{"id":8813,"date":"2024-05-31T10:39:12","date_gmt":"2024-05-31T01:39:12","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=8813"},"modified":"2025-06-07T10:22:46","modified_gmt":"2025-06-07T01:22:46","slug":"matplotlib-%e3%81%a7%e9%ab%98%e3%81%95-h-%e3%81%8b%e3%82%89%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%81%ae%e3%82%b0%e3%83%a9%e3%83%95%e3%82%92%e6%8f%8f%e3%81%8f","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/8813\/","title":{"rendered":"Matplotlib \u3067\u9ad8\u3055 h \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f"},"content":{"rendered":"

\u300c\u9ad8\u3055 h \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u554f\u984c\u3092\u9670\u95a2\u6570\u5b9a\u7406\u3092\u4f7f\u3063\u3066\u89e3\u3044\u3066\u307f\u308b<\/a>\u300d\u306e\u30da\u30fc\u30b8\u3067\u4f7f\u3063\u3066\u3044\u308b\u306e\u3067\u3002
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\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> matplotlib.pyplot<\/span> as<\/span> plt<\/span>\r\nimport<\/span> matplotlib.patches<\/span> as<\/span> patches<\/span>\r\nimport<\/span> numpy<\/span> as<\/span> np<\/span>\r\n\r\n# \u30b0\u30e9\u30d5\u3092 SVG \u3067 Notebook \u306b\u30a4\u30f3\u30e9\u30a4\u30f3\u8868\u793a<\/span>\r\n%<\/span>config<\/span> InlineBackend.figure_formats = ['svg']\r\n\r\nplt<\/span>.<\/span>rcParams<\/span>[<\/span>'mathtext.fontset'<\/span>]<\/span> =<\/span> 'cm'<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u89e3\u306e\u898f\u683c\u5316<\/h3>\n
\u300c\u9ad8\u3055 h \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u554f\u984c\u3092\u9670\u95a2\u6570\u5b9a\u7406\u3092\u4f7f\u3063\u3066\u89e3\u3044\u3066\u307f\u308b<\/a>\u300d\u306b\u307e\u3068\u3081\u3066\u3044\u308b\u3088\u3046\u306b\uff0c\u521d\u671f\u6761\u4ef6\u3092 $t = 0$ \u3067<\/p>\n
$$x = 0, \\quad y = h, \\quad v_x\u00a0 = v_0 \\cos\\theta, \\quad v_y = v_0 \\sin \\theta$$<\/p>\n
\u3068\u3057\u305f\u3068\u304d\u306e\u89e3\u306f<\/p>\n
\\begin{eqnarray}
\nx(t, \\theta) &=& v_0 \\cos\\theta\\cdot t \\\\
\ny(t, \\theta) &=& h + v_0 \\sin\\theta\\cdot t -\\frac{1}{2} g t^2
\n\\end{eqnarray}<\/p>\n
\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3092\u4e0e\u3048\u308b $\\theta_{\\rm m}$ \u306f<\/p>\n
$$\\theta_{\\rm m} = \\tan^{-1} \\sqrt{\\frac{v_0^2}{v_0^2 + 2 g h}}$$<\/p>\n
\u305d\u306e\u3068\u304d\u306e\u6ede\u7a7a\u6642\u9593 $\\tau_{\\rm m}$ \u306f<\/p>\n
$$\\tau_{\\rm m} = \\frac{v_0}{g \\sin \\theta_{\\rm m}}$$<\/p>\n
\u3053\u308c\u3089\u3092\u7cfb\u306b\u7279\u5fb4\u7684\u306a\u6642\u9593\u304a\u3088\u3073\u9577\u3055\u3067\u898f\u683c\u5316\u3059\u308b\u3068\uff0c\uff08\u8981\u306f $v_0 \\rightarrow 1, \\ g \\rightarrow 1$ \u3068\u3059\u308c\u3070\u3088\u3044\uff09<\/p>\n
\\begin{eqnarray}
\nx(t, \\theta) &\\Rightarrow& \\cos\\theta\\cdot t \\\\
