{"id":327,"date":"2022-01-06T15:59:53","date_gmt":"2022-01-06T06:59:53","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=327"},"modified":"2024-08-06T16:44:49","modified_gmt":"2024-08-06T07:44:49","slug":"%e6%b8%ac%e5%9c%b0%e7%b7%9a%e3%81%a8%e6%8e%a5%e7%b6%9a%e4%bf%82%e6%95%b0%e3%83%bb%e3%82%af%e3%83%aa%e3%82%b9%e3%83%88%e3%83%83%e3%83%95%e3%82%a7%e3%83%ab%e8%a8%98%e5%8f%b7","status":"publish","type":"page","link":"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\/%e6%b8%ac%e5%9c%b0%e7%b7%9a%e3%81%a8%e6%8e%a5%e7%b6%9a%e4%bf%82%e6%95%b0%e3%83%bb%e3%82%af%e3%83%aa%e3%82%b9%e3%83%88%e3%83%83%e3%83%95%e3%82%a7%e3%83%ab%e8%a8%98%e5%8f%b7\/","title":{"rendered":"\u6e2c\u5730\u7dda\u3068\u63a5\u7d9a\u4fc2\u6570\u30fb\u30af\u30ea\u30b9\u30c8\u30c3\u30d5\u30a7\u30eb\u8a18\u53f7"},"content":{"rendered":"

\u6642\u7a7a\u306e\u66f2\u304c\u308a\u5177\u5408\u3092\u8a18\u8ff0\u3059\u308b\u305f\u3081\u306b\u306f\uff0c\u307e\u305a\u66f2\u304c\u3063\u3066\u3044\u306a\u3044\u300c\u307e\u3063\u3059\u3050\u306a\u3082\u306e<\/strong><\/span>\u300d\u3092\u5b9a\u7fa9\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u305d\u308c\u304c\u6e2c\u5730\u7dda<\/strong><\/span>\u3067\u3042\u308b\u3002<\/p>\n

\u4e16\u754c\u7dda\u306e\u63a5\u30d9\u30af\u30c8\u30eb<\/h3>\n

\u307e\u305a\uff0c4\u6b21\u5143\u6642\u7a7a\u5185\u306e\u66f2\u7dda\u3067\u3042\u308b\u4e16\u754c\u7dda<\/strong><\/span> \\(x^{\\mu}(v)\\) \u3092\u8003\u3048\u308b\u3002\u3053\u3053\u3067 \\(v\\) \u306f\u4e16\u754c\u7dda<\/strong><\/span>\u306b\u76ee\u76db\u3092\u3064\u3051\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3042\u308a\uff0c\u5f8c\u8ff0\u3059\u308b\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f<\/strong><\/span>\u304c\u6210\u308a\u7acb\u3064\u6642\u306b\u306f\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf<\/strong><\/span>\u3068\u547c\u3070\u308c\u308b\u3002\u3053\u306e\u4e16\u754c\u7dda\u306e\u63a5\u30d9\u30af\u30c8\u30eb<\/strong><\/span> \\(\\boldsymbol{u}\\) \u3092\uff0c\u6210\u5206<\/strong><\/span> \\(u^{\\mu}\\) \u3068\u57fa\u672c\u30d9\u30af\u30c8\u30eb<\/strong><\/span> \\(\\boldsymbol{e}_{\\mu}\\) \u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3042\u3089\u308f\u3059\u3002
\n\\begin{equation}
\n\\boldsymbol{u} = u^{\\mu} \\boldsymbol{e}_{\\mu}
\n\\equiv \\frac{dx^{\\mu}}{dv} \\boldsymbol{e}_{\\mu}
\n\\end{equation}<\/p>\n

