{"id":105545,"date":"2024-01-29T05:47:49","date_gmt":"2024-01-29T05:47:49","guid":{"rendered":"https:\/\/science-hub.click\/%E7%A9%BA%E9%96%93%E5%86%85%E3%81%AE%E5%9B%9B%E5%85%83%E6%95%B0%E3%81%A8%E5%9B%9E%E8%BB%A2-%E5%AE%9A%E7%BE%A9\/"},"modified":"2024-01-29T05:47:49","modified_gmt":"2024-01-29T05:47:49","slug":"%E7%A9%BA%E9%96%93%E5%86%85%E3%81%AE%E5%9B%9B%E5%85%83%E6%95%B0%E3%81%A8%E5%9B%9E%E8%BB%A2-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=105545","title":{"rendered":"\u7a7a\u9593\u5185\u306e\u56db\u5143\u6570\u3068\u56de\u8ee2 &#8211; \u5b9a\u7fa9"},"content":{"rendered":"<div><div><h2>\u5c0e\u5165<\/h2><p>\u5358\u4f4d\u56db\u5143\u6570\u306f\u30013 \u6b21\u5143\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u5411\u304d\u3068\u56de\u8ee2\u3092\u8868\u3059\u4fbf\u5229\u306a\u6570\u5b66\u7684\u8868\u8a18\u6cd5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u30aa\u30a4\u30e9\u30fc\u89d2\u3068\u6bd4\u3079\u3066\u3001\u69cb\u6210\u304c\u7c21\u5358\u3067\u3001<span>\u30b8\u30f3\u30d0\u30eb\u306e\u30d6\u30ed\u30c3\u30ad\u30f3\u30b0<\/span>\u306e\u554f\u984c\u3092\u56de\u907f\u3067\u304d\u307e\u3059\u3002\u56de\u8ee2\u884c\u5217\u3068\u6bd4\u8f03\u3057\u3066\u3001\u6570\u5024\u7684\u306b\u5b89\u5b9a\u3057\u3066\u304a\u308a\u3001\u3088\u308a\u52b9\u7387\u7684\u3067\u3059\u3002\u30af\u30a9\u30fc\u30bf\u30cb\u30aa\u30f3\u306f\u3001<span><a href=\"https:\/\/science-hub.click\/?p=48530\">\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf \u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u30b9<\/a><\/span>\u3001\u30ed\u30dc\u30c3\u30c8\u5de5\u5b66\u3001<span><a href=\"https:\/\/science-hub.click\/?p=35368\">\u30ca\u30d3\u30b2\u30fc\u30b7\u30e7\u30f3<\/a><\/span>\u3001<span><a href=\"https:\/\/science-hub.click\/?p=13242\">\u5206\u5b50\u52d5\u529b\u5b66<\/a><\/span>\u3001<span><a href=\"https:\/\/science-hub.click\/?p=18792\">\u885b\u661f<\/a><\/span><span><a href=\"https:\/\/science-hub.click\/?p=61925\">\u5b87\u5b99\u529b\u5b66<\/a><\/span>\u306a\u3069\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306b\u63a1\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p><h2>\u30af\u30a9\u30fc\u30bf\u30cb\u30aa\u30f3\u3092\u4f7f\u7528\u3057\u305f\u56de\u8ee2\u64cd\u4f5c<\/h2><p>\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u4f7f\u7528\u3055\u308c\u308b\u30d7\u30ed\u30d1\u30c6\u30a3\u306e\u975e\u5e38\u306b\u53b3\u5bc6\u306a\u8aac\u660e\u306f\u3001Altmann \u306b\u3088\u3063\u3066<span>\u63d0\u4f9b\u3055\u308c\u3066\u3044\u307e\u3059<\/span>\u3002<\/p><h3><span>\u56de\u8ee2\u306e\u8d85\u7403\u9762<\/span><\/h3><h4><span>\u56de\u8ee2\u7a7a\u9593\u306e\u30a2\u30a4\u30c7\u30a2\u3092\u5f97\u308b<\/span><\/h4><p>\u5358\u4f4d\u56db\u5143\u6570\u306f\u3001\u6bd4\u8f03\u7684\u5358\u7d14\u306a\u65b9\u6cd5\u3067 3<span><a href=\"https:\/\/science-hub.click\/?p=84871\">\u6b21\u5143<\/a><\/span>\u306e\u56de\u8ee2\u306e\u6570\u5b66\u7684\u7a7a\u9593\u3092\u8868\u3057\u307e\u3059\u3002\u307e\u305a\u56de\u8ee2\u7a7a\u9593\u305d\u306e\u3082\u306e\u306b\u3064\u3044\u3066\u76f4\u611f\u7684\u306b\u7406\u89e3\u3059\u308b\u3053\u3068\u3067\u3001\u56de\u8ee2\u3068\u56db\u5143\u6570\u306e<span><a href=\"https:\/\/science-hub.click\/?p=1290\">\u5bfe\u5fdc<\/a><\/span>\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p><div><div> <figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/Q1CQK6SxKJw\/0.jpg\" style=\"width:100%;\"\/><\/figure><div>\u56de\u8ee2\u7a7a\u9593\u5185\u306e\u7570\u306a\u308b\u89d2\u5ea6\u3068\u7570\u306a\u308b\u8ef8\u306e 2 \u3064\u306e\u56de\u8ee2\u3002<span><a href=\"https:\/\/science-hub.click\/?p=66129\">\u30d9\u30af\u30c8\u30eb<\/a><\/span>\u306e<span><a href=\"https:\/\/science-hub.click\/?p=1846\">\u30ce\u30eb\u30e0<\/a><\/span>\u306f\u56de\u8ee2\u306e<span><a href=\"https:\/\/science-hub.click\/?p=63935\">\u632f\u5e45<\/a><\/span>\u306b\u95a2\u4fc2\u3057\u307e\u3059\u3002<\/div><\/div><\/div><p> 