\ny(t, \\theta) &\\Rightarrow& h + \\sin\\theta\\cdot t -\\frac{1}{2} t^2 \\\\
\n\\theta_{\\rm m} &\\Rightarrow& \\tan^{-1} \\sqrt{\\frac{1}{1 + 2 h}}\\\\
\n\\tau_{\\rm m} &\\Rightarrow& \\frac{1}{\\sin \\theta_{\\rm m}}
\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\u95a2\u6570\u306e\u5b9a\u7fa9<\/h3>\n
$x(t, \\theta), \\ y(t, \\theta, h), \\ \\theta_{\\rm m}(h), \\ \\tau_{\\rm m}(h)$ \u306e\u5b9a\u7fa9\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[2]:<\/div>\n
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def<\/span> x<\/span>(<\/span>t<\/span>,<\/span> theta<\/span>):<\/span>\r\n    return<\/span> np<\/span>.<\/span>cos<\/span>(<\/span>theta<\/span>)<\/span> *<\/span> t<\/span>\r\n\r\ndef<\/span> y<\/span>(<\/span>t<\/span>,<\/span> theta<\/span>,<\/span> h<\/span>):<\/span>\r\n    return<\/span> h<\/span> +<\/span> np<\/span>.<\/span>sin<\/span>(<\/span>theta<\/span>)<\/span> *<\/span> t<\/span> -<\/span> t<\/span>**<\/span>2<\/span>\/<\/span>2<\/span>\r\n\r\ndef<\/span> thetam<\/span>(<\/span>h<\/span>):<\/span>\r\n    return<\/span> np<\/span>.<\/span>arctan<\/span>(<\/span>np<\/span>.<\/span>sqrt<\/span>(<\/span>1<\/span>\/<\/span>(<\/span>1<\/span> +<\/span> 2<\/span>*<\/span>h<\/span>)))<\/span>\r\n\r\ndef<\/span> taum<\/span>(<\/span>h<\/span>):<\/span>\r\n    return<\/span> 1<\/span>\/<\/span>np<\/span>.<\/span>sin<\/span>(<\/span>thetam<\/span>(<\/span>h<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30b0\u30e9\u30d5\u4f8b 1<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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fig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>[<\/span>6.4<\/span>,<\/span> 4.8<\/span>])<\/span>\r\nax<\/span> =<\/span> fig<\/span>.<\/span>add_subplot<\/span>(<\/span>aspect<\/span>=<\/span>'equal'<\/span>)<\/span>\r\n#fig.tight_layout()<\/span>\r\n\r\nfor<\/span> i<\/span> in<\/span> range<\/span>(<\/span>0<\/span>,<\/span> 6<\/span>):<\/span>\r\n    h<\/span> =<\/span> 0.2<\/span>*<\/span>(<\/span>5<\/span> -<\/span> i<\/span>)<\/span>\r\n    thm<\/span> =<\/span> np<\/span>.<\/span>degrees<\/span>(<\/span>thetam<\/span>(<\/span>h<\/span>))<\/span>\r\n    Label<\/span> =<\/span> r<\/span>'$h=<\/span>%.1f<\/span>,\\ \\theta_{\\rm m}=<\/span>%.1f<\/span>^{\\circ}$'<\/span> %<\/span> (<\/span>h<\/span>,<\/span> thm<\/span>)<\/span>\r\n    t<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>0<\/span>,<\/span> taum<\/span>(<\/span>h<\/span>))<\/span>\r\n    plt<\/span>.<\/span>plot<\/span>(<\/span>x<\/span>(<\/span>t<\/span>,<\/span> thetam<\/span>(<\/span>h<\/span>)),<\/span> y<\/span>(<\/span>t<\/span>,<\/span> thetam<\/span>(<\/span>h<\/span>),<\/span> h<\/span>),<\/span> label<\/span>=<\/span>Label<\/span>)<\/span>\r\n\r\n# \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/span>\r\nplt<\/span>.