{"id":10403,"date":"2025-06-03T21:27:33","date_gmt":"2025-06-03T12:27:33","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=10403"},"modified":"2025-06-05T08:27:51","modified_gmt":"2025-06-04T23:27:51","slug":"%e5%9b%9e%e8%bb%a2%e7%b3%bb%e3%81%ab%e3%81%8a%e3%81%91%e3%82%8b%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e9%81%8b%e5%8b%95%ef%bc%9a%e3%83%95%e3%83%bc%e3%82%b3%e3%83%bc%e3%81%ae%e6%8c%af%e3%82%8a","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/10403\/","title":{"rendered":"\u56de\u8ee2\u7cfb\u306b\u304a\u3051\u308b\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\uff1a\u30d5\u30fc\u30b3\u30fc\u306e\u632f\u308a\u5b50"},"content":{"rendered":"<p>\u56de\u8ee2\u7cfb\u306b\u304a\u3051\u308b\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\uff0c\u300c<span style=\"font-family: helvetica, arial, sans-serif; color: #ff0000;\"><strong>\u4e00\u822c\u306b\u30d9\u30af\u30c8\u30eb\u3092\u5fae\u5206\u3059\u308b\u3068\u304d\u306f\uff0c\u6210\u5206\u3060\u3051\u3067\u306a\u304f\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u3082\u5fae\u5206\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u306e\u3060<\/strong><\/span>\u300d\u3068\u3044\u3046\u7acb\u5834\u3067\u8a08\u7b97\u3057\u3066\u307f\u308b\u3002\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u3092\u53c2\u8003\u306b\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e4%b8%80%e8%88%ac%e7%9b%b8%e5%af%be%e8%ab%96%e7%9a%84%e6%99%82%e7%a9%ba%e3%81%ae%e8%a1%a8%e3%81%97%e6%96%b9\/3%e6%ac%a1%e5%85%83%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e5%be%ae%e5%88%86\/\" target=\"_blank\" rel=\"noopener\">3\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306e\u5fae\u5206<\/a><\/li>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e4%b8%80%e8%88%ac%e7%9b%b8%e5%af%be%e8%ab%96%e7%9a%84%e6%99%82%e7%a9%ba%e3%81%ae%e8%a1%a8%e3%81%97%e6%96%b9\/3%e6%ac%a1%e5%85%83%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e5%be%ae%e5%88%86\/%e5%8f%82%e8%80%83%ef%bc%9a%e5%9b%9e%e8%bb%a2%e5%ba%a7%e6%a8%99%e7%b3%bb%e3%81%ab%e3%81%8a%e3%81%91%e3%82%8b%e5%9f%ba%e6%9c%ac%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e6%99%82%e9%96%93%e5%be%ae\/\" target=\"_blank\" rel=\"noopener\">\u88dc\u8db3\uff1a\u56de\u8ee2\u5ea7\u6a19\u7cfb\u306b\u304a\u3051\u308b\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306e\u6642\u9593\u5fae\u5206<\/a><\/li>\n<\/ul>\n<p><!--more--><\/p>\n<h3>\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f<\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10404 size-medium\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/tanfuriko1-300x324.png\" alt=\"\" width=\"300\" height=\"324\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/tanfuriko1-300x324.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/tanfuriko1-640x691.