{"id":227,"date":"2022-01-05T15:29:28","date_gmt":"2022-01-05T06:29:28","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=227"},"modified":"2024-05-20T12:07:37","modified_gmt":"2024-05-20T03:07:37","slug":"%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","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\/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\/","title":{"rendered":"\u88dc\u8db3\uff1a\u56de\u8ee2\u5ea7\u6a19\u7cfb\u306b\u304a\u3051\u308b\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306e\u6642\u9593\u5fae\u5206"},"content":{"rendered":"

<\/p>\n

\"\"<\/p>\n

\u56de\u8ee2\u5ea7\u6a19\u7cfb\u3078\u306e\u5ea7\u6a19\u5909\u63db<\/h3>\n

\uff08\u9759\u6b62\u3057\u3066\u3044\u308b\uff09\u6163\u6027\u7cfb \\(S\\) \u306e\u5ea7\u6a19\u3092 \\((x, y, z)\\)\uff0c\\(S\\) \u7cfb\u306b\u5bfe\u3057\u3066 \\(z\\) \u8ef8\u306e\u307e\u308f\u308a\u306b\u89d2\u901f\u5ea6 \\(\\omega\\) \u3067\u56de\u8ee2\u3057\u3066\u3044\u308b\u5ea7\u6a19\u7cfb \\(S’\\) \u306e\u5ea7\u6a19 \\((x’, y’, z’)\\) \u3068\u3059\u308b\u3068\uff0c\u5ea7\u6a19\u5909\u63db\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\u3002<\/p>\n

\\begin{eqnarray}
\nx’ &=&x \\cos \\omega t + y\\sin \\omega t \\\\
\ny’ &=&-x \\sin \\omega t + y \\cos \\omega t\\\\
\nz’ &=& z
\n\\end{eqnarray}<\/p>\n

\u3053\u306e\u9006\u5909\u63db\u306f<\/p>\n

\\begin{eqnarray}
\nx &=&\u00a0 x’ \\cos \\omega t -y’\\sin \\omega t \\\\
\ny &=& x’ \\sin \\omega t + y’ \\cos \\omega t\\\\
\nz &=& z’
\n\\end{eqnarray}<\/p>\n

\u56de\u8ee2\u7cfb\u306b\u304a\u3051\u308b\u57fa\u672c\u30d9\u30af\u30c8\u30eb<\/h3>\n

\u70b9 \\(P\\) \u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb \\(\\vec{r}\\) \u306f \\(S\\) \u7cfb\u306e\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u3068\u6210\u5206\u3092\u4f7f\u3063\u3066<\/p>\n

\\begin{eqnarray}
\n\\vec{r} &=& x\\,\\vec{e}_x + y\\,\\vec{e}_y + z\\,\\vec{e}_z \\\\
\n&=& (x’ \\cos \\omega t -y’\\sin \\omega t)\\,\\vec{e}_x + (x’ \\sin \\omega t + y’ \\cos \\omega t)\\,\\vec{e}_y\u00a0 +z’\\,\\vec{e}_z\\\\
\n&=& x’ (\\cos \\omega t\\,\\vec{e}_x + \\sin \\omega t\\,\\vec{e}_y) + y’ ( -\\sin \\omega t\\,\\vec{e}_x + \\cos \\omega t \\,\\vec{e}_y) + z’\\,\\vec{e}_z
\n\\end{eqnarray}<\/p>\n

\u4e00\u65b9\uff0c\u56de\u8ee2\u3057\u3066\u3044\u308b \\(S’\\) \u7cfb\u306e\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u3068\u6210\u5206\u3092\u4f7f\u3063\u3066\u66f8\u304f\u3068\uff0c<\/p>\n

\\begin{eqnarray}
\n\\vec{r}’ &=& x’\\,\\vec{e}’_{x} + y’\\,\\vec{e}’_{y} + z’\\,\\vec{e}’_{z}\\end{eqnarray}<\/p>\n

 <\/p>\n

\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u5ea7\u6a19\u7cfb\u306e\u53d6\u308a\u65b9\u306b\u3088\u3089\u306a\u3044\u4e0d\u5909\u306a\u5e7e\u4f55\u5b66\u7684\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3067\u3042\u308b\u304b\u3089\uff0c$$\\vec{r}’ = \\vec{r} $$ \u3053\u306e\u3053\u3068\u304b\u3089\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306e\u5909\u63db\u5f0f\u304c\u51fa\u3066\u304f\u308b\u3002<\/p>\n

\\begin{eqnarray}
\n\\vec{e}’_x &=& \\cos \\omega t\\,\\vec{e}_x + \\sin \\omega t\\,\\vec{e}_y\\\\
\n\\vec{e}’_y &=& -\\sin \\omega t\\,\\vec{e}_x + \\cos \\omega t \\,\\vec{e}_y \\\\
\n\\vec{e}’_z &=& \\vec{e}_z
\n\\end{eqnarray}<\/p>\n

\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306e\u6642\u9593\u65e2\u5b58\u6027<\/h3>\n

