{"id":7115,"date":"2023-12-18T17:00:13","date_gmt":"2023-12-18T08:00:13","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=7115"},"modified":"2023-12-18T17:03:32","modified_gmt":"2023-12-18T08:03:32","slug":"python-%e3%81%a7%e4%b8%87%e6%9c%89%e5%bc%95%e5%8a%9b%e3%81%ae%e9%81%8b%e5%8b%95%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e6%95%b0%e5%80%a4%e7%9a%84%e3%81%ab%e8%a7%a3%e3%81%84%e3%81%a6%e6%a5%95%e5%86%86","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e4%b8%87%e6%9c%89%e5%bc%95%e5%8a%9b%e3%81%ae%e9%81%8b%e5%8b%95%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e6%95%b0%e5%80%a4%e7%9a%84%e3%81%ab%e8%a7%a3%e3%81%8f%e6%ba%96%e5%82%99\/python-%e3%81%a7%e4%b8%87%e6%9c%89%e5%bc%95%e5%8a%9b%e3%81%ae%e9%81%8b%e5%8b%95%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e6%95%b0%e5%80%a4%e7%9a%84%e3%81%ab%e8%a7%a3%e3%81%84%e3%81%a6%e6%a5%95%e5%86%86\/","title":{"rendered":"Python \u3066\u3099\u4e07\u6709\u5f15\u529b\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u3066\u6955\u5186\u8ecc\u9053\u306e\u30a2\u30cb\u30e1\u3092\u3064\u304f\u308b"},"content":{"rendered":"
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\u300c\u4e07\u6709\u5f15\u529b\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u6e96\u5099<\/a>\u300d\u3067\u4e0b\u3054\u3057\u3089\u3048\u3057\u305f\u5f0f\u3092 Python \u3067\u6570\u5024\u7684\u306b\u89e3\u304d\uff0c\u6955\u5186\u904b\u52d5\u306e\u30a2\u30cb\u30e1\u3092\u3064\u304f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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

\u300c\u4e07\u6709\u5f15\u529b\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u6e96\u5099<\/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\u3085\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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\u5fc5\u8981\u306a\u30e2\u30b8\u30e5\u30fc\u30eb\u306e import<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[1]:<\/div>\n
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import<\/span> numpy<\/span> as<\/span> np<\/span>\r\nimport<\/span> matplotlib.pyplot<\/span> as<\/span> plt<\/span>\r\nfrom<\/span> matplotlib.animation<\/span> import<\/span> FuncAnimation<\/span>\r\nfrom<\/span> scipy.integrate<\/span> import<\/span> solve_ivp<\/span>\r\n\r\n# \u4ee5\u4e0b\u306f\u30b0\u30e9\u30d5\u3092 SVG \u3067 Notebook \u306b\u30a4\u30f3\u30e9\u30a4\u30f3\u8868\u793a\u3055\u305b\u308b\u8a2d\u5b9a<\/span>\r\n%<\/span>config<\/span> InlineBackend.figure_formats = ['svg']\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6570\u5024\u8a08\u7b97\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[2]:<\/div>\n
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# scipy.integrate.solve_ivp() \u306f<\/span>\r\n# dy\/dt = Fun(t, y) \u306e\u5f62\u3092\u89e3\u304f\u3002\u5909\u6570\u540d\u306f\u6c7a\u3081\u6253\u3061\u3002<\/span>\r\n\r\ndef<\/span> Fun<\/span>(<\/span>t<\/span>,<\/span> y<\/span>):<\/span>\r\n# solve.ivp() \u306b\u6e21\u3059\u95a2\u6570\u306e\u5f15\u6570\u306e\u9806\u756a\u306b\u6ce8\u610f\u3002t \u304c\u5148<\/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    Vx<\/span> =<\/span> y<\/span>[<\/span>2<\/span>]<\/span>\r\n    Vy<\/span> =<\/span> y<\/span>[<\/span>3<\/span>]<\/span>\r\n    F1<\/span> =<\/span> Vx<\/span>\r\n    F2<\/span> =<\/span> Vy<\/span>\r\n    F3<\/span> =<\/span> -<\/span>4<\/span>*<\/span>np<\/span>.