3 \u6b21\u5143\u3067\u306e\u5404\u56de\u8ee2\u306b\u306f\u3001\u7279\u5b9a\u306e\u8ef8\u3092<span><a href=\"https:\/\/science-hub.click\/?p=45508\">\u4e2d\u5fc3\u3068\u3057\u305f<\/a><\/span>\u7279\u5b9a\u306e<span><a href=\"https:\/\/science-hub.click\/?p=108487\">\u89d2\u5ea6<\/a><\/span>\u306e\u56de\u8ee2\u304c\u542b\u307e\u308c\u307e\u3059\u3002\u89d2\u5ea6\u304c 0 \u306e\u5834\u5408\u3001\u8ef8\u306f\u91cd\u8981\u3067\u306f\u306a\u3044\u305f\u3081\u3001 <span><a href=\"https:\/\/science-hub.click\/?p=5522\">0<\/a><\/span>\u5ea6\u306e\u56de\u8ee2\u306f\u56de\u8ee2\u7a7a\u9593\u5185\u306e\u5358\u7d14\u306a<span><a href=\"https:\/\/science-hub.click\/?p=43578\">\u70b9<\/a><\/span>\u306b\u306a\u308a\u307e\u3059 (\u3053\u308c\u304c\u6052\u7b49\u56de\u8ee2\u3067\u3059)\u3002\u89d2\u5ea6\u304c\u5c0f\u3055\u3044\u304c\u30bc\u30ed\u3067\u306f\u306a\u3044\u5834\u5408\u3001\u53ef\u80fd\u306a\u56de\u8ee2\u306e<span><a href=\"https:\/\/science-hub.click\/?p=57227\">\u30bb\u30c3\u30c8\u306f<\/a><\/span>\u56de\u8ee2\u30a2\u30a4\u30c7\u30f3\u30c6\u30a3\u30c6\u30a3\u3092\u56f2\u3080\u5c0f\u3055\u306a<span><a href=\"https:\/\/science-hub.click\/?p=100659\">\u7403<\/a><\/span>\u3067\u3042\u308a\u3001\u7403\u306e\u5404\u70b9\u306f\u7279\u5b9a\u306e\u65b9\u5411\u3092\u6307\u3059\u8ef8\u3092\u8868\u3057\u307e\u3059 (\u5929\u7403\u3068\u6bd4\u8f03\u3057\u3066\u304f\u3060\u3055\u3044)\u3002\u3088\u308a\u5927\u304d\u306a\u89d2\u5ea6\u306e\u56de\u8ee2\u306f\u5f90\u3005\u306b\u6052\u7b49\u56de\u8ee2\u304b\u3089\u9060\u3056\u304b\u308a\u3001\u534a\u5f84\u304c\u5897\u52a0\u3059\u308b\u540c\u5fc3\u7403\u3068\u3057\u3066\u60f3\u50cf\u3067\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6052\u7b49\u56de\u8ee2\u306e<span><a href=\"https:\/\/science-hub.click\/?p=30606\">\u8fd1\u508d<\/a><\/span>\u3067\u306f\u3001\u56de\u8ee2\u306e\u62bd\u8c61\u7a7a\u9593\u306f\u901a\u5e38\u306e 3 \u6b21\u5143\u7a7a\u9593\u306b\u4f3c\u3066\u3044\u307e\u3059 (\u7570\u306a\u308b\u534a\u5f84\u306e\u7403\u3067\u56f2\u307e\u308c\u305f\u4e2d\u5fc3\u70b9\u3068\u3057\u3066\u898b\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u56de\u8ee2\u89d2\u5ea6\u304c 180\u00b0 \u3092\u8d85\u3048\u308b\u3068\u3001\u985e\u4f3c\u306f\u305d\u3053\u3067\u7d42\u4e86\u3057\u307e\u3059)\u3002 \u3001\u7570\u306a\u308b\u8ef8\u306b\u6cbf\u3063\u305f\u56de\u8ee2\u306f\u767a\u6563\u3092\u505c\u6b62\u3057\u3001\u518d\u3073\u4e92\u3044\u306b\u985e\u4f3c\u3057\u59cb\u3081\u3001\u6700\u7d42\u7684\u306b\u89d2\u5ea6\u304c 360\u00b0 \u306b\u9054\u3059\u308b\u3068\u540c\u4e00 (\u540c\u4e00\u56de\u8ee2\u3068\u7b49\u3057\u304f\u306a\u308a\u307e\u3059) \u306b\u306a\u308a\u307e\u3059\u3002<\/p><div><div> <figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/4QToYqFdgdE\/0.jpg\" style=\"width:100%;\"\/><\/figure><div>\u6c34\u5e73\u8ef8 ( <i>xy<\/i>\u5e73\u9762\u306b\u542b\u307e\u308c\u308b\u8ef8) \u306e\u56de\u8ee2\u306e\u8d85\u7403\u9762\u3002<\/div><\/div><\/div><p>\u540c\u69d8\u306e\u73fe\u8c61\u304c\u7403\u306e<span><a href=\"https:\/\/science-hub.click\/?p=48998\">\u8868\u9762<\/a><\/span>\u3067\u3082\u89b3\u5bdf\u3055\u308c\u307e\u3059\u3002<span><a href=\"https:\/\/science-hub.click\/?p=33010\">\u5317\u6975<\/a><\/span>\u306b\u7acb\u3063\u3066\u3001\u305d\u3053\u304b\u3089\u3044\u304f\u3064\u304b\u306e\u65b9\u5411\u306b\u76f4\u7dda\uff08\u5b9f\u969b\u306b\u306f\u5b50\u5348\u7dda\uff09\u3092\u5f15\u304f\u3068\u3001\u305d\u308c\u3089\u306f\u767a\u6563\u3057\u3001<span><a href=\"https:\/\/science-hub.click\/?p=24872\">\u5357\u6975<\/a><\/span>\u3067\u518d\u3073\u53ce\u675f\u3057\u307e\u3059\u3002<span><a href=\"https:\/\/science-hub.click\/?p=73189\">\u5317\u6975<\/a><\/span>\u306e\u5468\u308a\u306b\u63cf\u304b\u308c\u305f\u534a\u5f84\u304c\u5897\u52a0\u3059\u308b\u540c\u5fc3\u5186 (\u5e73\u884c\u7dda) \u306f\u3001\u6975\u9593\u306e\u8ddd\u96e2\u304c\u30ab\u30d0\u30fc\u3055\u308c\u308b\u3068\u3001\u6700\u7d42\u7684\u306b\u306f<span><a