{"id":212,"date":"2022-01-05T14:44:16","date_gmt":"2022-01-05T05:44:16","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=212"},"modified":"2022-07-28T14:52:10","modified_gmt":"2022-07-28T05:52:10","slug":"%e5%85%89%e8%a1%8c%e5%b7%ae","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b%e3%81%ab%e3%82%88%e3%82%89%e3%81%aa%e3%81%84%e7%9b%b8%e5%af%be%e8%ab%96%e3%81%ae%e7%90%86%e8%a7%a3\/%e5%85%89%e8%a1%8c%e5%b7%ae\/","title":{"rendered":"\u5149\u884c\u5dee"},"content":{"rendered":"

\u5149\u884c\u5dee<\/strong><\/span>\u3068\u306f\uff0c\u5149\u6e90\u306b\u5bfe\u3059\u308b\u89b3\u6e2c\u8005\u306e\u901f\u5ea6\u306e\u9055\u3044\u306b\u3088\u3063\u3066\uff0c\u5149\u306e\u5165\u5c04\u89d2\u304c\u7570\u306a\u3063\u3066\u89b3\u6e2c\u3055\u308c\u308b\u73fe\u8c61\u3067\u3042\u308b\u3002<\/p>\n

\"\"<\/p>\n

\u5149\u306e\u4f1d\u64ad\u3092\u8868\u30594\u5143\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{k}\\) \u306f\uff0c\u632f\u52d5\u6570\uff0c \u89b3\u6e2c\u8005 \\(A, B\\) \u306e4\u5143\u901f\u5ea6\u304a\u3088\u3073\u5149\u306e\u4f1d\u64ad\u65b9\u5411\u3092\u8868\u3059\u7a7a\u9593\u7684\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3092\u4f7f\u3063\u3066\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u306e\u3067\u3042\u3063\u305f\u3002
\n$$ \\boldsymbol{k} = \\bar{\\omega} (\\bar{\\boldsymbol{u}} + \\bar{\\boldsymbol{\\gamma}})
\n= {\\omega} ({\\boldsymbol{u}} + {\\boldsymbol{\\gamma}})$$
\n$$\\therefore \\bar{\\boldsymbol{u}} + \\bar{\\boldsymbol{\\gamma}} = \\frac{\\omega}{\\bar{\\omega}} ({\\boldsymbol{u}} + {\\boldsymbol{\\gamma}})$$<\/p>\n

\u3053\u306e\u5f0f\u306e\u4e21\u8fba\u3068 \\(\\bar{\\boldsymbol{e}}\\) \u306e\u5185\u7a4d\u3092\u3068\u308b\u3068\uff0c\u5de6\u8fba\u306f
\n$$ \\bar{\\boldsymbol{e}}\\cdot (\\bar{\\boldsymbol{u}} + \\bar{\\boldsymbol{\\gamma}}) = \\bar{\\boldsymbol{e}}\\cdot\\bar{\\boldsymbol{\\gamma}} = \\cos \\bar{\\theta}$$<\/p>\n

\u4e00\u65b9\uff0c\u53f3\u8fba\u306f
\n\\begin{eqnarray}
\n\\color{red}{\\frac{\\omega}{\\bar{\\omega}}}
\n\\color{blue}{\\bar{\\boldsymbol{e}}\\cdot (\\boldsymbol{u} + \\boldsymbol{\\gamma}) }
\n&=& \\color{red}{\\frac{\\sqrt{1-V^2}}{1 – V\\cos\\theta}}
\n\\color{blue}{\\frac{1}{\\sqrt{1-V^2}} (\\boldsymbol{e} + V \\boldsymbol{u}) \\cdot(\\boldsymbol{u} + \\boldsymbol{\\gamma})}\\\\
\n&=& \\frac{1}{1 – V\\cos\\theta} (\\boldsymbol{e}\\cdot \\boldsymbol{\\gamma} + V \\boldsymbol{u} \\cdot \\boldsymbol{u} ) \\\\
\n&=& \\frac{\\cos\\theta -V}{1 – V\\cos\\theta}
\n\\end{eqnarray}
\n$$\\therefore \\ \\cos \\bar{\\theta} = \\frac{\\cos\\theta -V}{1 – V\\cos\\theta}$$<\/p>\n