\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f<\/h3>\n

\u6e2c\u5730\u7dda<\/strong><\/span>\u3068\u306f\u63a5\u30d9\u30af\u30c8\u30eb<\/strong><\/span>\u304c\u4e16\u754c\u7dda\u306b\u305d\u3063\u3066\u4e00\u5b9a<\/strong><\/span>\u3067\u3042\u308b\u3088\u3046\u306a\u300c\u307e\u3063\u3059\u3050\u306a<\/strong><\/span>\u300d\u7dda\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u3064\u307e\u308a
\n\\begin{equation}
\n\\frac{d\\boldsymbol{u}}{dv} = \\boldsymbol{0}
\n\\end{equation}
\n\u3067\u3042\u308b\u3088\u3046\u306a\u7dda\u3067\u3042\u308a\uff0c\u3053\u306e\u5f0f\u3092\uff08\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf<\/strong><\/span> \\(v\\) \u3067\u30d1\u30e9\u30e1\u30c8\u30e9\u30a4\u30ba\u3055\u308c\u305f\uff09\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f<\/strong><\/span>\u3068\u547c\u3076\u3002\u524d\u7bc0\u3067\u8ff0\u3079\u305f\u3088\u3046\u306b<\/p>\n

\u4e00\u822c\u306b\u30d9\u30af\u30c8\u30eb\u3092\u5fae\u5206\u3059\u308b\u3068\u304d\u306f\uff0c
\n\u6210\u5206\u3060\u3051\u3067\u306a\u304f\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u3082\u5fae\u5206\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b<\/strong><\/span><\/p>\n

\u304b\u3089\uff0c\u4e0a\u5f0f\u306f
\n\\begin{eqnarray}\\label{eq:geo1}
\n\\frac{d\\boldsymbol{u}}{dv} &=&
\n\\left( \\frac{\\partial u^{\\mu}}{\\partial x^{\\nu}}\\boldsymbol{e}_{\\mu}
\n+ u^{\\mu} \\frac{\\partial \\boldsymbol{e}_{\\mu}}{\\partial x^{\\nu}}\\right)
\n\\frac{d x^{\\nu}}{dv} \\\\
\n&=&\\frac{d u^{\\mu}}{dv}\\boldsymbol{e}_{\\mu}
\n+ \\boldsymbol{e}_{\\mu, \\nu}u^{\\mu} u^{\\nu} = \\boldsymbol{0}
\n\\end{eqnarray}
\n\u3068\u306a\u308b\u3002<\/p>\n

<\/a>\u504f\u5fae\u5206\u306e\u7c21\u7565\u8868\u8a18\u6cd5<\/h3>\n

\\(x^{\\nu}\\)\u3067\u306e\u504f\u5fae\u5206\u3092\u4e0b\u6dfb\u5b57\u306b\u30ab\u30f3\u30de \\({}_{, \\nu}\\) \u3067 $$\\displaystyle\\frac{\\partial \\boldsymbol{e}_{\\mu}}{\\partial x^{\\nu}} \\equiv \\boldsymbol{e}_{\\mu, \\nu}$$\u306a\u3069\u3068\u66f8\u304f\u306e\u306f\u8868\u793a\u7c21\u7565\u5316\u306e\u305f\u3081\u306e\u8868\u8a18\u6cd5\u3067\u3042\u308b\u3002\u672c\u30b5\u30a4\u30c8\u306e\u4ed6\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u3082\uff0c\u65ad\u308a\u306a\u304f\u4f7f\u3063\u3066\u3044\u308b\u5834\u5408\u304c\u3042\u308b\u3002<\/p>\n

\u76f8\u5bfe\u8ad6\u696d\u754c\u3067\u306f\u6975\u3081\u3066\u4e00\u822c\u7684\u306b\u5e83\u304f\u4f7f\u308f\u308c\u3066\u3044\u308b\u3053\u306e\u8868\u8a18\u6cd5\u3067\u3042\u308b\u304c\uff0c\u5b66\u90e8\u521d\u5b66\u5e74\u5411\u3051\u306e\u6570\u5b66\u306e\u30c6\u30ad\u30b9\u30c8\u3067\u306f\uff0c\u95a2\u6570 \\(f\\) \u306e\u5909\u6570 \\(x\\) \u306b\u95a2\u3059\u308b\u504f\u5fae\u5206\u3092
\n$$\\frac{\\partial f}{\\partial x}, \\ \\\u00a0 \\partial_x f, \\ \\ f_x$$
\n\u306a\u3069\u3068\u66f8\u304f\u3068\u3055\u308c\u3066\u3044\u308b\u3002Wikipedia \u306e\u300c\u504f\u5fae\u5206<\/a>\u300d\u306e\u9805\u3082\u53c2\u7167\u3002<\/p>\n