href=\"https:\/\/science-hub.click\/?p=80407\">\u5357\u6975<\/a><\/span>\u306e\u70b9\u306b\u5d29\u58ca\u3057\u307e\u3059\u3002\u79c1\u305f\u3061\u306f\u3001\u6975\u304b\u3089\u306e\u3055\u307e\u3056\u307e\u306a\u65b9\u5411 (\u3064\u307e\u308a\u3001\u3055\u307e\u3056\u307e\u306a\u7d4c\u7dda) \u3092\u3055\u307e\u3056\u307e\u306a\u56de\u8ee2<i>\u8ef8<\/i>\u306b\u3001\u305d\u3057\u3066\u5317\u6975\u307e\u3067\u306e\u3055\u307e\u3056\u307e\u306a\u8ddd\u96e2\u3092\u3055\u307e\u3056\u307e\u306a<i>\u89d2\u5ea6<\/i>\u306b\u540c\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u56de\u8ee2\u7a7a\u9593\u306e\u985e\u4f3c\u6027\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u7403\u306e\u8868\u9762\u306f 2 \u6b21\u5143\u3067\u3059\u304c\u3001\u56de\u8ee2\u8ef8\u306f\u3059\u3067\u306b 3 \u6b21\u5143\u3092\u4f7f\u7528\u3057\u3066\u3044\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u56de\u8ee2\u7a7a\u9593\u306f\u8d85\u7403\u3001\u3064\u307e\u308a 4 \u6b21\u5143\u306e\u7403\u306b\u3088\u3063\u3066\u30e2\u30c7\u30eb\u5316\u3055\u308c\u307e\u3059\u3002<span><a href=\"https:\/\/science-hub.click\/?p=69721\">\u5186\u304c<\/a><\/span>\u7403\u306e\u4e00\u90e8\u3067\u3042\u308b\u306e\u3068\u540c\u3058\u3088\u3046\u306b\u3001\u901a\u5e38\u306e\u7403\u3092\u8d85\u7403\u306e\u4e00\u90e8\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001 <i>xy<\/i>\u5e73\u9762\u5185\u306e\u8ef8\u306e\u56de\u8ee2\u306e\u307f\u3092\u8868\u3059\u30bb\u30af\u30b7\u30e7\u30f3\u3092\u53d6\u5f97\u3067\u304d\u307e\u3059 (\u53cd\u5bfe\u306e\u56f3\u3092\u53c2\u7167)\u3002\u56de\u8ee2\u89d2\u5ea6\u304c\u5317\u6975\u3068\u306e<span>\u7def\u5ea6<\/span>\u306e\u5dee\u306e<i>2 \u500d<\/i>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u5b9f\u969b\u3001\u8d64\u9053\u4e0a\u306e\u70b9\u306f 90 \u5ea6\u3067\u306f\u306a\u304f 180 \u5ea6\u306e\u56de\u8ee2\u3092\u8868\u3057\u3001\u5357\u6975\u306f 360 \u5ea6\u306e\u56de\u8ee2\u3092\u8868\u3057\u307e\u3059\u3002 180\u00b0\u306e\u534a\u56de\u8ee2\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p><p>\u5317\u6975\u3068\u5357\u6975\u306f\u540c\u3058\u56de\u8ee2\u3092\u8868\u3057\u3001\u5b9f\u969b\u3001\u3053\u308c\u306f\u4e92\u3044\u306e\u5bfe\u8e60\u70b9\u306b\u3042\u308b\u70b9\u306e\u4efb\u610f\u306e<span><a href=\"https:\/\/science-hub.click\/?p=62815\">\u30da\u30a2<\/a><\/span>\u306b\u5f53\u3066\u306f\u307e\u308a\u307e\u3059\u3002\u70b9\u304c\u30d9\u30af\u30c8\u30eb\u306b\u3088\u3063\u3066\u65b9\u5411\u4ed8\u3051\u3089\u308c\u305f\u8ef8\u306e\u5468\u308a\u306e\u89d2\u5ea6<span>\u03b1<\/span>\u306e\u56de\u8ee2\u306b\u5bfe\u5fdc\u3059\u308b\u5834\u5408<div class=\"math-formual notranslate\">$$ {\\vec{v}} $$<\/div> \u3001\u4ed6\u306e\u70b9\u306f\u89d2\u5ea6\u56de\u8ee2\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {360^\\circ &#8211; \\alpha} $$<\/div>\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u3092\u5411\u3044\u305f\u8ef8\u306e\u5468\u308a<div class=\"math-formual notranslate\">$$ {- \\vec{v}} $$<\/div> \u3002\u5b9f\u969b\u3001\u56de\u8ee2\u7a7a\u9593\u306f\u8d85\u7403\u305d\u306e\u3082\u306e\u3067\u306f\u306a\u304f\u3001\u4e92\u3044\u306e\u5bfe\u8e60\u70b9\u306b\u3042\u308b\u70b9\u3092\u8b58\u5225\u3059\u308b\u8d85\u7403\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u5358\u7d14\u5316\u306e\u305f\u3081\u306b\u3001\u305f\u3068\u3048\u534a\u5206\u304c\u5197\u9577 (\u4e8c\u91cd\u30ab\u30d0\u30fc) \u3067\u3042\u3063\u3066\u3082\u3001\u56de\u8ee2\u3092 4 \u6b21\u5143\u7403\u4e0a\u306e\u70b9\u3068\u3057\u3066\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p><h4><span>\u56de\u8ee2\u30b9\u30da\u30fc\u30b9\u3092\u69cb\u6210\u3059\u308b<\/span><\/h4><p>\u7def\u5ea6\u3068<span>\u7d4c\u5ea6<\/span>\u306a\u3069\u306e 2 \u3064\u306e\u5ea7\u6a19\u3092\u4f7f\u7528\u3057\u3066\u7403\u306e\u8868\u9762\u3092\u30d1\u30e9\u30e1\u30fc\u30bf\u5316\u3067\u304d\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u5317\u6975\u3068\u5357\u6975\u3067\u306f\u3001\u7403\u4e0a\u306e\u4ed6\u306e\u70b9\u3068\u672c\u8cea\u7684\u306b\u5909\u308f\u3089\u306a\u3044\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u7def\u5ea6\u3068\u7d4c\u5ea6\u306e\u52d5\u4f5c\u304c\u60aa\u304f\u306a\u308a\u307e\u3059 (\u52a3\u5316\u3057\u3066\u3044\u307e\u3059)\u3002\u5317\u6975\u3068\u5357\u6975 (\u7def\u5ea6 +90\u00b0 \u3068 -90\u00b0) \u3067\u306f\u3001\u7d4c\u5ea6\u306f<span><a href=\"https:\/\/science-hub.click\/?p=81037\">\u610f\u5473\u3092<\/a><\/span>\u5931\u3044\u307e\u3059\u3002<\/p><p> 2 \u3064\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6301\u3064<span><a href=\"https:\/\/science-hub.click\/?p=64577\">\u5ea7\u6a19\u7cfb\u306f<\/a><\/span>\u3053\u306e\u7e2e\u9000\u3092\u56de\u907f\u3067\u304d\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059 (\u3053\u308c\u306f\u30d8\u30a2\u30ea\u30fc \u30dc\u30fc\u30eb<span>\u5b9a\u7406<\/span>\u3067\u3059)\u3002\u3053\u306e\u3088\u3046\u306a\u554f\u984c\u306f\u3001\u7403\u3092 3 \u6b21\u5143\u7a7a\u9593\u306b\u57cb\u3081\u8fbc\u307f\u30013 \u3064\u306e <span><a href=\"https:\/\/science-hub.click\/?p=34348\">\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19<\/a><\/span>(\u3053\u3053\u3067\u306f<i>w<\/i> \u3001 <i>x<\/i> \u3001 <i>y<\/i> ) \u3092\u4f7f\u7528\u3057\u3066\u30d1\u30e9\u30e1\u30fc\u30bf\u5316\u3057\u3001\u5317\u6975\u3092 ( <i>w<\/i> , <i>x<\/i> , <i>y<\/i> ) = (1, 0, 0)\u3001\u5357\u6975\u306f ( <i>w<\/i> , <i>x<\/i> , <i>y<\/i> ) = (\u22121, 0, 0) \u306b\u3042\u308a\u3001\u8d64\u9053\u306f\u65b9\u7a0b\u5f0f<i>w<\/i> = 0 \u304a\u3088\u3073<i>x<\/i> <sup>2<\/sup> + <i>y<\/i> <sup>2<\/sup> = 1 \u306e\u5186\u306b\u306a\u308a\u307e\u3059\u3002\u7403\u4e0a\u306e\u70b9\u306f\u6b21\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3057\u307e\u3059\u3002\u5236\u7d04<i>w<\/i> <sup>2<\/sup> + <i>x<\/i> <sup>2<\/sup> + <i>y<\/i> <sup>2<\/sup> = 1 \u306a\u306e\u3067\u3001\u5ea7\u6a19\u306f 3 \u3064\u3042\u308a\u307e\u3059\u304c\u3001\u81ea\u7531\u5ea6\u306f\u5e38\u306b 2 \u306b\u306a\u308a\u307e\u3059\u3002\u7403\u306e\u70b9 ( <i>w<\/i> \u3001 <i>x<\/i> \u3001 <i>y<\/i> ) \u306f\u3001\u30d9\u30af\u30c8\u30eb\u306b\u3088\u3063\u3066\u65b9\u5411\u4ed8\u3051\u3089\u308c\u305f<span><a href=\"https:\/\/science-hub.click\/?p=4986\">\u6c34\u5e73<\/a><\/span>\u8ef8\u306e\u5468\u308a\u306e\u901a\u5e38\u7a7a\u9593\u306e\u56de\u8ee2\u3092\u8868\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\vec{v}\\begin{pmatrix}x\\\\y\\\\0\\end{pmatrix}} $$<\/div>\u305d\u3057\u3066\u30b3\u30fc\u30ca\u30fc<div class=\"math-formual notranslate\">$$ {\\alpha= 2 \\cos^{-1} w = 2 \\sin^{-1} \\sqrt{x^2 + y^2}} $$<\/div> \u3002<\/p><p>\u540c\u69d8\u306b\u30013 \u6b21\u5143\u7a7a\u9593\u306e\u56de\u8ee2\u7a7a\u9593\u3092\u8a18\u8ff0\u3059\u308b\u8d85\u7403\u306f 3 \u3064\u306e\u89d2\u5ea6 (\u30aa\u30a4\u30e9\u30fc\u89d2) \u3092\u4f7f\u7528\u3057\u3066\u30d1\u30e9\u30e1\u30fc\u30bf\u5316\u3067\u304d\u307e\u3059\u304c\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e<span><a href=\"https:\/\/science-hub.click\/?p=95765\">\u30d1\u30e9\u30e1\u30fc\u30bf<\/a><\/span><span><a href=\"https:\/\/science-hub.click\/?p=60199\">\u5316\u306f<\/a><\/span>\u8d85\u7403\u306e\u7279\u5b9a\u306e\u70b9\u3067\u7e2e\u9000\u3057\u3001\u6b21\u306e\u554f\u984c\u304c\u767a\u751f\u3057\u307e\u3059\u3002\u30b8\u30f3\u30d0\u30eb\u306e\u30d6\u30ed\u30c3\u30af\u3002\u3053\u308c\u306f\u30014 \u3064\u306e\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u5ea7\u6a19<i>w<\/i> \u3001 <i>x<\/i> \u3001 <i>y<\/i> \u3001 <i>z<\/i> ( <i>w<\/i> <sup>2<\/sup> + <i>x<\/i> <sup>2<\/sup> + <i>y<\/i> <sup>2<\/sup> + <i>z<\/i> <sup>2<\/sup> = 1) \u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u56de\u907f\u3067\u304d\u307e\u3059\u3002\u5ea7\u6a19\u70b9 ( <i>w<\/i> \u3001 <i>x<\/i> \u3001 <i>y<\/i> \u3001 <i>z<\/i> ) \u306f\u3001\u8ef8\u306e\u5468\u308a\u306e\u56de\u8ee2\u3092\u8868\u3057\u307e\u3059\u3002\u30d9\u30af\u30c8\u30eb\u306b\u3088\u3063\u3066\u5c0e\u304b\u308c\u308b<div class=\"math-formual notranslate\">$$ {\\vec{v}\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}} $$<\/div>\u305d\u3057\u3066\u30b3\u30fc\u30ca\u30fc<div class=\"math-formual notranslate\">$$ {\\alpha = 2 \\cos^{-1} w = 2 \\sin^{-1} \\sqrt{x^2+y^2+z^2}.