<\/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>\/<\/span>2<\/span>)<\/span>\r\n    F4<\/span> =<\/span> -<\/span>4<\/span>*<\/span>np<\/span>.<\/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>\/<\/span>2<\/span>)<\/span>\r\n    return<\/span> [<\/span>F1<\/span>,<\/span> F2<\/span>,<\/span> F3<\/span>,<\/span> F4<\/span>]<\/span>\r\n\r\n# \u96e2\u5fc3\u7387 e = 0.6<\/span>\r\ne<\/span> =<\/span> 0.6<\/span>\r\n\r\nt0<\/span> =<\/span> 0<\/span>\r\ntend<\/span> =<\/span> 1<\/span>\r\nt_span<\/span> =<\/span> [<\/span>t0<\/span>,<\/span> tend<\/span>]<\/span>\r\n# \u521d\u671f\u6761\u4ef6 X0, Y0, Vx0, Vy0<\/span>\r\nX0<\/span> =<\/span> 1<\/span>-<\/span>e<\/span>\r\nY0<\/span> =<\/span> 0<\/span>\r\nVx0<\/span> =<\/span> 0<\/span>\r\nVy0<\/span> =<\/span> 2<\/span>*<\/span>np<\/span>.<\/span>pi<\/span>*<\/span>np<\/span>.<\/span>sqrt<\/span>((<\/span>1<\/span>+<\/span>e<\/span>)<\/span>\/<\/span>(<\/span>1<\/span>-<\/span>e<\/span>))<\/span>\r\ny_ini<\/span> =<\/span> [<\/span>X0<\/span>,<\/span> Y0<\/span>,<\/span> Vx0<\/span>,<\/span> Vy0<\/span>]<\/span>\r\n\r\nNdiv<\/span> =<\/span> 36<\/span>\r\nt_list<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>t0<\/span>,<\/span> tend<\/span>,<\/span> Ndiv<\/span>+<\/span>1<\/span>)<\/span>\r\n\r\nsol<\/span> =<\/span> solve_ivp<\/span>(<\/span>Fun<\/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-14<\/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
\u6570\u5024\u89e3 sol<\/code> \u304b\u3089 X<\/code> \u3059\u306a\u308f\u3061 y[0]<\/code> \u3092\u53d6\u308a\u51fa\u3059\u306b\u306f\uff0csol.y[0]<\/code>\u3002\u6700\u5f8c\u306e\u9805\u306f sol.y[0][-1]<\/code>\u3002\u6700\u521d\u306e\u9805\uff08\u521d\u671f\u6761\u4ef6\uff09sol.y[0][0]<\/code> \u3068\u306e\u5dee\u3092\u78ba\u8a8d\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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X<\/span> =<\/span> sol<\/span>.<\/span>y<\/span>[<\/span>0<\/span>]<\/span>\r\nY<\/span> =<\/span> sol<\/span>.<\/span>y<\/span>[<\/span>1<\/span>]<\/span>\r\n\r\n# X \u306e\u8aa4\u5dee<\/span>\r\nprint<\/span>(<\/span>X<\/span>[<\/span>-<\/span>1<\/span>]<\/span>-<\/span>X<\/span>[<\/span>0<\/span>])<\/span>\r\n# Y \u306e\u8aa4\u5dee<\/span>\r\nprint<\/span>(<\/span>Y<\/span>[<\/span>-<\/span>1<\/span>]<\/span>-<\/span>Y<\/span>[<\/span>0<\/span>])<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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3.717026686445024e-13\r\n-2.693325467165164e-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[4]:<\/div>\n
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# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba\u306e\u8a2d\u5b9a<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>[<\/span>6<\/span>,<\/span>6<\/span>])<\/span>\r\n\r\n# \u7e26\u6a2a\u306e\u30a2\u30b9\u30da\u30af\u30c8\u6bd4\u3092\u7b49\u3057\u304f\u3057\u3066<\/span>\r\nplt<\/span>.<\/span>axes<\/span>()<\/span>.<\/span>set_aspect<\/span>(<\/span>'equal'<\/span>)<\/span>\r\n\r\n# \u8ef8\u306e\u8a2d\u5b9a<\/span>\r\nplt<\/span>.<\/span>axis<\/span>([<\/span>-<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> -<\/span>1.5<\/span>,<\/span> 1.5<\/span>])<\/span>\r\n\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>X<\/span>,<\/span> Y<\/span>,<\/span> s<\/span>=<\/span>20<\/span>,<\/span> c<\/span>=<\/span>'blue'<\/span>)<\/span>\r\n\r\n# x\u8ef8 y\u8ef8<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>3<\/span>,<\/span> 3<\/span>),<\/span> linewidth<\/span>=<\/span>0.6<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>3<\/span>,<\/span> 3<\/span>),<\/span> linewidth<\/span>=<\/span>0.6<\/span>);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6955\u5186\u8ecc\u9053\u3068\u91cd\u306d\u3066\u30b0\u30e9\u30d5\u306b<\/h3>\n