\u9759\u6b62\u6163\u6027\u7cfb \\(S\\) \u306e\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306f\u6642\u9593\u7684\u306b\uff08\u7a7a\u9593\u7684\u306b\u3082\uff09\u5909\u5316\u3057\u306a\u3044
\n$$\\dot{\\vec{e}}_x = \\dot{\\vec{e}}_y =\\dot{\\vec{e}}_z =\\vec{0}$$ \u3068\u3057\u3066\u3082\uff0c\u56de\u8ee2\u7cfb \\(S’\\) \u306e\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u6642\u9593\u4f9d\u5b58\u6027\u3092\u3082\u3064\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n

\\begin{eqnarray}
\n\\dot{\\vec{e}}’_x &=& (\\cos \\omega t\\,\\vec{e}_x + \\sin \\omega t\\,\\vec{e}_y)\\dot{} \\\\
\n&=& \\omega\\, (-\\sin \\omega t\\,\\vec{e}_x + \\cos \\omega t \\,\\vec{e}_y) \\\\
\n&=& \\omega\\,\\vec{e}’_y\\\\
\n\\dot{\\vec{e}}’_y &=& (-\\sin \\omega t\\,\\vec{e}_x + \\cos \\omega t \\,\\vec{e}_y)\\dot{} \\\\
\n&=& -\\omega\\, (\\cos \\omega t\\,\\vec{e}_x + \\sin \\omega t\\,\\vec{e}_y) \\\\
\n&=& -\\omega\\,\\vec{e}’_x \\\\
\n\\dot{\\vec{e}}’_z &=&\\dot{\\vec{e}}_z \\\\
\n&=& \\vec{0}
\n\\end{eqnarray}<\/p>\n

\u89d2\u901f\u5ea6\u30d9\u30af\u30c8\u30eb\u306e\u5c0e\u5165<\/h3>\n

\u3053\u3053\u3067\uff0c\u89d2\u901f\u5ea6\u30d9\u30af\u30c8\u30eb \\(\\vec{\\omega}\\) \u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5c0e\u5165\u3059\u308b\uff1a
\n$$\\vec{\\omega} \\equiv \\omega\\,\\vec{e}’_z \\,(= \\omega\\,\\vec{e}_z)$$<\/p>\n

\u3059\u306a\u308f\u3061\uff0c\\(\\vec{\\omega}\\) \u306f\u30d9\u30af\u30c8\u30eb\u306e\u5411\u304d\u304c\u56de\u8ee2\u8ef8\u3068\u305d\u306e\u56de\u8ee2\u306e\u5411\u304d\uff08\u53f3\u30cd\u30b8\u306e\u9032\u3080\u5411\u304d\uff09\uff0c\u5927\u304d\u3055 \\(|\\vec{\\omega}| = \\omega\\) \u304c\u89d2\u901f\u5ea6\uff08\u306e\u5927\u304d\u3055\uff09\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u308b\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u3002<\/p>\n

\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306e\u6642\u9593\u5fae\u5206\u3092\u89d2\u901f\u5ea6\u30d9\u30af\u30c8\u30eb\u3092\u4f7f\u3063\u3066\u8868\u3059<\/h3>\n

\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u540c\u58eb\u306e\u5916\u7a4d\u304c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3053\u3068\u3092\u4f7f\u3046\u3068\uff0c
\n$$\\vec{e}’_z \\times \\vec{e}’_x = \\vec{e}’_y, \\quad \\vec{e}’_z \\times \\vec{e}’_y = -\\vec{e}’_x, \\quad \\vec{e}’_z \\times \\vec{e}’_z = \\vec{0}$$ \u56de\u8ee2\u7cfb\u306b\u304a\u3051\u308b\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306e\u6642\u9593\u5fae\u5206\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002<\/p>\n

$$\\dot{\\vec{e}}’_x = \\vec{\\omega} \\times \\vec{e}’_x, \\quad \\dot{\\vec{e}}’_y = \\vec{\\omega} \\times \\vec{e}’_y, \\quad \\dot{\\vec{e}}’_z = \\vec{\\omega} \\times \\vec{e}’_z$$<\/p>\n

\u3061\u306a\u307f\u306b\uff0c\u3053\u306e\u6700\u7d42\u7684\u306a\u6642\u9593\u5fae\u5206\u306e\u5f0f\u306f\u30d9\u30af\u30c8\u30eb\u3067\u8868\u3055\u308c\u3066\u3044\u308b\u306e\u3067\uff0c\u5ea7\u6a19\u7cfb\u306e\u3068\u308a\u65b9\u306b\u4f9d\u5b58\u3057\u306a\u3044\u3002\u3064\u307e\u308a\uff0c\u3053\u306e\u5f0f\u306e\u5c0e\u51fa\u306e\u969b\u306b\u306f\uff0c\u89d2\u901f\u5ea6\u30d9\u30af\u30c8\u30eb \\(\\vec{\\omega}\\) \u304c \\(z’\\) \u8ef8\u306b\u5e73\u884c\u3067\u3042\u308b\u3053\u3068\u3092\u4eee\u5b9a\u3057\u305f\u304c\uff0c\u6700\u7d42\u7684\u306b\u5c0e\u51fa\u3055\u308c\u305f\u3053\u306e\u5f0f\u306f\uff0c\\(\\vec{\\omega}\\) \u304c\u3069\u306e\u65b9\u5411\u3092\u5411\u3044\u3066\u3044\u3066\u3082\u6210\u308a\u7acb\u3064\u4e00\u822c\u7684\u306a\u5f0f\u3067\u3042\u308b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

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