<\/span>xlim<\/span>(<\/span>0<\/span>,<\/span> 1.8<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylim<\/span>(<\/span>0<\/span>,<\/span> 1.2<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09<\/span>\r\nplt<\/span>.<\/span>grid<\/span>(<\/span>ls<\/span>=<\/span>':'<\/span>)<\/span>\r\n\r\n# \u8ef8\u30e9\u30d9\u30eb\uff0c\u30bf\u30a4\u30c8\u30eb<\/span>\r\nplt<\/span>.<\/span>xlabel<\/span>(<\/span>'$x$'<\/span>,<\/span> fontsize<\/span>=<\/span>12<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylabel<\/span>(<\/span>'$y$'<\/span>,<\/span> fontsize<\/span>=<\/span>12<\/span>)<\/span>\r\nplt<\/span>.<\/span>title<\/span>(<\/span>'\u9ad8\u3055 $h$ \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u5230\u9054\u8ddd\u96e2'<\/span>,<\/span> fontsize<\/span>=<\/span>12<\/span>)<\/span>\r\n\r\n# x\u8ef8 y\u8ef8<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'gray'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>1<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'gray'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>1<\/span>);<\/span>\r\n\r\nplt<\/span>.<\/span>legend<\/span>(<\/span>fontsize<\/span>=<\/span>9<\/span>);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30b0\u30e9\u30d5\u4f8b 2<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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fig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>[<\/span>6.4<\/span>,<\/span> 4.8<\/span>])<\/span>\r\nax<\/span> =<\/span> fig<\/span>.<\/span>add_subplot<\/span>(<\/span>aspect<\/span>=<\/span>'equal'<\/span>)<\/span>\r\nfig<\/span>.<\/span>tight_layout<\/span>()<\/span>\r\n\r\n# \u8ecc\u9053<\/span>\r\nh<\/span> =<\/span> 0.8<\/span>\r\nt<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>0<\/span>,<\/span> taum<\/span>(<\/span>h<\/span>))<\/span>\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>x<\/span>(<\/span>t<\/span>,<\/span> thetam<\/span>(<\/span>h<\/span>)),<\/span> y<\/span>(<\/span>t<\/span>,<\/span> thetam<\/span>(<\/span>h<\/span>),<\/span> h<\/span>),<\/span> c<\/span>=<\/span>'blue'<\/span>)<\/span>\r\n\r\n# \u9ad8\u3055 h<\/span>\r\nplt<\/span>.<\/span>plot<\/span>([<\/span>0<\/span>,<\/span> 0<\/span>],<\/span> [<\/span>0<\/span>,<\/span> h<\/span>],<\/span> c<\/span>=<\/span>'k'<\/span>)<\/span>\r\nax<\/span>.<\/span>text<\/span>(<\/span>0.04<\/span>,<\/span> h<\/span>\/<\/span>2<\/span>,<\/span> r<\/span>\"$h$\"<\/span>,<\/span> \r\n        fontsize<\/span>=<\/span>\"x-large\"<\/span>,<\/span> ha<\/span>=<\/span>\"center\"<\/span>,<\/span> va<\/span>=<\/span>\"center\"<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>)<\/span>\r\n\r\n# \u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 ell_m<\/span>\r\nlm<\/span> =<\/span> x<\/span>(<\/span>taum<\/span>(<\/span>h<\/span>),<\/span>thetam<\/span>(<\/span>h<\/span>))<\/span>\r\nplt<\/span>.