5\u30a1\u30a4\u30eb xy_e.txt<\/code> \u3092\u8aad\u307f\u8fbc\u307f\uff0c\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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%%<\/span>gnuplot<\/span>\r\n\r\nset xrange [-4.5:1.5]\r\nset yrange [-3:3]\r\nset zeroaxis\r\nset size ratio 1\r\nunset xtics\r\nunset ytics\r\n\r\nset title \"\u4e00\u5b9a\u6642\u9593\u9593\u9694\u3054\u3068\u306e\u4f4d\u7f6e\"\r\n\r\nplot \"xy_e.txt\" pt 7 ps 0.6 lc \"blue\" notitle \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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%%<\/span>gnuplot<\/span>\r\n\r\nset output \".\/ivp_e_fig01.svg\"\r\nreplot\r\nset output\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Python \u306b\u3088\u308b\u6570\u5024\u8a08\u7b97\u306e\u7d50\u679c xy_e.txt<\/code> \u3060\u3051\u3067\u306a\u304f\uff0c\u6955\u5186\u3084\u539f\u70b9\u3092\u8868\u3059\u70b9\u3082\u91cd\u306d\u3066\u63cf\u3044\u3066\u307f\u308b\u3002<\/p>\n
\u7126\u70b9\u306e1\u3064\u3092\u539f\u70b9\u3068\u3057\u305f\u6975\u5ea7\u6a19\u3067\u306f\uff0c\u6955\u5186\u306f<\/p>\n
$$r(\\phi) = \\frac{a (1-e^2)}{1 + e \\cos\\phi} $$<\/p>\n
\uff08\u3053\u306e\u307e\u307e\u3067\u3082 set polar<\/code> \u3067\u63cf\u3051\u305d\u3046\u3060\u304c\uff09\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5a92\u4ecb\u5909\u6570\u8868\u793a\u306b\u3057\u3066\uff0cset parametric<\/code> \u3068\u3057\u3066\u30b0\u30e9\u30d5\u3092\u63cf\u3044\u3066\u307f\u308b\u3002<\/p>\n
\\begin{eqnarray}
\nx(\\phi) &=& r(\\phi) \\cos\\phi \\\\
\ny(\\phi) &=& r(\\phi) \\sin\\phi
\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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%%<\/span>gnuplot<\/span>\r\n\r\n# \u6975\u5ea7\u6a19\u8868\u793a\u306e\u6955\u5186\r\nr(a, e, phi) = a*(1-e**2)\/(1+e*cos(phi))\r\nx(a, e, phi) = r(a, e, phi) * cos(phi)\r\ny(a, e, phi) = r(a, e, phi) * sin(phi)\r\n\r\n# Python \u306b\u3088\u308b\u6570\u5024\u8a08\u7b97\u306e\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6955\u5186\u306b\u306a\u308b\u30cf\u30ba\r\ne = 0.6\r\na = 1\/(1-e)\r\n\r\n# \u539f\u70b9\r\nset label 1 point pt 7 ps 1 lc \"black\" at 0, 0\r\n\r\nset parametric\r\nplot [phi=0:2*pi] x(a, e, phi), y(a, e, phi) lc \"red\" notitle, \\\r\n     \"xy_e.txt\" pt 7 ps 0.6 lc \"blue\" notitle\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\tdummy variable is t for curves, u\/v for surfaces<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[12]:<\/div>\n
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%%<\/span>gnuplot<\/span>\r\n\r\nset output \".\/ivp_e_fig02.svg\"\r\nreplot\r\nset output\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
\u300c\u4e0b\u3053\u3099\u3057\u3089\u3048\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\u300d\u306e Python & gnuplot \u7248\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":[15,11,22],"tags":[],"class_list":["post-4249","post","type-post","status-publish","format-standard","hentry","category-gnuplot","category-python","category-22","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t