\u5f97\u3089\u308c\u305f\u6570\u5024\u89e3\u304c\u78ba\u304b\u306b\u6955\u5186\u8ecc\u9053\u306b\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u3066\u307f\u308b\u3002<\/p>\n
\u8ecc\u9053\u9577\u534a\u5f84 $a$\uff0c\u96e2\u5fc3\u7387 $e$ \u306e\u6955\u5186\u306e\u5f0f\u306f<\/p>\n
\\begin{eqnarray}
\nr &=& \\frac{a(1-e^2)}{1 + e \\cos\\phi} \\\\
\nx &=& r \\cos\\phi \\\\
\ny &=& r \\sin\\phi
\n\\end{eqnarray}<\/p>\n
\u6570\u5024\u89e3\u3068\u3042\u308f\u305b\u308b\u305f\u3081\uff0c\u8ecc\u9053\u9577\u534a\u5f84 $a$ \u3067\u7121\u6b21\u5143\u5316\u3057\u305f\u5ea7\u6a19\u306f<\/p>\n
\\begin{eqnarray}
\nX &=& \\frac{r}{a} \\cos\\phi = \\frac{1-e^2}{1 + e \\cos\\phi} \\cos\\phi\\\\
\nY &=& \\frac{r}{a} \\sin\\phi = \\frac{1-e^2}{1 + e \\cos\\phi} \\sin\\phi
\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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def<\/span> Xdaen<\/span>(<\/span>e<\/span>,<\/span> phi<\/span>):<\/span>\r\n    R<\/span> =<\/span> (<\/span>1<\/span>-<\/span>e<\/span>**<\/span>2<\/span>)<\/span>\/<\/span>(<\/span>1<\/span>+<\/span>e<\/span>*<\/span>np<\/span>.<\/span>cos<\/span>(<\/span>phi<\/span>))<\/span>\r\n    return<\/span> R<\/span> *<\/span> np<\/span>.<\/span>cos<\/span>(<\/span>phi<\/span>)<\/span>\r\n\r\ndef<\/span> Ydaen<\/span>(<\/span>e<\/span>,<\/span> phi<\/span>):<\/span>\r\n    R<\/span> =<\/span> (<\/span>1<\/span>-<\/span>e<\/span>**<\/span>2<\/span>)<\/span>\/<\/span>(<\/span>1<\/span>+<\/span>e<\/span>*<\/span>np<\/span>.<\/span>cos<\/span>(<\/span>phi<\/span>))<\/span>\r\n    return<\/span> R<\/span> *<\/span> np<\/span>.<\/span>sin<\/span>(<\/span>phi<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6570\u5024\u89e3\u3068\u6955\u5186\u306e\u30b0\u30e9\u30d5\u3092\u91cd\u306d\u3066\u63cf\u3044\u3066\u307f\u308b\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[6]:<\/div>\n
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# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba\u306e\u8a2d\u5b9a<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>[<\/span>6<\/span>,<\/span>6<\/span>])<\/span>\r\n\r\n# \u7e26\u6a2a\u306e\u30a2\u30b9\u30da\u30af\u30c8\u6bd4\u3092\u7b49\u3057\u304f\u3057\u3066<\/span>\r\nplt<\/span>.<\/span>axes<\/span>()<\/span>.<\/span>set_aspect<\/span>(<\/span>'equal'<\/span>)<\/span>\r\n\r\n# \u8ef8\u306e\u8a2d\u5b9a<\/span>\r\nplt<\/span>.<\/span>axis<\/span>([<\/span>-<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> -<\/span>1.5<\/span>,<\/span> 1.5<\/span>])<\/span>\r\n\r\nphi<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>0<\/span>,<\/span> 2<\/span>*<\/span>np<\/span>.