2\u3064\u306e\u7a7a\u9593\u7684\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u306e\u306a\u3059\u89d2 \\(\\theta, \\bar{\\theta}\\) \u3092\uff0c\u5149\u306e\u5165\u5c04\u89d2 \\(\\varTheta, \\bar{\\varTheta}\\) \u3092\u4f7f\u3063\u3066\u3042\u3089\u308f\u3059\u3068\uff0c\\(\\theta = \\pi – \\bar{\\varTheta}, \\ \\bar{\\theta} = \\pi – \\bar{\\varTheta}\\) \u3067\u3042\u308b\u304b\u3089\uff0c
\n$$\\cos (\\pi – \\bar{\\varTheta}) = \\frac{\\cos(\\pi – \\varTheta) -V}{1 – V\\cos(\\pi – \\varTheta)}$$
\n$$-\\cos \\bar{\\varTheta} = \\frac{-\\cos\\varTheta -V}{1 + V\\cos\\varTheta}$$
\n$$\\therefore\\ \\cos \\bar{\\varTheta} = \\frac{\\cos\\varTheta +V}{1 + V\\cos\\varTheta}$$<\/p>\n

\\(0 < \\varTheta < \\pi\\) \u3068\u3057\u3066 \\(\\bar{\\varTheta}\\) \u3068 \\(\\varTheta\\) \u306e\u5927\u5c0f\u95a2\u4fc2\u3092\u307f\u308b\u305f\u3081\u306b\uff0c\u5f15\u304d\u7b97\u3092\u884c\u3046\u3002
\n\\begin{eqnarray}
\n\\cos \\bar{\\varTheta} – \\cos\\varTheta &=& \\frac{\\cos\\varTheta +V – \\cos\\varTheta(1+V\\cos\\varTheta)}{1 + V\\cos\\varTheta} \\\\
\n&=& \\frac{V \\sin^2\\varTheta}{1 +V\\cos\\varTheta} > 0
\n\\end{eqnarray}
\n$$ \\therefore \\ \\cos \\bar{\\varTheta} > \\cos\\varTheta$$<\/p>\n

\\(0 < \\varTheta < \\pi\\) \u304b\u3089\u5165\u5c04\u3059\u308b\u5149\u306b\u3064\u3044\u3066\u306f\uff0c\u30b3\u30b5\u30a4\u30f3\u306f\u5358\u8abf\u6e1b\u5c11\u95a2\u6570\u306a\u306e\u3067\uff0c
\n$$ \\bar{\\varTheta} < \\varTheta$$ \u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u306b\u3068\u3063\u3066\u306f\uff0c\u5149\u306f\u9032\u884c\u65b9\u5411\u306b\u300c\u5bc4\u3063\u3066\u300d\u304f\u308b\u3088\u3046\u306b\u898b\u3048\u308b\u3002\u305f\u3068\u3048\u9759\u6b62\u89b3\u6e2c\u8005\u306b\u3068\u3063\u3066\u5149\u6e90\u304c\u81ea\u8eab\u306e\u307e\u308f\u308a360\u5ea6\u306b\u5747\u7b49\u306b\u5206\u5e03\u3057\u3066\u3044\u308b\u3068\u3057\u3066\u3082\uff0c\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u306b\u3068\u3063\u3066\u306f\uff0c\u305d\u306e\u9032\u884c\u65b9\u5411\u306b\u5149\u6e90\u304c\u5bc4\u3063\u3066\u304d\u3066\u96c6\u4e2d\u3059\u308b\u3088\u3046\u306b\u898b\u3048\u308b\u3002\u3053\u308c\u304c\uff08\u7279\u6b8a\u76f8\u5bfe\u8ad6\u7684\u52b9\u679c\u3068\u3057\u3066\u306e\uff09\u5149\u884c\u5dee<\/span>\u3067\u3042\u308b\u3002<\/strong><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

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