<\/span>plot<\/span>([<\/span>0<\/span>,<\/span> lm<\/span>],<\/span> [<\/span>0<\/span>,<\/span> 0<\/span>],<\/span> c<\/span>=<\/span>'tab:red'<\/span>)<\/span>\r\nax<\/span>.<\/span>text<\/span>(<\/span>lm<\/span>\/<\/span>2<\/span>-<\/span>0.1<\/span>,<\/span> 0.09<\/span>,<\/span> \r\n        r<\/span>\"$\\ell_{\\rm m}=\\frac{v_0^2}<\/span>{g}<\/span> \\sqrt{1 + \\frac<\/span>{2gh}<\/span>{v_0^2}}$\"<\/span>,<\/span>\r\n        fontsize<\/span>=<\/span>\"x-large\"<\/span>,<\/span> ha<\/span>=<\/span>\"center\"<\/span>,<\/span> va<\/span>=<\/span>\"center\"<\/span>,<\/span> c<\/span>=<\/span>'tab:red'<\/span>)<\/span>\r\n\r\n# \u521d\u671f\u4f4d\u7f6e<\/span>\r\nplt<\/span>.<\/span>scatter<\/span>([<\/span>0<\/span>],[<\/span>h<\/span>],<\/span> c<\/span>=<\/span>'blue'<\/span>)<\/span>\r\n# \u521d\u901f\u5ea6\u30d9\u30af\u30c8\u30eb <\/span>\r\nv0x<\/span> =<\/span> 0.3<\/span>*<\/span>np<\/span>.<\/span>cos<\/span>(<\/span>thetam<\/span>(<\/span>h<\/span>))<\/span>\r\nv0y<\/span> =<\/span> 0.3<\/span>*<\/span>np<\/span>.<\/span>sin<\/span>(<\/span>thetam<\/span>(<\/span>h<\/span>))<\/span>\r\nplt<\/span>.<\/span>quiver<\/span>([<\/span>0<\/span>],<\/span> [<\/span>h<\/span>],<\/span> [<\/span>v0x<\/span>],<\/span> [<\/span>v0y<\/span>],<\/span> color<\/span>=<\/span>\"blue\"<\/span>,<\/span> lw<\/span> =<\/span> 2<\/span>,<\/span> zorder<\/span>=<\/span>10<\/span>,<\/span>\r\n          angles<\/span>=<\/span>'xy'<\/span>,<\/span> scale_units<\/span>=<\/span>'xy'<\/span>,<\/span> scale<\/span>=<\/span>1<\/span>\r\n          )<\/span>\r\nax<\/span>.<\/span>text<\/span>(<\/span>v0x<\/span>+<\/span>0.04<\/span>,<\/span> h<\/span>+<\/span>v0y<\/span>+<\/span>0.04<\/span>,<\/span> r<\/span>'$v_0$'<\/span>,<\/span>\r\n        fontsize<\/span>=<\/span>\"x-large\"<\/span>,<\/span> ha<\/span>=<\/span>\"center\"<\/span>,<\/span> va<\/span>=<\/span>\"center\"<\/span>,<\/span> c<\/span>=<\/span>'blue'<\/span>)<\/span>\r\nplt<\/span>.<\/span>plot<\/span>([<\/span>0<\/span>,<\/span>0.13<\/span>],[<\/span>h<\/span>,<\/span>h<\/span>],<\/span>lw<\/span>=<\/span>0.5<\/span>,<\/span>ls<\/span>=<\/span>'--'<\/span>,<\/span>c<\/span>=<\/span>'blue'<\/span>)<\/span>\r\n\r\n# \u89d2\u5ea6 theta_i \u90e8\u5206<\/span>\r\narci<\/span> =<\/span> patches<\/span>.<\/span>Arc<\/span>(<\/span>\r\n        xy<\/span>=<\/span>(<\/span>0<\/span>,<\/span> h<\/span>),<\/span> width<\/span>=<\/span>0.2<\/span>,<\/span> height<\/span>=<\/span>0.2<\/span>,<\/span> \r\n        theta1<\/span>=<\/span>0<\/span>,<\/span> theta2<\/span>=<\/span>np<\/span>.<\/span>degrees<\/span>(<\/span>thetam<\/span>(<\/span>h<\/span>)),<\/span> ec<\/span>=<\/span>\"blue\"<\/span>,<\/span> lw<\/span>=<\/span>1<\/span>)<\/span>\r\nax<\/span>.<\/span>add_patch<\/span>(<\/span>arci<\/span>)<\/span>\r\nax<\/span>.