<\/span>pi<\/span>,<\/span> 361<\/span>)<\/span>\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>Xdaen<\/span>(<\/span>e<\/span>,<\/span> phi<\/span>),<\/span> Ydaen<\/span>(<\/span>e<\/span>,<\/span> phi<\/span>),<\/span> \r\n         linewidth<\/span> =<\/span> 0.5<\/span>,<\/span> c<\/span>=<\/span>'red'<\/span>,<\/span> label<\/span>=<\/span>\"\u6955\u5186\"<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>X<\/span>,<\/span> Y<\/span>,<\/span> 'ob'<\/span>,<\/span> markersize<\/span> =<\/span> 2<\/span>,<\/span> label<\/span>=<\/span>'\u6570\u5024\u89e3'<\/span>)<\/span>\r\n\r\n# x\u8ef8 y\u8ef8<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>3<\/span>,<\/span> 3<\/span>),<\/span> linewidth<\/span>=<\/span>0.6<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>3<\/span>,<\/span> 3<\/span>),<\/span> linewidth<\/span>=<\/span>0.6<\/span>)<\/span>\r\nplt<\/span>.<\/span>legend<\/span>();<\/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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\u554f\u984c<\/h3>\n
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  1. \u96e2\u5fc3\u7387 $e$ \u3092\u5909\u3048\u3066\u6570\u5024\u8a08\u7b97\u3092\u884c\u3046\u3002<\/li>\n
  2. \u4e00\u5b9a\u6642\u9593\u9593\u9694\u3054\u3068\u306e\u4f4d\u7f6e\u3092\u30a2\u30cb\u30e1\u306b\u3059\u308b\u3002\n
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    1. \u30b7\u30fc\u30f31\uff1a\u8ecc\u9053\u304c\u6955\u5186\u306b\u306a\u308b\u69d8\u5b50\u306e\u30a2\u30cb\u30e1\u3002<\/li>\n
    2. \u30b7\u30fc\u30f32\uff1a\u6955\u5186\u4e0a\u306b\u4e00\u5b9a\u6642\u9593\u9593\u9694\u3054\u3068\u3092\u4f4d\u7f6e\u3092\u793a\u3059\u30a2\u30cb\u30e1\u3002<\/li>\n
    3. \u30b7\u30fc\u30f33\uff1a\u4e00\u5b9a\u6642\u9593\u9593\u9694\u3054\u3068\u306b\u6383\u304f\u6247\u5f62\u3092\u5857\u308a\u3064\u3076\u3059\u30a2\u30cb\u30e1\u3002<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n
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      <\/div>\n
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      \u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u4f5c\u6210<\/h3>\n
      \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081 Ndiv \u306f\u5927\u304d\u3081\u306b\u3068\u3063\u3066\u6570\u5024\u7a4d\u5206<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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      In\u00a0[7]:<\/div>\n
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      # \u96e2\u5fc3\u7387 e = 0.6<\/span>\r\ne<\/span> =<\/span> 0.6<\/span>\r\n\r\nt0<\/span> =<\/span> 0<\/span>\r\ntend<\/span> =<\/span> 1<\/span>\r\nt_span<\/span> =<\/span> [<\/span>t0<\/span>,<\/span> tend<\/span>]<\/span>\r\n# \u521d\u671f\u6761\u4ef6 X0, Y0, Vx0, Vy0<\/span>\r\nX0<\/span> =<\/span> 1<\/span>-<\/span>e<\/span>\r\nY0<\/span> =<\/span> 0<\/span>\r\nVx0<\/span> =<\/span> 0<\/span>\r\nVy0<\/span> =<\/span> 2<\/span>*<\/span>np<\/span>.<\/span>pi<\/span>*<\/span>np<\/span>.<\/span>sqrt<\/span>((<\/span>1<\/span>+<\/span>e<\/span>)<\/span>\/<\/span>(<\/span>1<\/span>-<\/span>e<\/span>))<\/span>\r\ny_ini<\/span> =<\/span> [<\/span>X0<\/span>,<\/span> Y0<\/span>,<\/span> Vx0<\/span>,<\/span> Vy0<\/span>]<\/span>\r\n\r\n# \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081 Ndiv \u306f\u5927\u304d\u3081\u306b<\/span>\r\nNdiv<\/span> =<\/span> 360<\/span>\r\nt_list<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>t0<\/span>,<\/span> tend<\/span>,<\/span> Ndiv<\/span>+<\/span>1<\/span>)<\/span>\r\n\r\nsol<\/span> =<\/span> solve_ivp<\/span>(<\/span>Fun<\/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-14<\/span>)<\/span>\r\n\r\n# \u5f8c\u3005\u306e\u3053\u3068\u3092\u8003\u3048\u3066\u30ea\u30b9\u30c8\u306b\u5909\u63db\u3057\u3066\u304a\u304f<\/span>\r\nX<\/span> =<\/span> sol<\/span>.<\/span>y<\/span>[<\/span>0<\/span>]<\/span>.<\/span>tolist<\/span>()<\/span>\r\nY<\/span> =<\/span> sol<\/span>.<\/span>y<\/span>[<\/span>1<\/span>]<\/span>.<\/span>tolist<\/span>()<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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      <\/div>\n
