{"id":8461,"date":"2022-06-08T21:35:18","date_gmt":"2022-06-08T12:35:18","guid":{"rendered":"http:\/\/web.tohoku.ac.jp\/yusa\/?p=8461"},"modified":"2022-08-06T13:25:03","modified_gmt":"2022-08-06T04:25:03","slug":"physicsa","status":"publish","type":"post","link":"https:\/\/web.tohoku.ac.jp\/yusa\/index.php\/2022\/physicsa\/","title":{"rendered":"R4\u5e74\u5ea6\u7269\u7406\u5b66A"},"content":{"rendered":"\n

R4\u5e74\u5ea6\u7269\u7406\u5b66A\uff08\u306e\u524d\u534a\u90e8\uff09\u3067\u306f\u3001\u9ad8\u6821\u306e\u7269\u7406\u304b\u3089\u5927\u5b66\u306e\u7269\u7406\u3078\u3001\u5373\u3061\u5fae\u5206\u7a4d\u5206\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u304b\u3089\uff08\u9ad8\u6821\u3067\u306f\u500b\u5225\u306e\u6cd5\u5247\u3068\u3057\u3066\u7fd2\u3063\u3066\u3044\u305f\uff09\u6570\u591a\u304f\u306e\u6cd5\u5247\u304c\u5c0e\u51fa\u3055\u308c\u308b\u3053\u3068\u306e\u8aac\u660e\u3092\u4e3b\u3068\u3057\u3066\u884c\u3044\u307e\u3057\u305f\u3002\u307e\u305f\u3001\u7269\u7406\u73fe\u8c61\u3092\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u8a18\u8ff0\u3057\u3001\u89e3\u304f\u3001\u3068\u3044\u3046\u3053\u3068\u306e\u5fc5\u8981\u6027\u3068\u91cd\u8981\u6027\u3082\u3001\u305d\u308c\u306a\u308a\u306b\u8aac\u660e\u3057\u305f\u3064\u3082\u308a\u3067\u306f\u3042\u308a\u307e\u3059\u3002\u305f\u3060\u305d\u306e\u4e00\u65b9\u3067\u3001\u4ed6\u306e\u30af\u30e9\u30b9\u3068\u6bd4\u3079\u308b\u3068\u5177\u4f53\u7684\u306a\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u306b\u8cbb\u3084\u3057\u305f\u6642\u9593\u306f\u5c11\u306a\u304b\u3063\u305f\u3068\u3082\u601d\u3044\u307e\u3059\u3002\u671f\u672b\u30c6\u30b9\u30c8\u306b\u304a\u3044\u3066\u306f\u3044\u304f\u3064\u304b\u554f\u984c\u3092\u89e3\u3044\u3066\u3082\u3089\u308f\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093<\/span>1<\/sup><\/a><\/span>\u306e\u3067\u3001\u307e\u3042\u3053\u3053\u3089\u3078\u3093\u306f\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u3063\u3066\u304a\u3044\u3066\u306d<\/span>2<\/sup><\/a><\/span>\u3068\u3044\u3046\u610f\u56f3\u3067\u3001\u3044\u304f\u3064\u304b\u306e\u4f8b\u984c\u3092\u306e\u3063\u3051\u3066\u304a\u304d\u307e\u3059<\/span>3<\/sup><\/a><\/span>\u3002<\/p>\n\n\n\n

\u554f\u984c\uff11<\/h4>\n\n\n\n

\u3070\u306d\u306e\u7aef\u90e8\u306b\u8cea\u91cfm\u306e\u8cea\u70b9\u304c\u3042\u308b\u3002\u8cea\u70b9\u306b\u50cd\u304f\u529bF<\/span>\u306f\u3070\u306d\u306e\u4f38\u3073x<\/span>\u306e4\u4e57<\/span>4<\/sup><\/a><\/span>\u306b\u6bd4\u4f8b\u3057\u3001F=-kx^4<\/span>\u3068\u8868\u73fe\u3055\u308c\u308b\u3082\u306e\u3068\u3059\u308b\u3002\u3070\u306d\u3092\u3064\u308a\u5408\u3044\u306e\u4f4d\u7f6e\u304b\u3089\u9577\u3055a<\/span>\u5f15\u3063\u5f35\u3063\u3066\u9759\u304b\u306b\u624b\u3092\u96e2\u3057\u305f\u5834\u5408\u3001\u8cea\u70b9\u306e\u6700\u9ad8\u901f\u5ea6\u3092\u6c42\u3081\u3088\u3002<\/p>\n\n\n\n