<\/span>text<\/span>(<\/span>0.11<\/span>,<\/span> h<\/span>+<\/span>0.01<\/span>,<\/span> \r\n        r<\/span>\"$\\theta_{\\rm m} = \\tan^{-1}\\sqrt{\\frac{v_0^2}{v_0^2 + 2 g h}}$\"<\/span>,<\/span> \r\n        fontsize<\/span>=<\/span>\"x-large\"<\/span>,<\/span> c<\/span>=<\/span>'blue'<\/span>)<\/span>\r\n\r\n# \u89d2\u5ea6 theta_f \u90e8\u5206<\/span>\r\narcf<\/span> =<\/span> patches<\/span>.<\/span>Arc<\/span>(<\/span>\r\n        xy<\/span>=<\/span>(<\/span>lm<\/span>,<\/span> 0<\/span>),<\/span> width<\/span>=<\/span>0.2<\/span>,<\/span> height<\/span>=<\/span>0.2<\/span>,<\/span> \r\n        theta1<\/span>=<\/span>90<\/span>+<\/span>np<\/span>.<\/span>degrees<\/span>(<\/span>thetam<\/span>(<\/span>h<\/span>)),<\/span> theta2<\/span>=<\/span>180<\/span>,<\/span> ec<\/span>=<\/span>\"blue\"<\/span>,<\/span> lw<\/span>=<\/span>1<\/span>)<\/span>\r\nax<\/span>.<\/span>add_patch<\/span>(<\/span>arcf<\/span>)<\/span>\r\nax<\/span>.<\/span>text<\/span>(<\/span>1.23<\/span>,<\/span> 0.05<\/span>,<\/span> r<\/span>\"$\\theta_{\\rm f} = \\frac{\\pi}<\/span>{2}<\/span> - \\theta_{\\rm m}$\"<\/span>,<\/span> \r\n        fontsize<\/span>=<\/span>\"x-large\"<\/span>,<\/span> c<\/span>=<\/span>'blue'<\/span>)<\/span>\r\n\r\n# \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/span>\r\nplt<\/span>.<\/span>xlim<\/span>(<\/span>-<\/span>0.02<\/span>,<\/span> 1.8<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylim<\/span>(<\/span>-<\/span>0.01<\/span>,<\/span> 1.2<\/span>)<\/span>\r\n\r\n# \u30bf\u30a4\u30c8\u30eb<\/span>\r\nplt<\/span>.<\/span>title<\/span>(<\/span>r<\/span>'\u9ad8\u3055 $h$ \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\uff1a\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $\\ell_{\\rm m}$ \u306e\u5834\u5408\u306e\u8ecc\u9053'<\/span>)<\/span>\r\n\r\n# \u76ee\u76db\u8a2d\u5b9a<\/span>\r\nax<\/span>.<\/span>axis<\/span>(<\/span>False<\/span>);<\/span>\r\n\r\n# x\u8ef8 y\u8ef8<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'gray'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>1<\/span>,<\/span> zorder<\/span>=<\/span>0<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'gray'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>1<\/span>,<\/span> zorder<\/span>=<\/span>0<\/span>);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30b0\u30e9\u30d5\u4f8b 3<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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fig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>[<\/span>6.4<\/span>,<\/span> 4.8<\/span>])<\/span>\r\nax<\/span> =<\/span> fig<\/span>.<\/span>add_subplot<\/span>(<\/span>aspect<\/span>=<\/span>'equal'<\/span>)<\/span>\r\nfig<\/span>.