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      \u307e\u305a\u306f\u9014\u4e2d\u307e\u3067\u306e\u8ecc\u9053\u3092\u63cf\u304f<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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      <\/div>\n
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      \u6570\u5024\u8a08\u7b97\u306e\u7d50\u679c\u306f X<\/code> \u3068 Y<\/code> \u306b\u683c\u7d0d\u3055\u308c\u305f\u306e\u3067\uff0c\u9069\u5b9c\uff08\u9593\u5f15\u304d\u3057\u305f\u308a\u3057\u3066\uff09\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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      In\u00a0[8]:<\/div>\n
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      # \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba\u306e\u8a2d\u5b9a<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>[<\/span>6<\/span>,<\/span>6<\/span>])<\/span>\r\nax<\/span> =<\/span> fig<\/span>.<\/span>add_subplot<\/span>()<\/span>\r\n\r\n# \u5916\u67a0\u3068\u76ee\u76db\u3092\u975e\u8868\u793a\u306b<\/span>\r\nax<\/span>.<\/span>axis<\/span>(<\/span>'off'<\/span>)<\/span>\r\n\r\n# \u30b0\u30e9\u30d5\u306e\u7e26\u6a2a\u306e\u30a2\u30b9\u30da\u30af\u30c8\u6bd4\u3092 equal \u306b\u3002<\/span>\r\nax<\/span>.<\/span>set_aspect<\/span>(<\/span>'equal'<\/span>)<\/span>\r\n\r\n# \u8ef8\u306e\u8a2d\u5b9a<\/span>\r\nplt<\/span>.<\/span>axis<\/span>([<\/span>-<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> -<\/span>1.5<\/span>,<\/span> 1.5<\/span>])<\/span>\r\n\r\ni<\/span> =<\/span> 3<\/span>\r\n# i*10 \u756a\u76ee\u307e\u3067\u306e\u8ecc\u9053<\/span>\r\nxi<\/span> =<\/span> X<\/span>[:<\/span>i<\/span>*<\/span>10<\/span>]<\/span>\r\nyi<\/span> =<\/span> Y<\/span>[:<\/span>i<\/span>*<\/span>10<\/span>]<\/span>\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>xi<\/span>,<\/span> yi<\/span>)<\/span>\r\n\r\n# i*10 \u756a\u76ee\u306e\u4f4d\u7f6e\u306b\u8d64\u4e38<\/span>\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>X<\/span>[<\/span>i<\/span>*<\/span>10<\/span>],<\/span> Y<\/span>[<\/span>i<\/span>*<\/span>10<\/span>],<\/span> \"or\"<\/span>,<\/span> markersize<\/span> =<\/span> 3<\/span>)<\/span>\r\n\r\n# x\u8ef8 y\u8ef8<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>3<\/span>,<\/span> 3<\/span>),<\/span> linewidth<\/span>=<\/span>0.6<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>3<\/span>,<\/span> 3<\/span>),<\/span> linewidth<\/span>=<\/span>0.6<\/span>);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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      <\/div>\n
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      <\/p>\n
      \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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      <\/div>\n
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      FuncAnimation()<\/code> \u3067\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u4f5c\u6210<\/h5>\n