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/tanfuriko1-1423x1536.png 1423w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/tanfuriko1-1897x2048.png 1897w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/tanfuriko1-750x810.png 750w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>\u5358\u632f\u308a\u5b50\u306e\u304a\u3082\u308a\u306e\u8cea\u91cf\u3092 $m$\uff0c\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092 $\\boldsymbol{r}$ \u3068\u3059\u308b\u3068\uff0c\u304a\u3082\u308a\u306b\u306f\u925b\u76f4\u4e0b\u5411\u304d\u306e\u91cd\u529b $-m \\boldsymbol{g}$ \u3068\uff0c\uff08\u4f38\u3073\u7e2e\u307f\u3057\u306a\u3044\u8cea\u91cf\u304c\u7121\u8996\u3067\u304d\u308b\uff09\u30ef\u30a4\u30e4\u30fc\u304b\u3089\u306e\u5f35\u529b $\\boldsymbol{T}$ \u304c\u306f\u305f\u3089\u3044\u3066\u3044\u308b\u306e\u3067\uff0c\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f<\/p>\n<p>$$m \\frac{d^2 \\boldsymbol{r}}{dt^2} = -m \\boldsymbol{g} + \\boldsymbol{T}$$<\/p>\n<p>\u3053\u3053\u3067 $\\boldsymbol{g}$ \u306f\u91cd\u529b\u52a0\u901f\u5ea6\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308a\uff0c\u925b\u76f4\u4e0a\u5411\u304d\u3092 $z$ \u8ef8\u306b\u3068\u3063\u3066\u3044\u308b\u306e\u3067<\/p>\n<p>$$\\boldsymbol{g} = (0, 0, g)$$<\/p>\n<p>$z$ \u6210\u5206\u306e $g$ \u306f\u91cd\u529b\u52a0\u901f\u5ea6\u306e\u5927\u304d\u3055\u3092\u3042\u3089\u308f\u3059\u3002<\/p>\n<p>\u5358\u632f\u308a\u5b50\u306e\u652f\u70b9\uff08\u56fa\u5b9a\u70b9\uff09\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092 $\\boldsymbol{R} = (0, 0, R)$ \u3068\u3057\uff0c\u652f\u70b9\u304b\u3089\u306e\u76f8\u5bfe\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb $\\boldsymbol{\\ell}$ \u3092<\/p>\n<p>$$\\boldsymbol{\\ell}\\equiv \\boldsymbol{r} -\\boldsymbol{R}$$<\/p>\n<p>\u3068\u5b9a\u7fa9\u3059\u308b\u3002\u652f\u70b9\u306f\u56fa\u5b9a\u3055\u308c\u3066\u3044\u308b\u306e\u3067 $$\\dfrac{dR}{dt} = 0$$<\/p>\n<p>\u307e\u305f\uff0c\u5358\u632f\u308a\u5b50\u306f\u4f38\u3073\u7e2e\u307f\u3057\u306a\u3044\u306e\u3067 $$\\ell \\equiv \\sqrt{\\boldsymbol{\\ell}\\cdot\\boldsymbol{\\ell}} = \\mbox{const.}$$<\/p>\n<p>\u904b\u52d5\u65b9\u7a0b\u5f0f\u306e\u4e21\u8fba\u306b\u76f8\u5bfe\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb $\\boldsymbol{\\ell}$ \u3092\u5916\u7a4d\u3057\u3066\u3084\u308a\uff0c$\\boldsymbol{\\ell}$ \u306b\u5bfe\u3059\u308b\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u5f62\u306b\u3057\u3066\u3084\u308b\u3068<\/p>\n<p>$$m \\boldsymbol{\\ell}\\times \\frac{d^2 \\boldsymbol{\\ell}}{dt^2} = -m \\boldsymbol{\\ell}\\times\\boldsymbol{g} + \\boldsymbol{\\ell}\\times\\boldsymbol{T}$$<\/p>\n<p>\u5f35\u529b $\\boldsymbol{T}$ \u306f $\\boldsymbol{\\ell}$ \u306b\u5e73\u884c\u3067\u3042\u308b\u304b\u3089\uff08\u5411\u304d\u306f\u53cd\u5bfe\uff09<\/p>\n<p>$$\\boldsymbol{\\ell}\\times\\boldsymbol{T} = \\boldsymbol{0}$$<\/p>\n<p>\u5f93\u3063\u3066\uff0c\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f\u6700\u7d42\u7684\u306b<\/p>\n<p>$$ \\boldsymbol{\\ell}\\times \\ddot{\\boldsymbol{\\ell}} = -\\boldsymbol{\\ell}\\times\\boldsymbol{g} \\tag{1}$$<\/p>\n<p>\u3068\u306a\u308b\u3002\u5f35\u529b $\\boldsymbol{T}$ \u304c\u3042\u3089\u308f\u308c\u306a\u3044\u3088\u3046\u307e\u3068\u3081\u305f\u306e\u304c\u30dd\u30a4\u30f3\u30c8\u3067\u3042\u308a\uff0c\u3053\u306e\u3088\u3046\u306b\u30d9\u30af\u30c8\u30eb\u5f62\u3067\u8868\u3059\u3053\u3068\u306b\u3088\u3063\u3066\uff0c\u3053\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f\u6163\u6027\u7cfb\u3067\u3082\u56de\u8ee2\u7cfb\u306e\u3088\u3046\u306a\u975e\u6163\u6027\u7cfb\u3067\u3082\u305d\u306e\u307e\u307e\u306e\u5f62\u3067\u6210\u308a\u7acb\u3064\u3002\u3053\u308c\u3082\u5927\u4e8b\u306a\u30dd\u30a4\u30f3\u30c8\u3002<\/p>\n<h3>\u6163\u6027\u7cfb\u306b\u304a\u3051\u308b\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5<\/h3>\n<p>\u6163\u6027\u7cfb\u306b\u304a\u3044\u3066\u306f\u4e00\u5b9a\u3067\u3042\u308b\u57fa\u672c\u30d9\u30af\u30c8\u30eb $\\boldsymbol{e}_x, \\boldsymbol{e}_y, \\boldsymbol{e}_z$ \u306e\u8868\u8a18\u306f\u7701\u7565\u3057\u3066\u6210\u5206\u306e\u307f\u3092\u8868\u8a18\u3059\u308b\u3053\u3068\u306b\u3057\u3066\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\boldsymbol{g} &amp;=&amp; (0, 0, g) \\\\<br \/>\n\\boldsymbol{\\ell} &amp;=&amp; (\\ell_x, \\ell_y, \\ell_z) \\\\<br \/>\n&amp;=&amp; (x, y, z -R) \\\\<br \/>\n&amp;\\equiv&amp; ( \\ell \\sin\\theta \\cos\\phi, \\ell \\sin\\theta \\sin\\phi, -\\ell \\cos\\theta) \\quad (z -R &lt; 0)<br \/>\n\\end{eqnarray}<\/p>\n<p>\u307e\u305a\uff0c\u904b\u52d5\u65b9\u7a0b\u5f0f $(1)$ \u306e $z$ \u6210\u5206\u306f\uff0c\u5de6\u8fba\u304c<\/p>\n<p>\\begin{eqnarray}<br \/>\n(\\boldsymbol{\\ell}\\times \\ddot{\\boldsymbol{\\ell}})_z &amp;=&amp; \\ell_x\\,\\ddot{\\ell}_y -\\ell_y\\,\\ddot{\\ell}_x \\\\<br \/>\n&amp;=&amp; \\frac{d}{dt} \\left( \\ell_x\\, \\dot{\\ell}_y -\\ell_y\\, \\dot{\\ell}_x\\right)\\\\<br \/>\n&amp;=&amp; \\frac{d}{dt} \\left(\\ell_x^2 \\frac{d}{dt} \\left(\\frac{\\ell_y}{\\ell_x} \\right) \\right)\\\\<br \/>\n&amp;=&amp; \\ell^2 \\frac{d}{dt} \\left( \\sin^2\\theta\\, \\dot{\\phi}\\right)<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3067\u3042\u308a\uff0c\u53f3\u8fba\u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\n-\\left(\\boldsymbol{\\ell}\\times\\boldsymbol{g}\\right)_z &amp;=&amp; -(\\ell_x\\, g_y -\\ell_y\\, g_x) = 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u5f93\u3063\u3066\u5de6\u8fba\u3068\u53f3\u8fba\u3092\u7b49\u53f7\u3067\u3064\u306a\u3050\u3068\uff0c$(1)$ \u5f0f\u306e $z$ \u6210\u5206\u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\frac{d}{dt} \\left( \\sin^2\\theta\\, \\dot{\\phi}\\right) &amp;=&amp; 0 \\\\<br \/>\n\\therefore\\ \\\u00a0 \u00a0\\sin^2\\theta\\, \\dot{\\phi} &amp;=&amp; \\mbox{const.} \\tag{2}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u6761\u4ef6\u3068\u3057\u3066\uff0c\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u306f $x = 0, y = 0$ \uff08\u652f\u70b9\u306e\u925b\u76f4\u65b9\u5411\u771f\u4e0b\uff09\u3092\u901a\u308b\u3068\u3059\u308b\u3068\uff0c\u305d\u306e\u3068\u304d $\\theta = 0$ \u3067\u3042\u308b\u304b\u3089 $(2)$ \u5f0f\u306e\u53f3\u8fba\u306e\u5b9a\u6570 $\\mbox{const.} $ \u306f\u30bc\u30ed\u3002\u5f93\u3063\u3066<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\sin^2\\theta\\, \\dot{\\phi} &amp;=&amp; 0 \\\\<br \/>\n\\therefore\\ \\ \\dot{\\phi} &amp;=&amp; 0 \\\\<br \/>\n\\therefore\\ \\ \\phi &amp;=&amp; \\mbox{const.}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3068\u306a\u308b\u3002\u3053\u306e\u3053\u3068\u306f\uff0c\u632f\u52d5\u9762\u304c\u4e00\u5b9a\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u4ee5\u5f8c\u306f\u7c21\u5358\u306e\u305f\u3081\u306b<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\phi &amp;=&amp; \\mbox{const.