[\u30dd\u30a4\u30f3\u30c8\/\u7565\u89e3]<\/p>\n\n\n\n

\u904b\u52d5\u65b9\u7a0b\u5f0f\u304b\u3089\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247\u304c\u3069\u306e\u3088\u3046\u306b\u5c0e\u304b\u308c\u308b\u306e\u304b\u3001\u307e\u305f\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u3068\u306f\u4f55\u304b\u3001\u3069\u306e\u69d8\u306b\u8868\u3055\u308c\u308b\u3079\u304d\u3082\u306e\u306a\u306e\u304b\u3001\u3092\u7406\u89e3\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3002\u554f\u984c\u305d\u306e\u3082\u306e\u306f\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247\u3092\u4f7f\u3063\u3066\u89e3\u304f\u306e\u304c\u697d\u3002\\frac{1}{2}m(\\frac{dx}{dt})^2+U=\u4e00\u5b9a<\/span>\u3068\u306a\u308b\u308f\u3051\u3060\u304c\u3001\u529b\u304c\u4f38\u3073\u306b\u6bd4\u4f8b\u3059\u308b\u308f\u3051\u3067\u306f\u306a\u3044\u306e\u3067U<\/span>\u306f\\frac{1}{2}kx^2<\/span>\u3068\u306f\u306a\u3089\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3002\u3082\u3061\u308d\u3093\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u3082\u3088\u3044\u3002<\/p>\n\n\n\n

\u554f\u984c\uff12<\/h4>\n\n\n\n

\u6642\u523b0\u306b\u304a\u3044\u3066\u3001\u8cea\u70b9m<\/span>\u3092\u6c34\u5e73\u9762\u306b\u5bfe\u3057\u3066\u89d2\u5ea6\\theta<\/span>\u3001\u521d\u901fv_0<\/span>\u3067\u5c04\u51fa\u3059\u308b\u3002\u8cea\u70b9\u306b\u5bfe\u3057\u3066\u306f\u925b\u76f4\u4e0b\u5411\u304d\u306b\u91cd\u529bmg<\/span>\u304c\u3001\u9032\u884c\u65b9\u5411\u9006\u5411\u304d\u306b\u901f\u3055\u306b\u6bd4\u4f8b\u3059\u308b\u7c98\u6027\u529b\uff08\u7a7a\u6c17\u306b\u3088\u308b\u62b5\u6297\uff09\u304c\u50cd\u304f\u3082\u306e\u3068\u3059\u308b\u3002\u6642\u523b0\u306b\u304a\u3051\u308b\u8cea\u70b9\u306e\u6c34\u5e73\u65b9\u5411\u4f4d\u7f6e\u3092x_0<\/span>\u3001\u925b\u76f4\u65b9\u5411\u4f4d\u7f6e\u3092y_0<\/span>\u3068\u3057\u305f\u3068\u304d\u3001\u6642\u523bt<\/span>\u306b\u304a\u3051\u308b\u8cea\u70b9\u306e\u4f4d\u7f6e\u3092t<\/span>\u306e\u95a2\u6570\u3068\u3057\u3066\u8868\u305b\u3002\u305f\u3060\u3057\u7c98\u6027\u4fc2\u6570\u3092\\gamma<\/span>\u3068\u3059\u308b\u3002<\/p>\n\n\n\n