<\/span>tight_layout<\/span>()<\/span>\r\n\r\n# \u8ecc\u9053<\/span>\r\nh<\/span> =<\/span> 0.8<\/span>\r\nt<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>0<\/span>,<\/span> taum<\/span>(<\/span>h<\/span>))<\/span>\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>x<\/span>(<\/span>t<\/span>,<\/span> thetam<\/span>(<\/span>h<\/span>)),<\/span> y<\/span>(<\/span>t<\/span>,<\/span> thetam<\/span>(<\/span>h<\/span>),<\/span> h<\/span>),<\/span> c<\/span>=<\/span>'blue'<\/span>,<\/span>lw<\/span>=<\/span>2<\/span>)<\/span>\r\n\r\n# \u9ad8\u3055 h<\/span>\r\n#plt.plot([0, 0], [0, h], c='k')<\/span>\r\nax<\/span>.<\/span>text<\/span>(<\/span>0<\/span>,<\/span> h<\/span>\/<\/span>2<\/span>,<\/span> r<\/span>\"$h$\"<\/span>,<\/span> \r\n        fontsize<\/span>=<\/span>\"xx-large\"<\/span>,<\/span> ha<\/span>=<\/span>\"center\"<\/span>,<\/span> va<\/span>=<\/span>\"center\"<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>)<\/span>\r\nplt<\/span>.<\/span>quiver<\/span>([<\/span>0<\/span>],<\/span> [<\/span>0.45<\/span>],<\/span> [<\/span>0<\/span>],<\/span> [<\/span>h<\/span>-<\/span>0.45<\/span>],<\/span> color<\/span>=<\/span>\"k\"<\/span>,<\/span>  zorder<\/span>=<\/span>10<\/span>,<\/span> width<\/span>=<\/span>0.003<\/span>,<\/span>\r\n          angles<\/span>=<\/span>'xy'<\/span>,<\/span> scale_units<\/span>=<\/span>'xy'<\/span>,<\/span> scale<\/span>=<\/span>1<\/span>\r\n          )<\/span>\r\nplt<\/span>.<\/span>quiver<\/span>([<\/span>0<\/span>],<\/span> [<\/span>0.35<\/span>],<\/span> [<\/span>0<\/span>],<\/span> [<\/span>-<\/span>0.35<\/span>],<\/span> color<\/span>=<\/span>\"k\"<\/span>,<\/span>  zorder<\/span>=<\/span>10<\/span>,<\/span> width<\/span>=<\/span>0.003<\/span>,<\/span>\r\n          angles<\/span>=<\/span>'xy'<\/span>,<\/span> scale_units<\/span>=<\/span>'xy'<\/span>,<\/span> scale<\/span>=<\/span>1<\/span>\r\n          )<\/span>\r\n\r\n# \u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 ell_m<\/span>\r\nlm<\/span> =<\/span> x<\/span>(<\/span>taum<\/span>(<\/span>h<\/span>),<\/span>thetam<\/span>(<\/span>h<\/span>))<\/span>\r\n#plt.plot([0, lm], [0, 0], c='tab:red')<\/span>\r\nax<\/span>.<\/span>text<\/span>(<\/span>lm<\/span>\/<\/span>2<\/span>-<\/span>0.1<\/span>,<\/span> 0<\/span>,<\/span> \r\n        r<\/span>\"$\\ell_{\\rm m}=\\frac{v_0^2}<\/span>{g}<\/span> \\sqrt{1 + \\frac<\/span>{2gh}<\/span>{v_0^2}}$\"<\/span>,<\/span>\r\n        fontsize<\/span>=<\/span>\"xx-large\"<\/span>,<\/span> ha<\/span>=<\/span>\"center\"<\/span>,<\/span> va<\/span>=<\/span>\"center\"<\/span>,<\/span> c<\/span>=<\/span>'tab:red'<\/span>)<\/span>\r\nplt<\/span>.<\/span>quiver<\/span>([<\/span>0.98<\/span>],<\/span> [<\/span>0<\/span>],<\/span> [<\/span>lm<\/span>-<\/span>0.98<\/span>],<\/span> [<\/span>0<\/span>],<\/span> color<\/span>=<\/span>\"tab:red\"<\/span>,<\/span>  zorder<\/span>=<\/span>10<\/span>,<\/span> width<\/span>=<\/span>0.003<\/span>,<\/span>\r\n          angles<\/span>=<\/span>'xy'<\/span>,<\/span> scale_units<\/span>=<\/span>'xy'<\/span>,<\/span> scale<\/span>=<\/span>1<\/span>\r\n          )<\/span>\r\nplt<\/span>.