} \\Rightarrow 0 \\\\<br \/>\n\\therefore \\ \\ \\ell_x &amp;\\Rightarrow&amp; \\ell \\sin\\theta \\\\<br \/>\n\\ell_y &amp;\\Rightarrow&amp;0<br \/>\n\\end{eqnarray}<br \/>\n\u3068\u3057\u3066\u8a08\u7b97\u3092\u7d9a\u3051\u308b\u3002<\/p>\n<p>\u904b\u52d5\u65b9\u7a0b\u5f0f $(1)$ \u306e $x$ \u6210\u5206\u306f\uff0c\u5de6\u8fba\u304c<\/p>\n<p>$$(\\boldsymbol{\\ell}\\times \\ddot{\\boldsymbol{\\ell}})_x = \\ell_y\\, \\ddot{\\ell}_z -\\ell_z\\, \\ddot{\\ell}_y = 0$$<\/p>\n<p>\u53f3\u8fba\u3082<\/p>\n<p>$$-\\left(\\boldsymbol{\\ell}\\times\\boldsymbol{g}\\right)_x = -(\\ell_y\\, g_z -\\ell_z\\, g_y) = 0$$<\/p>\n<p>\u3068\u306a\u308b\u3002\u6700\u5f8c\u306b\u904b\u52d5\u65b9\u7a0b\u5f0f $(1)$ \u306e $y$ \u6210\u5206\u306f\uff0c\u5de6\u8fba\u304c<\/p>\n<p>\\begin{eqnarray}<br \/>\n(\\boldsymbol{\\ell}\\times \\ddot{\\boldsymbol{\\ell}})_y &amp;=&amp; \\ell_z\\, \\ddot{\\ell}_x -\\ell_x\\, \\ddot{\\ell}_z\\\\<br \/>\n&amp;=&amp; \\frac{d}{dt} \\left(\\ell_z\\, \\dot{\\ell}_x -\\ell_x\\, \\dot{\\ell}_z \\right)\\\\<br \/>\n&amp;=&amp; \\frac{d}{dt} \\left(\\ell_z^2 \\frac{d}{dt} \\left(\\frac{\\ell_x}{\\ell_z} \\right) \\right)\\\\<br \/>\n&amp;=&amp; \\frac{d}{dt} \\left(\\ell^2 \\cos^2\\theta\\, \\frac{d}{dt} \\left(\\frac{\\sin\\theta}{-\\cos\\theta} \\right) \\right)\\\\<br \/>\n&amp;=&amp; -\\ell^2 \\ddot{\\theta}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u53f3\u8fba\u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\n-\\left(\\boldsymbol{\\ell}\\times\\boldsymbol{g}\\right)_y &amp;=&amp; -(\\ell_z\\, g_x -\\ell_x\\, g_z) \\\\<br \/>\n&amp;=&amp; \\ell g\\,\\sin\\theta<br \/>\n\\end{eqnarray}<\/p>\n<p>\u5de6\u8fba\u3068\u53f3\u8fba\u3092\u7b49\u53f7\u3067\u7d50\u3076\u3068\uff0c\u6700\u7d42\u7684\u306b\u904b\u52d5\u65b9\u7a0b\u5f0f $(1)$ \u306e $y$ \u6210\u5206\u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\n-\\ell^2 \\ddot{\\theta} &amp;=&amp; \\ell g\\,\\sin\\theta \\\\<br \/>\n\\therefore\\ \\ \\ddot{\\theta} &amp;=&amp; -\\frac{g}{\\ell} \\sin\\theta<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3053\u306e\u5f0f\u306e\u5c0e\u51fa\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u3082\u53c2\u8003\u306b\u3002<\/p>\n<ul>\n<li><a href=\"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\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%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\/\" target=\"_blank\" rel=\"noopener\">\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u6e96\u5099<\/a>\n<ul>\n<li><a href=\"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\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%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\/#i\" target=\"_blank\" rel=\"noopener\">\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u306e\u5c0e\u51fa<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>\u56de\u8ee2\u7cfb\u306b\u304a\u3051\u308b\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5<\/h3>\n<p>\u56de\u8ee2\u7cfb\u306b\u304a\u3044\u3066\u3082\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f\u540c\u3058 $(1)$ \u5f0f\u3067\u3042\u308b\u3002\u56de\u8ee2\u7cfb\u306e\u3088\u3046\u306a\u975e\u6163\u6027\u7cfb\u306b\u304a\u3044\u3066\u3082\uff0c\u30d9\u30af\u30c8\u30eb\u5f62\u3067\u66f8\u304b\u308c\u305f $(1)$ \u5f0f\u3092\u305d\u306e\u307e\u307e\u4f7f\u3063\u3066\u8a08\u7b97\u3092\u3059\u3059\u3081\u308b\u306e\u304c\u3053\u306e\u30da\u30fc\u30b8\u306e\u65b9\u91dd\u3002<\/p>\n<p>\u305f\u3060\u3057\uff0c$\\boldsymbol{\\ell}$ \u306f\uff0c\u6163\u6027\u7cfb\u306b\u5bfe\u3057\u3066\u4e00\u5b9a\u306e\u89d2\u901f\u5ea6\u30d9\u30af\u30c8\u30eb $\\boldsymbol{\\omega}$ \u3067\u56de\u8ee2\u3059\u308b\u56de\u8ee2\u7cfb\u306e\u57fa\u672c\u30d9\u30af\u30c8\u30eb $\\boldsymbol{e}_{x&#8217;}, \\boldsymbol{e}_{y&#8217;}, \\boldsymbol{e}_{z&#8217;}$ \u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\uff1a<\/p>\n<p>$$\\boldsymbol{\\ell} = \\ell_{x&#8217;} \\,\\boldsymbol{e}_{x&#8217;} + \\ell_{y&#8217;}\\, \\boldsymbol{e}_{y&#8217;} + \\ell_{y&#8217;}\\, \\boldsymbol{e}_{y&#8217;} $$<\/p>\n<p>\u56de\u8ee2\u7cfb\u3067\u3042\u308b\u304b\u3089<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\dot{\\boldsymbol{e}}_{x&#8217;} &amp;=&amp; \\boldsymbol{\\omega}\\times \\boldsymbol{e}_{x&#8217;} \\\\<br \/>\n\\dot{\\boldsymbol{e}}_{y&#8217;} &amp;=&amp; \\boldsymbol{\\omega}\\times \\boldsymbol{e}_{y&#8217;} \\\\<br \/>\n\\dot{\\boldsymbol{e}}_{z&#8217;} &amp;=&amp; \\boldsymbol{\\omega}\\times \\boldsymbol{e}_{z&#8217;}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3053\u306e\u3078\u3093\u306e\u4e8b\u60c5\u306b\u3064\u3044\u3066\u306f\uff0c\u82e5\u5e72\u8868\u8a18\u304c\u7570\u306a\u308b\u304c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u306b\u307e\u3068\u3081\u3066\u3044\u308b\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e4%b8%80%e8%88%ac%e7%9b%b8%e5%af%be%e8%ab%96%e7%9a%84%e6%99%82%e7%a9%ba%e3%81%ae%e8%a1%a8%e3%81%97%e6%96%b9\/3%e6%ac%a1%e5%85%83%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e5%be%ae%e5%88%86\/\" target=\"_blank\" rel=\"noopener\">3\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306e\u5fae\u5206<\/a><\/li>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e4%b8%80%e8%88%ac%e7%9b%b8%e5%af%be%e8%ab%96%e7%9a%84%e6%99%82%e7%a9%ba%e3%81%ae%e8%a1%a8%e3%81%97%e6%96%b9\/3%e6%ac%a1%e5%85%83%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e5%be%ae%e5%88%86\/%e5%8f%82%e8%80%83%ef%bc%9a%e5%9b%9e%e8%bb%a2%e5%ba%a7%e6%a8%99%e7%b3%bb%e3%81%ab%e3%81%8a%e3%81%91%e3%82%8b%e5%9f%ba%e6%9c%ac%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e6%99%82%e9%96%93%e5%be%ae\/\" target=\"_blank\" rel=\"noopener\">\u88dc\u8db3\uff1a\u56de\u8ee2\u5ea7\u6a19\u7cfb\u306b\u304a\u3051\u308b\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306e\u6642\u9593\u5fae\u5206<\/a><\/li>\n<\/ul>\n<p><span style=\"font-family: helvetica, arial, sans-serif; color: #ff0000;\"><strong>\u30d9\u30af\u30c8\u30eb\u306e\u5fae\u5206\u306e\u969b\u306b\u306f\uff0c\u6210\u5206\u306e\u5fae\u5206\u3060\u3051\u3067\u306a\u304f\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u3082\u5fae\u5206\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u306e\u3060<\/strong><\/span>\u3068\u3044\u3046\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u8a08\u7b97\u3092\u3059\u308b\u3081\u308b\u3068\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\ddot{\\boldsymbol{\\ell}} &amp;=&amp; \\ddot{\\ell}_{x&#8217;}\\,\\boldsymbol{e}_{x&#8217;} + \\ddot{\\ell}_{y&#8217;}\\,\\boldsymbol{e}_{y&#8217;}+\\ddot{\\ell}_{z&#8217;}\\,\\boldsymbol{e}_{z&#8217;} \\\\<br \/>\n&amp;&amp; + 2 (\\dot{\\ell}_{x&#8217;}\\,\\dot{\\boldsymbol{e}}_{x&#8217;} + \\dot{\\ell}_{y&#8217;}\\,\\dot{\\boldsymbol{e}}_{y&#8217;}+\\dot{\\ell}_{z&#8217;}\\,\\dot{\\boldsymbol{e}}_{z&#8217;}) \\\\<br \/>\n&amp;&amp; + \\ell_{x&#8217;} \\,\\ddot{\\boldsymbol{e}}_{x&#8217;} + \\ell_{y&#8217;} \\,\\ddot{\\boldsymbol{e}}_{y&#8217;}+\\ell_{z&#8217;} \\,\\ddot{\\boldsymbol{e}}_{z&#8217;} \\\\<br \/>\n&amp;=&amp; \\ddot{\\ell}_{x&#8217;}\\,\\boldsymbol{e}_{x&#8217;} + \\ddot{\\ell}_{y&#8217;}\\,\\boldsymbol{e}_{y&#8217;}+\\ddot{\\ell}_{z&#8217;}\\,\\boldsymbol{e}_{z&#8217;} \\\\<br \/>\n&amp;&amp; + 2\\boldsymbol{\\omega}\\times(\\dot{\\ell}_{x&#8217;}\\,\\boldsymbol{e}_{x&#8217;} +\\dot{\\ell}_{y&#8217;}\\,\\boldsymbol{e}_{y&#8217;}+{\\color{blue}{\\dot{\\ell}_{z&#8217;}\\,\\boldsymbol{e}_{z&#8217;}}}) \\\\<br \/>\n&amp;&amp; + {\\color{blue}{ \\boldsymbol{\\omega}\\times (\\boldsymbol{\\omega} \\times \\boldsymbol{\\ell})}}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u5730\u7403\u81ea\u8ee2\u306b\u3088\u308b\u9060\u5fc3\u529b\u306e\u52b9\u679c ${\\color{blue}{\\boldsymbol{\\omega}\\times (\\boldsymbol{\\omega} \\times \\boldsymbol{\\ell})}}$ \u3068\uff0c\u30b3\u30ea\u30aa\u30ea\u306e\u529b\u306e\u3046\u3061\u306e\u901f\u5ea6\u306e\u925b\u76f4\u6210\u5206\u306e\u5bc4\u4e0e\u306e\u9805 ${\\color{blue}{\\dot{\\ell}_{z&#8217;}\\,\\boldsymbol{e}_{z&#8217;}}}$ \u306f\u4ed6\u306b\u6bd4\u3079\u3066\u5c0f\u3055\u3044\u306e\u3067\u7121\u8996\u3059\u308b\u3068\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\ddot{\\boldsymbol{\\ell}} &amp;\\simeq&amp;\\ddot{\\ell}_{x&#8217;}\\,\\boldsymbol{e}_{x&#8217;} + \\ddot{\\ell}_{y&#8217;}\\,\\boldsymbol{e}_{y&#8217;}+\\ddot{\\ell}_{z&#8217;}\\,\\boldsymbol{e}_{z&#8217;} +2\\boldsymbol{\\omega}\\times(\\dot{\\ell}_{x&#8217;}\\,\\boldsymbol{e}_{x&#8217;} +\\dot{\\ell}_{y&#8217;}\\,\\boldsymbol{e}_{y&#8217;})<br \/>\n\\end{eqnarray}<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-10457\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/tanfuriko2-300x338.png\" alt=\"\" width=\"300\" height=\"338\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/tanfuriko2-300x338.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/tanfuriko2-640x720.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/tanfuriko2-1364x1536.png 1364w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/tanfuriko2-1819x2048.png 1819w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/tanfuriko2-750x844.png 750w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>\u56f3\u306e\u3088\u3046\u306b\uff0c\u6163\u6027\u7cfb\u306e $xy$ \u5e73\u9762\u3092\u8d64\u9053\u9762\u3068\u3057\uff0c\u7def\u5ea6\uff08\u5317\u7def\uff09$\\lambda$ \u306e\u5730\u70b9\u306e\u925b\u76f4\u4e0a\u5411\u304d\u3092 $z&#8217;$ \u8ef8\u3068\u3059\u308b\u3068\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\boldsymbol{R} &amp;=&amp; R \\,\\boldsymbol{e}_{z&#8217;} \\\\<br \/>\n\\boldsymbol{g} &amp;=&amp; g\\, \\boldsymbol{e}_{z&#8217;} \\\\<br \/>\n\\boldsymbol{\\omega} &amp;=&amp; -\\omega\\,\\cos\\lambda\\, \\boldsymbol{e}_{x&#8217;} + \\omega\\,\\sin\\lambda\\, \\boldsymbol{e}_{z&#8217;} \\\\<br \/>\n\\therefore\\ \\ \\boldsymbol{\\omega}\\times \\boldsymbol{e}_{x&#8217;} &amp;=&amp; \\omega\\,\\sin\\lambda\\, \\boldsymbol{e}_{y&#8217;} \\\\<br \/>\n\\boldsymbol{\\omega}\\times \\boldsymbol{e}_{y&#8217;} &amp;=&amp; -\\omega\\,\\sin\\lambda\\, \\boldsymbol{e}_{x&#8217;}-\\omega\\,\\cos\\lambda\\,\u00a0 \\boldsymbol{e}_{z&#8217;}\\\\<br \/>\n\\end{eqnarray}<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\therefore\\ \\ \\ddot{\\boldsymbol{\\ell}} &amp;\\simeq&amp; (\\ddot{\\ell}_{x&#8217;} -2\\omega \\dot{\\ell}_{y&#8217;}\\sin\\lambda)\\,\\boldsymbol{e}_{x&#8217;} \\\\<br \/>\n&amp;&amp; + (\\ddot{\\ell}_{y&#8217;} +2\\omega \\dot{\\ell}_{x&#8217;}\\sin\\lambda)\\,\\boldsymbol{e}_{y&#8217;} \\\\<br \/>\n&amp;&amp; + (\\ddot{\\ell}_{z&#8217;} -2\\omega \\dot{\\ell}_{y&#8217;}\\cos\\lambda)\\,\\boldsymbol{e}_{z&#8217;} \\\\<br \/>\n&amp;\\equiv&amp; \\ddot{\\ell}_{x&#8217;} \\,\\boldsymbol{e}_{x&#8217;} + \\ddot{\\ell}_{y&#8217;} \\,\\boldsymbol{e}_{y&#8217;}+\\ddot{\\ell}_{z&#8217;} \\,\\boldsymbol{e}_{z&#8217;}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u904b\u52d5\u65b9\u7a0b\u5f0f $(1)$ \u306e $z&#8217;$ \u6210\u5206\u306f\uff0c\u5de6\u8fba\u304c<\/p>\n<p>\\begin{eqnarray}<br \/>\n(\\boldsymbol{\\ell}\\times\\ddot{\\boldsymbol{\\ell}})_{z&#8217;} &amp;=&amp;<br \/>\n\\ell_{x&#8217;}\\,\\ddot{\\ell}_{y&#8217;} -\\ell_{y&#8217;} \\,\\ddot{\\ell}_{x&#8217;} \\\\<br \/>\n&amp;=&amp;<br \/>\n\\ell_{x&#8217;}\\left( \\ddot{\\ell}_{y&#8217;} +2\\omega \\dot{\\ell}_{x&#8217;}\\sin\\lambda\\right)<br \/>\n-\\ell_{y&#8217;}\\left( \\ddot{\\ell}_{x&#8217;} -2\\omega \\dot{\\ell}_{y&#8217;}\\sin\\lambda\\right)\\\\<br \/>\n&amp;=&amp; \\frac{d}{dt} \\left\\{\\ell_{x&#8217;}^2 \\frac{d}{dt}\\left(\\frac{\\ell_{y&#8217;}}{\\ell_{x&#8217;}} \\right) +\\omega\\left(\\ell_{x&#8217;}^2+\\ell_{y&#8217;}^2\\right)\\sin\\lambda\\right\\}\\\\<br \/>\n&amp;=&amp; \\ell^2 \\, \\frac{d}{dt}\\left\\{ \\sin^2\\theta&#8217; \\dot{\\phi}&#8217; + \\omega \\sin^2\\theta&#8217; \\, \\sin\\lambda\\right\\}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3053\u3053\u3067\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\ell_{x&#8217;} &amp;=&amp; \\ell \\sin\\theta&#8217; \\,\\cos\\phi&#8217; \\\\<br \/>\n\\ell_{y&#8217;} &amp;=&amp; \\ell \\sin\\theta&#8217; \\,\\sin\\phi&#8217;<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3068\u304a\u3044\u305f\u3002\u53f3\u8fba\u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\n-\\left(\\boldsymbol{\\ell}\\times \\boldsymbol{g}\\right)_{z&#8217;} &amp;=&amp; -\\left(\\ell_{x&#8217;}\\,g_{y&#8217;} -\\ell_{y&#8217;} \\,g_{x&#8217;} \\right) \\\\<br \/>\n&amp;=&amp; 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u5f93\u3063\u3066\u5de6\u8fba\u3068\u53f3\u8fba\u3092\u7b49\u53f7\u3067\u3080\u3059\u3076\u3068\uff0c\u904b\u52d5\u65b9\u7a0b\u5f0f $(1)$ \u306e $z&#8217;$ \u6210\u5206\u304b\u3089\u5f97\u3089\u308c\u308b\u5f0f\u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\frac{d}{dt}\\left\\{ \\sin^2\\theta&#8217; \\dot{\\phi}&#8217; + \\omega \\sin^2\\theta&#8217; \\, \\sin\\lambda\\right\\} &amp;=&amp; 0 \\\\<br \/>\n\\therefore\\ \\ \\sin^2\\theta&#8217; \\dot{\\phi}&#8217; + \\omega \\sin^2\\theta&#8217; \\, \\sin\\lambda &amp;=&amp; \\mbox{const.