[\u30dd\u30a4\u30f3\u30c8\/\u7565\u89e3]<\/p>\n\n\n\n

\u5fae\u5206\u65b9\u7a0b\u5f0f\u3068\u3057\u3066\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u305f\u3066\u3001\u305d\u308c\u3092\u89e3\u304f\u3053\u3068\u3067\u904b\u52d5\u306e\u69d8\u5b50\u3092\u8868\u73fe\u3059\u308b\u3001\u3068\u3044\u3046\u3053\u3068\u304c\u3067\u304d\u3066\u3044\u308b\u304b\u3002x<\/span>\u3001y<\/span>\u65b9\u5411\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f\u305d\u308c\u305e\u308cm\\frac{d^2x(t)}{dt^2}=-\\gamma\\frac{dx(t)}{dt}<\/span>\u3001
m\\frac{d^2y(t)}{dt^2}=-\\gamma\\frac{dy(t)}{dt}-mg<\/span>\u3053\u3044\u3064\u3089\u3092\u3001\u521d\u671f\u6761\u4ef6x(0)=x_0<\/span>\u3001\\frac{dx}{dt}|_{t=0}=v_0 \\cos\\theta<\/span>\u3001y(0)=y_0<\/span>\u3001\\frac{dx}{dt}|_{t=0}=v_0 \\sin\\theta<\/span>\u306e\u4e0b\u3067\u89e3\u3051\u3070\u3088\u3044\u3002\u7c98\u6027\u4fc2\u6570\\gamma<\/span>\u306e\u5024\u306b\u3088\u3063\u3066\u6c34\u5e73\u65b9\u5411\u5230\u9054\u8ddd\u96e2\u304c\u3069\u306e\u3088\u3046\u306b\u5909\u308f\u308b\u304b\u3068\u304b\u8272\u3005\u3068\u554f\u984c\u306f\u4f5c\u308c\u308b\u306e\u3067\u3001\u904b\u52d5\u306e\u69d8\u5b50\u3092\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u8a18\u8ff0\u3057\u3001\u305d\u308c\u3092\u89e3\u304f\u3068\u3044\u3046\u3053\u3068\u306b\u306f\u6163\u308c\u3066\u304a\u304f\u3053\u3068\u3002<\/p>\n\n\n\n

\u554f\u984c\uff13<\/h4>\n\n\n\n

\u7c97\u3044\u6c34\u5e73\u9762\u3092\u904b\u52d5\u3059\u308b\u8cea\u91cfm<\/span>\u306e\u7269\u4f53\u304c\u3070\u306d\u5b9a\u6570k<\/span>\u306e\u3070\u306d\u306b\u885d\u7a81\u3059\u308b\u3002\u7269\u4f53\u3068\u6c34\u5e73\u9762\u3068\u306e\u52d5\u6469\u64e6\u4fc2\u6570\u306f\\mu'<\/span>\u3067\u3042\u308b\u3002\u7269\u4f53\u304c\u3070\u306d\u306b\u63a5\u89e6\u3057\u59cb\u3081\u308b\u6642\u306e\u901f\u3055\u306fv_0<\/span>\u3067\u3042\u3063\u305f\u3002\u7269\u4f53\u304c\u3070\u306d\u306b\u63a5\u89e6\u3057\u305f\u77ac\u9593\u3092\u6642\u523b0\u3068\u3057\u3066\u3001\u3070\u306d\u306e\u7e2e\u307f\u3092\u6642\u523bt<\/span>\u306e\u95a2\u6570\u3068\u3057\u3066\u8868\u3057\u3001\u3070\u306d\u304c\u6700\u3082\u7e2e\u3080\u6642\u523b\u3068\u305d\u306e\u3068\u304d\u306e\u3070\u306d\u306e\u7e2e\u307f\u3092\u793a\u305b\u3002<\/p>\n\n\n\n