<\/span>quiver<\/span>([<\/span>0.43<\/span>],<\/span> [<\/span>0<\/span>],<\/span> [<\/span>-<\/span>0.43<\/span>],<\/span> [<\/span>0<\/span>],<\/span> color<\/span>=<\/span>\"tab:red\"<\/span>,<\/span>  zorder<\/span>=<\/span>10<\/span>,<\/span> width<\/span>=<\/span>0.003<\/span>,<\/span>\r\n          angles<\/span>=<\/span>'xy'<\/span>,<\/span> scale_units<\/span>=<\/span>'xy'<\/span>,<\/span> scale<\/span>=<\/span>1<\/span>\r\n          )<\/span>\r\n\r\n# \u521d\u671f\u4f4d\u7f6e<\/span>\r\nplt<\/span>.<\/span>scatter<\/span>([<\/span>0<\/span>],[<\/span>h<\/span>],<\/span> c<\/span>=<\/span>'blue'<\/span>)<\/span>\r\n# \u521d\u901f\u5ea6\u30d9\u30af\u30c8\u30eb <\/span>\r\nv0x<\/span> =<\/span> 0.3<\/span>*<\/span>np<\/span>.<\/span>cos<\/span>(<\/span>thetam<\/span>(<\/span>h<\/span>))<\/span>\r\nv0y<\/span> =<\/span> 0.3<\/span>*<\/span>np<\/span>.<\/span>sin<\/span>(<\/span>thetam<\/span>(<\/span>h<\/span>))<\/span>\r\nplt<\/span>.<\/span>quiver<\/span>([<\/span>0<\/span>],<\/span> [<\/span>h<\/span>],<\/span> [<\/span>v0x<\/span>],<\/span> [<\/span>v0y<\/span>],<\/span> color<\/span>=<\/span>\"blue\"<\/span>,<\/span>  zorder<\/span>=<\/span>10<\/span>,<\/span>\r\n          angles<\/span>=<\/span>'xy'<\/span>,<\/span> scale_units<\/span>=<\/span>'xy'<\/span>,<\/span> scale<\/span>=<\/span>1<\/span>\r\n          )<\/span>\r\nax<\/span>.<\/span>text<\/span>(<\/span>v0x<\/span>+<\/span>0.04<\/span>,<\/span> h<\/span>+<\/span>v0y<\/span>+<\/span>0.04<\/span>,<\/span> r<\/span>'$v_0$'<\/span>,<\/span>\r\n        fontsize<\/span>=<\/span>\"x-large\"<\/span>,<\/span> ha<\/span>=<\/span>\"center\"<\/span>,<\/span> va<\/span>=<\/span>\"center\"<\/span>,<\/span> c<\/span>=<\/span>'blue'<\/span>)<\/span>\r\nplt<\/span>.<\/span>plot<\/span>([<\/span>0<\/span>,<\/span>0.13<\/span>],[<\/span>h<\/span>,<\/span>h<\/span>],<\/span>lw<\/span>=<\/span>0.5<\/span>,<\/span>ls<\/span>=<\/span>'--'<\/span>,<\/span>c<\/span>=<\/span>'blue'<\/span>)<\/span>\r\n\r\n# \u89d2\u5ea6 theta_i \u90e8\u5206<\/span>\r\narci<\/span> =<\/span> patches<\/span>.<\/span>Arc<\/span>(<\/span>\r\n        xy<\/span>=<\/span>(<\/span>0<\/span>,<\/span> h<\/span>),<\/span> width<\/span>=<\/span>0.2<\/span>,<\/span> height<\/span>=<\/span>0.2<\/span>,<\/span> \r\n        theta1<\/span>=<\/span>0<\/span>,<\/span> theta2<\/span>=<\/span>np<\/span>.<\/span>degrees<\/span>(<\/span>thetam<\/span>(<\/span>h<\/span>)),<\/span> ec<\/span>=<\/span>\"blue\"<\/span>,<\/span> lw<\/span>=<\/span>1<\/span>)<\/span>\r\nax<\/span>.<\/span>add_patch<\/span>(<\/span>arci<\/span>)<\/span>\r\nax<\/span>.<\/span>text<\/span>(<\/span>0.11<\/span>,<\/span> h<\/span>+<\/span>0.01<\/span>,<\/span> \r\n        r<\/span>\"$\\theta_{\\rm m} = \\tan^{-1}\\sqrt{\\frac{v_0^2}{v_0^2 + 2 g h}}$\"<\/span>,<\/span> \r\n        fontsize<\/span>=<\/span>\"x-large\"<\/span>,<\/span> c<\/span>=<\/span>'blue'<\/span>)<\/span>\r\n\r\n# \u89d2\u5ea6 theta_f \u90e8\u5206<\/span>\r\narcf<\/span> =<\/span> patches<\/span>.