} \\tag{3}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u6761\u4ef6\u3068\u3057\u3066\uff0c\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u304c $x&#8217; = 0, y&#8217; = 0$ \u3092\u901a\u308b\u3068\u3059\u308b\u3068\uff0c\u305d\u306e\u3068\u304d $\\theta&#8217; = 0$ \u3067\u3042\u308b\u304b\u3089 $(3)$ \u5f0f\u306e\u53f3\u8fba\u306e\u5b9a\u6570\u306f\u30bc\u30ed\u3002\u5f93\u3063\u3066<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\dot{\\phi}&#8217; + \\omega\u00a0 \\, \\sin\\lambda &amp;=&amp; 0 \\\\<br \/>\n\\therefore\\ \\ \\frac{d\\phi\u2019}{dt} &amp;=&amp; -\\omega\\, \\sin\\lambda<br \/>\n\\end{eqnarray}<\/p>\n<p>\u56de\u8ee2\u7cfb\u3067\u898b\u308b\u3068\uff0c\u5358\u632f\u308a\u5b50\u306e\u632f\u52d5\u9762\u306f\u4e00\u5b9a\u3067\u306f\u306a\u3044\u3002\u7def\u5ea6\uff08\u5317\u7def\uff09$\\lambda$ \u306e\u5730\u70b9\u3067\u306f\u5358\u4f4d\u6642\u9593\u3042\u305f\u308a $\\omega\\, \\sin\\lambda$ \u3060\u3051\uff0c\u5730\u7403\u81ea\u8ee2\u3068\u9006\u5411\u304d\u306b\u56de\u8ee2\u3059\u308b\u3002\u3053\u306e\u3088\u3046\u306b\u3057\u3066\uff0c\u30d5\u30fc\u30b3\u30fc\u306e\u632f\u308a\u5b50\u306e\u632f\u52d5\u9762\u304c\u56de\u8ee2\u3059\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u305f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u56de\u8ee2\u7cfb\u306b\u304a\u3051\u308b\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\uff0c\u300c\u4e00\u822c\u306b\u30d9\u30af\u30c8\u30eb\u3092\u5fae\u5206\u3059\u308b\u3068\u304d\u306f\uff0c\u6210\u5206\u3060\u3051\u3067\u306a\u304f\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u3082\u5fae\u5206\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u306e\u3060\u300d\u3068\u3044\u3046\u7acb\u5834\u3067\u8a08\u7b97\u3057\u3066\u307f\u308b\u3002\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u3092\u53c2\u8003\u306b\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/10403\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n<ul>\n<li>3\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306e\u5fae\u5206<\/li>\n<li>\u88dc\u8db3\uff1a\u56de\u8ee2\u5ea7\u6a19\u7cfb\u306b\u304a\u3051\u308b\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306e\u6642\u9593\u5fae\u5206<\/li>\n<\/ul>\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":[24],"tags":[],"class_list":["post-10403","post","type-post","status-publish","format-standard","hentry","category-24","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/10403","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=10403"}],"version-history":[{"count":59,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/10403\/revisions"}],"predecessor-version":[{"id":10465,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/10403\/revisions\/10465"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=10403"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=10403"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=10403"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}