[\u30dd\u30a4\u30f3\u30c8\/\u7565\u89e3]<\/p>\n\n\n\n

\u554f\u984c\uff12\u306e\u3082\u3046\u3061\u3087\u3063\u3068\u8907\u96d1\u306a\u30d1\u30bf\u30fc\u30f3\u3002\u904b\u52d5\u65b9\u7a0b\u5f0fm\\frac{d^2x}{dt^2}=-kx-\\mu'mg<\/span>\u3092\u307e\u3058\u3081\u306b\u89e3\u304f\u3068\u3001\u5909\u6570\u5909\u5316\u6cd5\u3068\u304b\u3092\u304c\u308a\u304c\u308a\u4f7f\u3063\u3066\u3001x=v_0\\sqrt{\\frac{m}{k}}sin\\sqrt{\\frac{k}{m}}t+\\frac{\\mu'mg}{k}cos\\sqrt{\\frac{k}{m}}t-\\frac{\\mu'mg}{k}<\/span>\u3002\u3070\u306d\u304c\u6700\u3082\u7e2e\u3080\u306e\u306f\u901f\u3055\u304c0\u306b\u306a\u308b\u6642\u306a\u306e\u3067\u3001\\frac{dx}{dt}=0<\/span>\u3088\u308a\u3001v_0cos\\sqrt{\\frac{k}{m}}t-\\frac{\\mu'mg}{k}\\sqrt{\\frac{k}{m}}sin\\sqrt{\\frac{k}{m}}t=0<\/span>\u3002\u3088\u3063\u3066\u305d\u306e\u6642\u306e\u6642\u523bt'<\/span>\u306ftan\\sqrt{\\frac{k}{m}}t'=\\frac{v_0k}{\\mu'mg}\\sqrt{\\frac{m}{k}}<\/span>\u3092\u6e80\u8db3\u3059\u308b\u3002\u5373\u3061\u3001\u3070\u306d\u304c\u6700\u3082\u7e2e\u3080\u6642\u523b\u306ft'=arctan(\\frac{v_0k}{\\mu'mg}\\sqrt{\\frac{m}{k}})\/\\sqrt{k\/m}<\/span>\u3002\u3053\u306e\u3068\u304dcos\\sqrt{\\frac{k}{m}}t'=\\mu'mg\/\\{(\\mu'mg)^2+v_0^2km\\}^{1\/2}<\/span>\u3001sin\\sqrt{\\frac{k}{m}}t'=v_0k\\sqrt{m\/k}\/\\{(\\mu'mg)^2+v_0^2km\\}^{1\/2}<\/span>\u3002\u3053\u308c\u3092\u904b\u52d5\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001\u6700\u5927\u306e\u7e2e\u307f\u306f\\frac{1}{k}\\{-\\mu'mg+\\sqrt{(\\mu'mg)^2+v_0^2km}\\}<\/span>\u3002<\/p>\n\n\n\n

\u5c1a\u3001\u6559\u79d1\u66f8\u306e\u554f\u984c4.3-1\u3067\u554f\u308f\u308c\u3066\u3044\u308b\u3070\u306d\u304c\u6700\u5927\u3067\u3069\u308c\u304f\u3089\u3044\u7e2e\u3080\u304b\u306f\u3001\u305d\u308c\u306f\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u3070\u306d\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\uff0b\u6469\u64e6\u306b\u3088\u308b\u4ed5\u4e8b\u306b\u5909\u63db\u3055\u308c\u305f\u3068\u8003\u3048\u308c\u3070\u3001\\frac{1}{2}mv_0^2=\\frac{1}{2}kx^2+\\mu'mgx<\/span>\u3068\u3057\u3066\u3001\u3059\u3050\u306b\u6c42\u307e\u308b<\/span>5<\/sup><\/a><\/span>\u3002<\/p>\n\n\n\n

\u554f\u984c\uff14<\/h4>\n\n\n\n

\u8cea\u91cfm<\/span>\u306e\u8cea\u70b9\u306e\u904b\u52d5\u65b9\u7a0b\u5f0fm\\frac{d^2\\vec{r}}{dt^2}=\\vec{F}<\/span>\u304b\u3089\u8cea\u70b9\u306b\u50cd\u304f\u30c8\u30eb\u30af\u3068\u8cea\u70b9\u306e\u89d2\u904b\u52d5\u91cf\u306e\u95a2\u4fc2\u3092\u5c0e\u304d\u3001\u4e2d\u5fc3\u529b\u306e\u307f\u3092\u53d7\u3051\u3066\u904b\u52d5\u3059\u308b\u8cea\u70b9\u306f\u9762\u7a4d\u901f\u5ea6\u4e00\u5b9a\u3068\u306a\u308b\u3053\u3068\u3092\u793a\u305b\u3002\u5c1a\u3053\u3053\u3067\u9762\u7a4d\u901f\u5ea6\u3068\u306f\u8cea\u70b9\u3068\u529b\u306e\u4e2d\u5fc3\u3092\u7d50\u3076\u7dda\u5206\u304c\u5358\u4f4d\u6642\u9593\u3042\u305f\u308a\u306b\u6383\u904e\u3059\u308b\u9762\u7a4d\u306e\u3053\u3068\u3092\u3044\u3046\u3002<\/p>\n\n\n\n