      \u7279\u5b9a\u306e i<\/code> \u306e\u5024\u306e\u3068\u3053\u308d\u306e\u30b0\u30e9\u30d5\u304c\u3067\u304d\u305f\u3089\uff0c\u5f53\u8a72\u30b3\u30fc\u30c9\u3092 def func(i):<\/code> \u306e\u4e2d\u306b\u30b3\u30d4\u307a\u3057\u3066 FuncAnimation()<\/code> \u3092\u547c\u3079\u3070\uff0c\u30d1\u30e9\u30d1\u30e9\u30a2\u30cb\u30e1\u3092\u3064\u304f\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3093\u3060\u3063\u305f\u3088\u306d\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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      In\u00a0[9]:<\/div>\n
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      # \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba\u306e\u8a2d\u5b9a<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>[<\/span>6<\/span>,<\/span>6<\/span>])<\/span>\r\nax<\/span> =<\/span> fig<\/span>.<\/span>add_subplot<\/span>()<\/span>\r\n\r\n# \u30b0\u30e9\u30d5\u306e\u7e26\u6a2a\u306e\u30a2\u30b9\u30da\u30af\u30c8\u6bd4\u3092 equal \u306b\u3002<\/span>\r\nax<\/span>.<\/span>set_aspect<\/span>(<\/span>'equal'<\/span>)<\/span>\r\n\r\ndef<\/span> func<\/span>(<\/span>i<\/span>):<\/span>\r\n    # \u524d\u306e frame \u3092\u6d88\u3059<\/span>\r\n    plt<\/span>.<\/span>cla<\/span>()<\/span>\r\n\r\n    # \u5916\u67a0\u3068\u76ee\u76db\u3092\u975e\u8868\u793a\u306b<\/span>\r\n    ax<\/span>.<\/span>axis<\/span>(<\/span>'off'<\/span>)<\/span>\r\n\r\n    # \u8ef8\u306e\u8a2d\u5b9a<\/span>\r\n    plt<\/span>.<\/span>axis<\/span>([<\/span>-<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> -<\/span>1.5<\/span>,<\/span> 1.5<\/span>])<\/span>\r\n    \r\n    # i*10 \u756a\u76ee\u307e\u3067\u306e\u8ecc\u9053<\/span>\r\n    xi<\/span> =<\/span> X<\/span>[:<\/span>i<\/span>*<\/span>10<\/span>]<\/span>\r\n    yi<\/span> =<\/span> Y<\/span>[:<\/span>i<\/span>*<\/span>10<\/span>]<\/span>\r\n    plt<\/span>.<\/span>plot<\/span>(<\/span>xi<\/span>,<\/span> yi<\/span>,<\/span> linewidth<\/span> =<\/span> 0.5<\/span>)<\/span>\r\n\r\n    # i*10 \u756a\u76ee\u306e\u4f4d\u7f6e\u306b\u8d64\u4e38<\/span>\r\n    plt<\/span>.<\/span>plot<\/span>(<\/span>X<\/span>[<\/span>i<\/span>*<\/span>10<\/span>],<\/span> Y<\/span>[<\/span>i<\/span>*<\/span>10<\/span>],<\/span> \"or\"<\/span>,<\/span> markersize<\/span> =<\/span> 3<\/span>)<\/span>\r\n\r\n    # x\u8ef8 y\u8ef8<\/span>\r\n    plt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>3<\/span>,<\/span> 3<\/span>),<\/span> linewidth<\/span>=<\/span>0.6<\/span>)<\/span>\r\n    plt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>3<\/span>,<\/span> 3<\/span>),<\/span> linewidth<\/span>=<\/span>0.6<\/span>)<\/span>\r\n\r\n    plt<\/span>.<\/span>title<\/span>(<\/span>\"\u30b1\u30d7\u30e9\u30fc\u306e\u7b2c1\u6cd5\u5247\uff1a\u6955\u5186\u8ecc\u9053\"<\/span>)<\/span>\r\n\r\nframes<\/span> =<\/span> 36<\/span>\r\nani<\/span> =<\/span> FuncAnimation<\/span>(<\/span>fig<\/span>,<\/span> func<\/span>,<\/span>  \r\n        interval<\/span> =<\/span> 100<\/span>,<\/span> \r\n        frames<\/span> =<\/span> range<\/span>(<\/span>frames<\/span>))<\/span>\r\n\r\nani<\/span>.<\/span>save<\/span>(<\/span>\"anim01.mp4\"<\/span>,<\/span> dpi<\/span>=<\/span>300<\/span>)<\/span>\r\nani<\/span>.<\/span>save<\/span>(<\/span>\"anim01.gif\"<\/span>,<\/span> dpi<\/span>=<\/span>150<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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