<\/span>Arc<\/span>(<\/span>\r\n        xy<\/span>=<\/span>(<\/span>lm<\/span>,<\/span> 0<\/span>),<\/span> width<\/span>=<\/span>0.2<\/span>,<\/span> height<\/span>=<\/span>0.2<\/span>,<\/span> \r\n        theta1<\/span>=<\/span>90<\/span>+<\/span>np<\/span>.<\/span>degrees<\/span>(<\/span>thetam<\/span>(<\/span>h<\/span>)),<\/span> theta2<\/span>=<\/span>180<\/span>,<\/span> ec<\/span>=<\/span>\"blue\"<\/span>,<\/span> lw<\/span>=<\/span>1<\/span>)<\/span>\r\nax<\/span>.<\/span>add_patch<\/span>(<\/span>arcf<\/span>)<\/span>\r\nax<\/span>.<\/span>text<\/span>(<\/span>1.23<\/span>,<\/span> 0.05<\/span>,<\/span> r<\/span>\"$\\theta_{\\rm f} = \\frac{\\pi}<\/span>{2}<\/span> - \\theta_{\\rm m}$\"<\/span>,<\/span> \r\n        fontsize<\/span>=<\/span>\"x-large\"<\/span>,<\/span> c<\/span>=<\/span>'blue'<\/span>)<\/span>\r\n\r\n# \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/span>\r\nplt<\/span>.<\/span>xlim<\/span>(<\/span>-<\/span>0.05<\/span>,<\/span> 1.8<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylim<\/span>(<\/span>-<\/span>0.1<\/span>,<\/span> 1.05<\/span>)<\/span>\r\n\r\n# \u30bf\u30a4\u30c8\u30eb<\/span>\r\nplt<\/span>.<\/span>title<\/span>(<\/span>r<\/span>'\u9ad8\u3055 $h$ \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\uff1a\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $\\ell_{\\rm m}$ \u306e\u5834\u5408\u306e\u8ecc\u9053'<\/span>)<\/span>\r\n\r\n# \u76ee\u76db\u8a2d\u5b9a<\/span>\r\nax<\/span>.<\/span>axis<\/span>(<\/span>False<\/span>);<\/span>\r\n\r\n# x\u8ef8 y\u8ef8<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'gray'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> c<\/span>=<\/span>'lightgray'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>,<\/span> zorder<\/span>=<\/span>0<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'gray'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> c<\/span>=<\/span>'lightgray'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>,<\/span> zorder<\/span>=<\/span>0<\/span>);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\"\"<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
\u300c\u9ad8\u3055 h \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u554f\u984c\u3092\u9670\u95a2\u6570\u5b9a\u7406\u3092\u4f7f\u3063\u3066\u89e3\u3044\u3066\u307f\u308b\u300d\u306e\u30da\u30fc\u30b8\u3067\u4f7f\u3063\u3066\u3044\u308b\u306e\u3067\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":[13,25,21],"tags":[],"class_list":["post-8813","post","type-post","status-publish","format-standard","hentry","category-matplotlib","category-25","category-21","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