[\u30dd\u30a4\u30f3\u30c8\/\u7565\u89e3]<\/p>\n\n\n\n

\u904b\u52d5\u65b9\u7a0b\u5f0f\u304b\u3089\u89d2\u904b\u52d5\u91cf\u306e\u5f0f\u3092\u5c0e\u51fa\u3067\u304d\u308b\u304b\uff08\u30d9\u30af\u30c8\u30eb\u306e\u5916\u7a4d\u306e\u6027\u8cea\u3092\u7406\u89e3\u3057\u3066\u3044\u308b\u304b\uff09\u3002<\/p>\n\n\n\n

\u554f\u984c\uff15<\/h4>\n\n\n\n

\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u539f\u70b9\u306b\u9759\u6b62\u3057\u3066\u304a\u308ax<\/span>\u8ef8\u306b\u5bfe\u3057\u3066\u89d2\u5ea6\\alpha<\/span>\u65b9\u5411\u306b\u91cd\u3055\u306e\u7121\u8996\u3067\u304d\u308b\u68d2\u3092\u6709\u3059\u308b\u8cea\u70b91\u3068\u3001y<\/span>\u8ef8\u306b\u5e73\u884c\u306b\u79fb\u52d5\u3059\u308b\u8cea\u70b92\u3092\u8003\u3048\u308b\u3002\u8cea\u70b92\u304c(lcos\\alpha, lsin\\alpha)<\/span>\u306b\u304a\u3044\u3066\u68d2\u306b\u885d\u7a81\u3057\u3001\u4ee5\u5f8c\u306f\u8cea\u70b91\u3001\u68d2\u3001\u8cea\u70b92\u304c\u4e00\u4f53\u3068\u306a\u3063\u3066\u904b\u52d5\u3059\u308b\u3082\u306e\u3068\u3059\u308b\u3002\u885d\u7a81\u524d\u5f8c\u3067\u8cea\u70b9\u306e\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u548c\u304c\\alpha<\/span>\u306b\u3088\u308a\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\u6c42\u3081\u3088\u3002\u305f\u3060\u3057\u8cea\u70b91\u3068\u8cea\u70b92\u306e\u8cea\u91cf\u3092\u305d\u308c\u305e\u308cm_1<\/span>\u3001m_2<\/span>\u3068\u3057\u3001\u8cea\u70b92\u306e\u885d\u7a81\u524d\u306e\u901f\u5ea6\u3092v_{2,0}<\/span>\u3068\u3059\u308b\u3002\uff08\u6559\u79d1\u66f86.5(3)\u306e\u554f\u984c\u3092\u5c11\u3057\u8a73\u3057\u304f\uff09<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

[\u30dd\u30a4\u30f3\u30c8\/\u7565\u89e3] <\/p>\n\n\n\n

\uff12\u8cea\u70b9\u306e\u885d\u7a81\u306b\u3064\u3044\u3066\u7406\u89e3\u3057\u3066\u3044\u308b\u304b\uff08\u9ad8\u6821\u306e\u7bc4\u56f2\u3060\u3051\u3067\u306f\u306a\u304f\u89d2\u904b\u52d5\u91cf\u4fdd\u5b58\u306e\u3068\u3053\u308d\u307e\u3067\uff09\u3002<\/p>\n\n\n\n

\u5916\u529b\u304c\u50cd\u3044\u3066\u3044\u306a\u3044\u306e\u3067\u3001\u7cfb\u306e\u904b\u52d5\u91cf\\vec{p}<\/span>\u3068\u89d2\u904b\u52d5\u91cf\\vec{L}<\/span>\u306f\u4fdd\u5b58\u3059\u308b\u3002<\/p>\n\n\n\n

\u885d\u7a81\u5f8c\u306e\u91cd\u5fc3\u306e\u904b\u52d5\u3092\u8003\u3048\u308b\u3002\u885d\u7a81\u524d\u306f\\vec{p}=m_1(0, 0)^T+m_2(0, v_{2,0})^T<\/span>\u3002\u3088\u3063\u3066\u885d\u7a81\u5f8c\u306e\u91cd\u5fc3\u306e\u901f\u5ea6\\vec{V}<\/span>\u306f(m_1+m_2)\\vec{V}=(0,m_2v_{2,0})^T<\/span>\u3088\u308a\\vec{V}=(0, m_2v_{2,0}\/(m_1+m_2))^T<\/span>\u3002\u885d\u7a81\u6642\u306e\u91cd\u5fc3\u306e\u4f4d\u7f6e\u306f(m_2lcos\\alpha\/(m_1+ m_2), m_2lsin\\alpha\/(m_1+m_2))<\/span>\u306a\u306e\u3067\u3001\u885d\u7a81\u304c\u6642\u523b0\u3060\u3068\u3059\u308b\u3068\u3001\u6642\u523bt<\/span>\u306b\u304a\u3051\u308b\u91cd\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\\vec{R}<\/span>\u306f\\vec{R}=\\frac{m_2}{m_1+m_2}(lcos\\alpha, lsin\\alpha+v_{2,0}t)^T<\/span>\u3002<\/p>\n\n\n\n

\u6b21\u306b\u91cd\u5fc3\u5468\u308a\u306e\u89d2\u904b\u52d5\u91cf\\vec{L}_0<\/span>\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001\\vec{L}_0=\\frac{m_1}{m_1+m_2}(lcos\\alpha, lsin\\alpha,0)^T\\times m_2(0, v_{2,0},0)^T<\/span>(\u91cd\u5fc3\u304b\u3089\u885d\u7a81\u70b9\u307e\u3067\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u00d7\u8cea\u70b92\u306e\u904b\u52d5\u91cf\u30d9\u30af\u30c8\u30eb\u3002xy\u5e73\u9762\u3067\u306e\u56de\u8ee2\u306e\u8868\u73fe\u306e\u305f\u3081\u306b\uff13\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066\u8868\u3057\u305f)\u3002\u8a08\u7b97\u9032\u3081\u3066\\vec{L}_0=(0, 0, \\frac{m_1m_2lcos\\alpha v_{2,0}}{m_1+m_2})^T<\/span>\u3002\u3088\u3063\u3066\u89d2\u901f\u5ea6\u4e00\u5b9a\u3067\u56de\u8ee2\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n\n\n\n

\u56de\u8ee2\u306e\u89d2\u901f\u5ea6\\omega<\/span>\u3092\u6c42\u3081\u308b\u3002\u91cd\u5fc3\u304b\u30892\u8cea\u70b9\u307e\u3067\u306e\u8ddd\u96e2\u306fl_1=\\frac{m_2}{m_1+m_2}l, l_2=\\frac{m_1}{m_1+m_2}l<\/span>\u3002\u3088\u3063\u3066\u3001\u91cd\u5fc3\u5468\u308a\u306e\u89d2\u904b\u52d5\u91cf\u306fm_1 l_1^2\\omega+m_2 l_2^2\\omega=\\frac{m_1m_2}{m_1+m_2}l^2\\omega^2<\/span>\u3068\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u308c\u304c\u4e0a\u3067\u5f97\u3089\u308c\u305f\\frac{m_1m_2lcos\\alpha}{m_1+m_2}<\/span>\u306b\u7b49\u3057\u3044\u306e\u3067\u3001\\omega=\\frac{lcos\\alpha v_{2,0}}{l^2}<\/span>\u3068\u306a\u308b\u3002<\/p>\n\n\n\n

\u7cfb\u306e\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u3010\u91cd\u5fc3\u306e\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u3011\uff0b\u30102\u8cea\u70b9\u306e\u63db\u7b97\u8cea\u91cf\u3092\u6709\u3059\u308b1\u8cea\u70b9\u304c2\u8cea\u70b9\u306e\u76f8\u5bfe\u904b\u52d5\u3068\u540c\u3058\u904b\u52d5\u3092\u3059\u308b\u3068\u304d\u306e\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u3011\u3067\u3082\u4e0e\u3048\u3089\u308c\u308b\u3002\u91cd\u5fc3\u306e\u904b\u52d5\u72b6\u614b\u306f\u885d\u7a81\u306e\u524d\u3068\u5f8c\u3067\u540c\u3058\u306a\u306e\u3067\u3001\uff12\u3064\u76ee\u306e\u3010\u3011\u306e\u5897\u6e1b\u306e\u307f\u3092\u8003\u3048\u308c\u3070\u3088\u3044\u3002\u885d\u7a81\u524d\u306f\u660e\u3089\u304b\u306b\\frac{1}{2}m_2v_{2,0}^2<\/span>\u3002\u885d\u7a81\u5f8c\u306f\u3001\u8cea\u70b91\u304b\u3089\u898b\u305f\u8cea\u70b92\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f(l_2cos\\omega t, l_2sin\\omega t)^T-(l_1 cos(\\omega t+\\pi), l_1 sin(\\omega t+\\pi))^T=(l_2+l_1)(cos\\omega t, sin\\omega t)^T=l(cos\\omega t, sin\\omega t)^T<\/span>\u306a\u306e\u3067\u3001\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\\frac{1}{2}m(l\\omega)^2=\\frac{1}{2}m\\frac{(lcos\\alpha)^2}{l^2}v_{2,0}^2<\/span>\u3002<\/p>\n\n\n\n

\u4ee5\u4e0a\u3088\u308a\u3001\u885d\u7a81\u5f8c\u306e\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u885d\u7a81\u524d\u306e(cos\\alpha)^2<\/span>\u500d\u306b\u306a\u308b\uff08cos\\alpha=1<\/span>\u306e\u5834\u5408\u3001\u885d\u7a81\u306e\u65b9\u5411\u3068\u52d5\u304d\u51fa\u3059\u65b9\u5411\u304c\u540c\u3058\u306a\u306e\u3067\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u30ed\u30b9\u304c\u306a\u3044\u3001\u3068\u3082\u307f\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u308b\uff09\u3002<\/p>\n\n\n\n

\u554f\u984c\uff16<\/h4>\n\n\n\n

\u554f\u984c\uff15\u306b\u304a\u3044\u3066\u8cea\u70b9\uff11\u304c\u539f\u70b9\u306b\u56fa\u5b9a\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u885d\u7a81\u5f8c\u306e\u904b\u52d5\u306f\u3069\u306e\u3088\u3046\u306b\u306a\u308b\u304b\u3002\uff08\u3053\u308c\u3082\u6559\u79d1\u66f86.5(3)\uff09 <\/p>\n\n\n\n

[\u30dd\u30a4\u30f3\u30c8\/\u7565\u89e3]<\/p>\n\n\n\n

\u307e\u305a\u5b9a\u6027\u7684\u306b\u8003\u3048\u3066\u307f\u308b\u3002\u8cea\u70b91\u304c\u52d5\u304b\u306a\u3044\u308f\u3051\u3060\u304b\u3089\u3001\u7247\u958b\u304d\u306e\u30c9\u30a2\u306b\u4f53\u5f53\u305f\u308a\u3057\u305f\u3088\u3046\u306a\u72b6\u614b\u306a\u308f\u3051\u306a\u306e\u3067\u3001\u8cea\u70b91\u3092\u4e2d\u5fc3\u306b\u3057\u3066\u56de\u8ee2\u3059\u308b\u3068\u601d\u308f\u308c\u308b<\/span>6<\/sup><\/a><\/span>\u3002<\/p>\n\n\n\n

\u3067\u3001\u5b9a\u91cf\u7684\u306b\u8b70\u8ad6\u3059\u308b\u305f\u3081\u306b\u306fm_1 \\gt\\gt m_2<\/span>\u306e\u72b6\u6cc1\u3092\u8003\u3048\u308c\u3070\u3088\u3044\u3002\\vec{R}=\\frac{m_2}{m_1+m_2}(a, lsin\\alpha+v_{2,0}t)^T\\fallingdotseq 0<\/span>\u306a\u306e\u3067\u3001\u91cd\u5fc3\u306e\u4f4d\u7f6e\u306f\u52d5\u304b\u306a\u3044\u3002\u307e\u305f\u3001m_1\\gt\\gt m_2<\/span>\u3088\u308a\u3001\u91cd\u5fc3\u306e\u4f4d\u7f6e\u306fm_1<\/span>\u306b\u4e00\u81f4\u3059\u308b\u3002\u89d2\u904b\u52d5\u91cf\u306f\\vec{L}=\\frac{m_1}{m_1+m_2}(lcos\\alpha, lsin\\alpha)^T \\times m_2 (0,v_{2,0})^T<\/span>\u30023\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3067\u66f8\u304f\u3068(0, 0, \\frac{m_1 m_2 a v_{2,0}}{m_1+m_2})^T \\fallingdotseq (0, 0, m_2av_{2,0})^T<\/span>\u3002\u3088\u3063\u3066\u89d2\u901f\u5ea6\\omega=\\frac{av_{2,0}}{l^2}<\/span>\u3067\u56de\u8ee2\u3059\u308b\u3002\u5c1a\u3053\u3053\u3067\u8cea\u70b92\u306e\u901f\u5ea6\u306fl\\omega=\\frac{av_{2,0}}{l}<\/span>\u3088\u308a\\vec{v}_2=\\frac{av_{2,0}}{l}(-sin\\alpha, cos\\alpha)^T<\/span>\u3068\u306a\u308a\u3001\u904b\u52d5\u91cf\u306f\u4fdd\u5b58\u3057\u3066\u3044\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3002<\/p>\n\n\n\n

\n","protected":false},"excerpt":{"rendered":"

R4\u5e74\u5ea6\u7269\u7406\u5b66A\uff08\u306e\u524d\u534a\u90e8\uff09\u3067\u306f\u3001\u9ad8\u6821\u306e\u7269\u7406\u304b\u3089\u5927\u5b66\u306e\u7269\u7406\u3078\u3001\u5373\u3061\u5fae\u5206\u7a4d\u5206\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u304b\u3089\uff08\u9ad8\u6821\u3067\u306f\u500b\u5225\u306e\u6cd5\u5247\u3068\u3057\u3066\u7fd2\u3063\u3066\u3044\u305f\uff09\u6570\u591a\u304f\u306e … <\/p>\n","protected":false},"author":1,"featured_media":8463,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[97],"tags":[],"class_list":["post-8461","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-lecture"],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/web.tohoku.ac.jp\/yusa\/wp-content\/uploads\/2022\/06\/physA_2022.png?fit=410%2C289&ssl=1","_links":{"self":[{"href":"https:\/\/web.tohoku.ac.jp\/yusa\/index.php\/wp-json\/wp\/v2\/posts\/8461","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/web.tohoku.ac.jp\/yusa\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/web.tohoku.ac.jp\/yusa\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/web.tohoku.ac.jp\/yusa\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/web.tohoku.ac.jp\/yusa\/index.php\/wp-json\/wp\/v2\/comments?post=8461"}],"version-history":[{"count":105,"href":"https:\/\/web.tohoku.ac.jp\/yusa\/index.php\/wp-json\/wp\/v2\/posts\/8461\/revisions"}],"predecessor-version":[{"id":8641,"href":"https:\/\/web.tohoku.ac.jp\/yusa\/index.php\/wp-json\/wp\/v2\/posts\/8461\/revisions\/8641"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/web.tohoku.ac.jp\/yusa\/index.php\/wp-json\/wp\/v2\/media\/8463"}],"wp:attachment":[{"href":"https:\/\/web.tohoku.ac.jp\/yusa\/index.php\/wp-json\/wp\/v2\/media?parent=8461"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/web.tohoku.ac.jp\/yusa\/index.php\/wp-json\/wp\/v2\/categories?post=8461"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/web.tohoku.ac.jp\/yusa\/index.php\/wp-json\/wp\/v2\/tags?post=8461"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}