} $$<\/div><\/p><h3><span>\u56de\u8ee2\u304b\u3089\u56db\u5143\u6570\u3078<\/span><\/h3><h4><span>\u30af\u30a9\u30fc\u30bf\u30cb\u30aa\u30f3\u306e\u6982\u8981<\/span><\/h4><p><span><a href=\"https:\/\/science-hub.click\/?p=26454\">\u4ee3\u6570<\/a><\/span>\u306e\u901a\u5e38\u306e\u898f\u5247\u306b\u6e96\u62e0\u3057\u3001\u3055\u3089\u306b\u898f\u5247<b>i<\/b> <sup>2<\/sup> = \u22121 \u306b\u5f93\u3046\u62bd\u8c61\u8a18\u53f7<b>i \u3092<\/b>\u5c0e\u5165\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u8907\u7d20\u6570\u3092\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u8907\u7d20\u6570\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306e\u3059\u3079\u3066\u306e\u30eb\u30fc\u30eb\u3092\u518d\u73fe\u3059\u308b\u306b\u306f\u5341\u5206\u3067\u3059\u3002\u305f\u3068\u3048\u3070\u3001 <div class=\"math-formual notranslate\">$$ {(a + b \\mathbf{i}) (c + d \\mathbf{i}) = a c + a d \\mathbf{i} + b \\mathbf{i} c + b \\mathbf{i} d \\mathbf{i} = a c + a d \\mathbf{i} + b c \\mathbf{i} + b d \\mathbf{i}^2 = (a c &#8211; b d) + (b c + a d) \\mathbf{i}} $$<\/div> \u3002<\/p><p>\u540c\u69d8\u306b\u3001\u56db\u5143\u6570\u306f\u3001\u898f\u5247<b>i<\/b> <sup>2<\/sup> = <b>j<\/b> <sup>2<\/sup> = <b>k<\/b> <sup>2<\/sup> = <b>ijk<\/b> = \u22121 \u3068\u3001<span><a href=\"https:\/\/science-hub.click\/?p=57404\">\u4e57\u7b97<\/a><\/span>\u306e\u53ef\u63db\u6027<i>\u3092\u9664\u304f<\/i>\u901a\u5e38\u306e\u4ee3\u6570\u898f\u5247\u3092\u6e80\u305f\u3059\u62bd\u8c61\u8a18\u53f7<b>i<\/b> \u3001 <b>j<\/b> \u3001 <b>k \u3092<\/b>\u5c0e\u5165\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3067\u304d\u307e\u3059 (\u3088\u304f\u77e5\u3089\u308c\u305f\u4f8b\u3067\u3059)\u3002\u975e\u53ef\u63db\u4e57\u7b97\u306f\u884c\u5217\u4e57\u7b97\u3067\u3059)\u3002\u3059\u3079\u3066\u306e\u8a08\u7b97\u30eb\u30fc\u30eb\u306f\u3053\u308c\u3089\u306e\u5b9a\u7fa9\u304b\u3089\u751f\u3058\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u6b21\u306e\u3088\u3046\u306b\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059<div class=\"math-formual notranslate\">$$ {(a + b\\mathbf{i} + c\\mathbf{j} + d\\mathbf{k}) (e + f\\mathbf{i} + g\\mathbf{j} + h\\mathbf{k}) = (ae &#8211; bf &#8211; cg &#8211; dh) + (af + be + ch &#8211; dg) \\mathbf{i} + (ag + ce + df &#8211; bh) \\mathbf{j} + (ah + de + bg &#8211; cf) \\mathbf{k}} $$<\/div> \u3002<\/p><p>\u865a\u6570\u90e8<div class=\"math-formual notranslate\">$$ {b\\mathbf{i} + c\\mathbf{j} + d\\mathbf{k}} $$<\/div>\u30af\u30a9\u30fc\u30bf\u30cb\u30aa\u30f3\u306e \u306f\u30d9\u30af\u30c8\u30eb\u306e\u3088\u3046\u306b\u52d5\u4f5c\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\vec{v}\\begin{pmatrix}b\\\\c\\\\d\\end{pmatrix}} $$<\/div> 3 \u6b21\u5143\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e \u3067\u3042\u308a\u3001\u5b9f\u6570\u90e8\u306f\u6b21\u306e<span><a href=\"https:\/\/science-hub.click\/?p=39965\">\u30b9\u30ab\u30e9\u30fc<\/a><\/span>\u3092<i>\u6301\u3061\u307e\u3059<\/i>\u3002 <div class=\"math-formual notranslate\">$$ {\\mathbb{R}} $$<\/div> \u3002\u30af\u30a9\u30fc\u30bf\u30cb\u30aa\u30f3\u3092\u30b8\u30aa\u30e1\u30c8\u30ea\u3067\u4f7f\u7528\u3059\u308b\u5834\u5408\u3001<i>\u30b9\u30ab\u30e9\u30fc\u3068\u30d9\u30af\u30c8\u30eb<\/i>\u3068\u3057\u3066\u5b9a\u7fa9\u3059\u308b\u3068\u4fbf\u5229\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {a + b\\mathbf{i} + c\\mathbf{j} + d\\mathbf{k} = a + \\vec{v}} $$<\/div> \u3002<\/p><p>\u5b66\u6821\u3067\u30d9\u30af\u30c8\u30eb\u3092\u52c9\u5f37\u3057\u305f\u4eba\u306f\u3001<i>\u30d9\u30af\u30c8\u30eb<\/i>\u306b<i>\u6570\u5024<\/i>\u3092\u52a0\u7b97\u3059\u308b\u3053\u3068\u3001\u307e\u305f\u306f 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092<i>\u639b\u3051\u5408\u308f\u305b\u308b<\/i>\u3053\u3068\u304c\u5947\u5999\u306b\u611f\u3058\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u306a\u305c\u306a\u3089\u3001\u3053\u308c\u3089\u306e\u6f14\u7b97\u306f\u901a\u5e38\u306f\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3089\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u3053\u308c\u304c\u56db\u5143\u6570\u306e\u5b9f\u90e8\u3068\u865a\u90e8\u306e\u5358\u306a\u308b\u8868\u8a18\u3067\u3042\u308b\u3053\u3068\u3092\u899a\u3048\u3066\u304a\u304f\u3068\u3001\u3088\u308a\u6b63\u5f53\u306a\u3082\u306e\u306b\u306a\u308a\u307e\u3059\u3002<\/p><p>\u30af\u30a9\u30fc\u30bf\u30cb\u30aa\u30f3\u306e\u4e57\u7b97\u306f\u3001<span><a href=\"https:\/\/science-hub.click\/?p=58959\">\u30d9\u30af\u30c8\u30eb\u7a4d<\/a><\/span>\u3068\u30d9\u30af\u30c8\u30eb\u306e<span><a href=\"https:\/\/science-hub.click\/?p=69519\">\u5185\u7a4d<\/a><\/span>(\u5b9f\u969b\u306b\u306f\u6700\u521d\u306f\u30af\u30a9\u30fc\u30bf\u30cb\u30aa\u30f3\u304b\u3089\u30a4\u30f3\u30b9\u30d4\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u5f97\u305f\u3082\u306e) \u306e\u73fe\u4ee3\u8a9e\u3067\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u30eb\u30fc\u30eb<b>i<\/b> <sup>2<\/sup> = <b>j<\/b> <sup>2<\/sup> = <b>k<\/b> <sup>2<\/sup> = <b>ijk<\/b> = \u22121 \u306e\u4ee3\u308f\u308a\u306b\u30012 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u4e57\u7b97\u306e\u30eb\u30fc\u30eb\u304c\u3042\u308a\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\vec{v} \\vec{w} = \\vec{v} \\wedge \\vec{w} &#8211; \\vec{v} \\cdot \\vec{w}} $$<\/div> \u3001 \u307e\u305f\u306f \uff1a <\/p><ul><li><div class=\"math-formual notranslate\">$$ {\\vec{v} \\vec{w}} $$<\/div>\u30d9\u30af\u30c8\u30eb\u306e\u4e57\u7b97\u3067\u3059\u3002 <\/li><li><div class=\"math-formual notranslate\">$$ {\\vec{v} \\wedge \\vec{w}} $$<\/div>\u306f\u30d9\u30af\u30c8\u30eb\u7a4d (\u30d9\u30af\u30c8\u30eb)\u3001 <\/li><li><div class=\"math-formual notranslate\">$$ {\\vec{v} \\cdot \\vec{w}} $$<\/div>\u306f\u30c9\u30c3\u30c8\u7a4d (\u6570\u5024) \u3067\u3059\u3002<\/li><\/ul><p>\u30d9\u30af\u30c8\u30eb\u306e\u4e57\u7b97\u306f (\u5916\u7a4d\u306e\u305f\u3081) \u53ef\u63db\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u30b9\u30ab\u30e9\u30fc\u9593\u304a\u3088\u3073\u30b9\u30ab\u30e9\u30fc\u3068\u30d9\u30af\u30c8\u30eb\u306e\u9593\u306e\u4e57\u7b97\u306f\u53ef\u63db\u3067\u3059\u3002\u3053\u308c\u3089\u306e\u898f\u5247\u304b\u3089\u76f4\u3061\u306b\u6b21\u306e\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {(s + \\vec{v}) (t + \\vec{w}) = (s t &#8211; \\vec{v} \\cdot \\vec{w}) + (s \\vec{w} + t \\vec{v} + \\vec{v} \\wedge \\vec{w})} $$<\/div> \u3002<\/p><p>\u975e\u30bc\u30ed\u56db\u5143\u6570\u306e<span><a href=\"https:\/\/science-hub.click\/?p=35670\">\u9006<\/a><\/span>(\u5de6\u3068\u53f3) \u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {(s + \\vec{v})^{-1} = \\frac{s &#8211; \\vec{v}}{s^2 + |\\vec{v}|^2}} $$<\/div> \u3001\u76f4\u63a5\u8a08\u7b97\u306b\u3088\u3063\u3066\u691c\u8a3c\u3067\u304d\u308b\u3088\u3046\u306b\u3002<\/p><h4><span>\u56de\u8ee2\u3068\u56db\u5143\u6570\u306e\u95a2\u4fc2<\/span><\/h4><p>\u524d\u8ff0\u3057\u305f\u3088\u3046\u306b\u3001 ( <i>w<\/i> , <i>x<\/i> , <i>y<\/i> , <i>z<\/i> ) \u3092\u56de\u8ee2\u306e\u5ea7\u6a19\u3068\u3057\u307e\u3059\u3002\u30af\u30a9\u30fc\u30bf\u30cb\u30aa\u30f3\u3092\u5b9a\u7fa9\u3057\u307e\u3057\u3087\u3046\u3002 <div class=\"math-formual notranslate\">$$ {q = w + x\\mathbf{i} + y\\mathbf{j} + z\\mathbf{k} = w + \\vec{u}\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix} = \\cos (\\alpha\/2) + \\vec{u} \\sin (\\alpha\/2)} $$<\/div>\u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {\\vec{u}} $$<\/div>\u306f\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u3042\u308b\u3044\u306f\u307e\u305f<div class=\"math-formual notranslate\">$$ {\\vec{v}} $$<\/div>\u5b9f\u5ea7\u6a19\u304c\u30bc\u30ed\u306e\u56db\u5143\u6570\u3068\u307f\u306a\u3055\u308c\u308b\u30013 \u6b21\u5143\u7a7a\u9593\u5185\u306e\u901a\u5e38\u306e\u30d9\u30af\u30c8\u30eb\u3002\u6b21\u306b\u3001\u56db\u5143\u6570\u306e\u7a4d\u304c\u6b21\u306e\u3053\u3068\u3092\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059 (\u6b21\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3092\u53c2\u7167)\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {q \\vec{v} q^{-1}} $$<\/div><\/dd><\/dl><p>\u30d9\u30af\u30c8\u30eb\u3092\u8fd4\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\vec{v}} $$<\/div>\u306e\u65b9\u5411\u306e\u8ef8\u306e\u5468\u308a\u306b\u89d2\u5ea6<span>\u03b1<\/span>\u3060\u3051\u56de\u8ee2\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\vec{u}} $$<\/div> \u3002\u8996\u7dda\u304c\u540c\u3058\u65b9\u5411\u3092\u5411\u3044\u3066\u3044\u308b\u5834\u5408\u3001\u56de\u8ee2\u306f\u6642\u8a08\u56de\u308a\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\vec{u}} $$<\/div> \u3002\u3053\u306e\u6f14\u7b97\u306f\u3001 <i>q<\/i>\u306b\u3088\u308b\u5171\u5f79\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p><p>\u3057\u305f\u304c\u3063\u3066<i>\u3001<\/i>\u56db\u5143\u6570\u306e\u4e57\u7b97\u306f\u56de\u8ee2\u306e\u5408\u6210\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002p \u3068<i>q \u304c<\/i>\u56de\u8ee2\u3092\u8868\u3059\u56db\u5143\u6570\u3067\u3042\u308b\u5834\u5408\u3001 <i>pq<\/i>\u306b\u3088\u308b\u56de\u8ee2 (\u5171\u5f79) \u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {p q \\vec{v} (p q)^{-1} = p q \\vec{v} q^{-1} p^{-1} = p (q \\vec{v} q^{-1}) p^{-1}} $$<\/div> \u3001<\/dd><\/dl><p>\u3053\u308c\u306f\u3001 <i>q<\/i>\u3067\u56de\u8ee2 (\u5171\u5f79) \u3057\u3001\u6b21\u306b<i>p<\/i>\u3067\u56de\u8ee2\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p><p>\u56de\u8ee2\u306e\u9006\u56db\u5143\u6570\u306f\u9006\u56de\u8ee2\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {q^{-1} (q \\vec{v} q^{-1}) q = \\vec{v}} $$<\/div> \u3002\u30af\u30a9\u30fc\u30bf\u30cb\u30aa\u30f3\u306e 2 \u4e57\u306f\u3001\u540c\u3058\u8ef8\u306e\u5468\u308a\u3067\u540c\u3058\u89d2\u5ea6\u3092 2 \u56de\u56de\u8ee2\u3059\u308b\u3053\u3068\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u3088\u308a\u4e00\u822c\u7684\u306b\u306f\u3001 <i>q<\/i> <sup><i>n \u306f\u3001<\/i><\/sup> <i>q<\/i>\u3068\u540c\u3058\u8ef8\u306e\u5468\u308a\u306e\u89d2\u5ea6\u306e<i>n<\/i>\u500d\u306e\u56de\u8ee2\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u4efb\u610f\u306e\u5b9f\u6570<i>n<\/i>\u306b\u62e1\u5f35\u3067\u304d\u3001\u7a7a\u9593\u306e\u56de\u8ee2\u9593\u3067\u4e2d\u9593\u56de\u8ee2\u3092<span><a href=\"https:\/\/science-hub.click\/?p=93205\">\u6d41\u52d5\u7684\u306b<\/a><\/span>\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u304c\u7403\u9762\u7dda\u5f62\u88dc\u9593 ( <span title=\"Slerp (\u30da\u30fc\u30b8\u304c\u5b58\u5728\u3057\u307e\u305b\u3093)\">Slerp<\/span> ) \u3067\u3059\u3002<\/p><h4><span>\u56db\u5143\u6570\u306e\u5171\u5f79\u3068\u7a7a\u9593\u306e\u56de\u8ee2\u306e\u7b49\u4fa1\u6027\u306e<span><a href=\"https:\/\/science-hub.click\/?p=52981\">\u5b9f\u8a3c<\/a><\/span><\/span><\/h4><p>\u3069\u3061\u3089\u304b<div class=\"math-formual notranslate\">$$ {\\vec{u}} $$<\/div>\u5358\u4f4d\u30d9\u30af\u30c8\u30eb (\u56de\u8ee2\u8ef8) \u3068\u6b21\u306e\u3044\u305a\u308c\u304b<div class=\"math-formual notranslate\">$$ {q = \\cos \\frac{\\alpha}{2} + \\vec{u} \\sin \\frac{\\alpha}{2}} $$<\/div> \u3002\u79c1\u305f\u3061\u306e\u76ee\u6a19\u306f\u3001\u305d\u308c\u3092\u793a\u3059\u3053\u3068\u3067\u3059<\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\vec{v&#8217;} = q \\vec{v} q^{-1} = \\left( \\cos \\frac{\\alpha}{2} + \\vec{u} \\sin \\frac{\\alpha}{2} \\right) \\, \\vec{v} \\, \\left( \\cos \\frac{\\alpha}{2} &#8211; \\vec{u} \\sin \\frac{\\alpha}{2} \\right)} $$<\/div><\/dd><\/dl><p>\u30d9\u30af\u30c8\u30eb\u3092\u8fd4\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\vec{v}} $$<\/div>\u306e\u65b9\u5411\u306e\u8ef8\u306e\u5468\u308a\u306b\u89d2\u5ea6<span>\u03b1<\/span>\u3060\u3051\u56de\u8ee2\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\vec{u}} $$<\/div> \u3002\u5c55\u958b\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\begin{array}{lll} \\vec{v&#8217;} &amp;=&amp; \\vec{v} \\cos^2 \\frac{\\alpha}{2} + (\\vec{u}\\vec{v} &#8211; \\vec{v}\\vec{u}) \\sin \\frac{\\alpha}{2} \\cos \\frac{\\alpha}{2} &#8211; \\vec{u}\\vec{v}\\vec{u} \\sin^2 \\frac{\\alpha}{2} \\\\ &amp;=&amp; \\vec{v} \\cos^2 \\frac{\\alpha}{2} + 2 (\\vec{u} \\wedge \\vec{v}) \\sin \\frac{\\alpha}{2} \\cos \\frac{\\alpha}{2} &#8211; (\\vec{v} (\\vec{u} \\cdot \\vec{u}) &#8211; 2 \\vec{u} (\\vec{u} \\cdot \\vec{v})) \\sin^2 \\frac{\\alpha}{2} \\\\ &amp;=&amp; \\vec{v} (\\cos^2 \\frac{\\alpha}{2} &#8211; \\sin^2 \\frac{\\alpha}{2}) + (\\vec{u} \\wedge \\vec{v}) (2 \\sin \\frac{\\alpha}{2} \\cos \\frac{\\alpha}{2}) + \\vec{u} (\\vec{u} \\cdot \\vec{v}) (2 \\sin^2 \\frac{\\alpha}{2}) \\\\ &amp;=&amp; \\vec{v} \\cos \\alpha + (\\vec{u} \\wedge \\vec{v}) \\sin \\alpha + \\vec{u} (\\vec{u} \\cdot \\vec{v}) (1 &#8211; \\cos \\alpha) \\\\ &amp;=&amp; (\\vec{v} &#8211; \\vec{u} (\\vec{u} \\cdot \\vec{v})) \\cos \\alpha + (\\vec{u} \\wedge \\vec{v}) \\sin \\alpha + \\vec{u} (\\vec{u} \\cdot \\vec{v}) \\\\ &amp;=&amp; \\vec{v}_{\\bot} \\cos \\alpha + (\\vec{u} \\wedge \\vec{v}_{\\bot}) \\sin \\alpha + \\vec{v}_{\\|} \\end{array}} $$<\/div><\/dd><\/dl><p>\u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {\\vec{v}_{\\bot}} $$<\/div>\u305d\u3057\u3066<div class=\"math-formual notranslate\">$$ {\\vec{v}_{\\|}} $$<\/div>\u306e\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u3067\u3059<div class=\"math-formual notranslate\">$$ {\\vec{v}} $$<\/div>\u305d\u308c\u305e\u308c\u76f4\u4ea4\u304a\u3088\u3073\u540c\u4e00\u76f4\u7dda\u4e0a\u306b\u3042\u308b<div class=\"math-formual notranslate\">$$ {\\vec{u}} $$<\/div> \u3002\u3053\u308c\u306f\u3001\u6b21\u306e\u65b9\u5411\u306e\u8ef8\u306e\u5468\u308a\u306e\u89d2\u5ea6<span>\u03b1<\/span>\u306e\u56de\u8ee2\u3092\u4e0e\u3048\u308b\u30aa\u30ea\u30f3\u30c7 \u30ed\u30c9\u30ea\u30b2\u30b9\u306e\u516c\u5f0f\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\vec{u}} $$<\/div> \u3002<\/p><h3><span>\u4f8b<\/span><\/h3><h4><span>\u6d3b\u7528\u306b\u3088\u308b\u30a2\u30af\u30b7\u30e7\u30f3<\/span><\/h4><div><div><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/uKWLPU8gfIY\/0.jpg\" style=\"width:100%;\"\/><\/figure><div>\u6700\u521d\u306e<span><a href=\"https:\/\/science-hub.click\/?p=100875\">\u5bfe\u89d2\u7dda<\/a><\/span>\u3092\u4e2d\u5fc3\u306b 120 \u5ea6\u56de\u8ee2\u3059\u308b\u3068\u3001i\u3001j\u3001k \u304c\u5186\u72b6\u306b\u56de\u8ee2\u3057\u307e\u3059\u3002<\/div><\/div><\/div><p>\u306e\u65b9\u5411\u306e\u8ef8\u306e\u5468\u308a\u306e\u56de\u8ee2<i>f \u3092<\/i>\u8003\u3048\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\vec{v} = \\mathbf{i} + \\mathbf{j} + \\mathbf{k}} $$<\/div>\u89d2\u5ea6\u306f 120\u00b0\u3001\u3064\u307e\u308a<sup>2\u03c0<\/sup> \/ <sub>3<\/sub>\u30e9\u30b8\u30a2\u30f3\u3067\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\alpha = \\frac{2 \\pi}{3}} $$<\/div><\/dd><\/dl><p>\u306e\u57fa\u6e96<div class=\"math-formual notranslate\">$$ {\\vec{v}} $$<\/div>\u306f\u221a3\u3001\u534a\u89d2\u306f<sup>\u03c0<\/sup> \/ <sub>3<\/sub> (60\u00b0)\u3001\u3053\u306e\u534a\u89d2\u306e<span><a href=\"https:\/\/science-hub.click\/?p=18862\">\u4f59\u5f26<\/a><\/span>\u306f<sup>1<\/sup> \/ <sub>2<\/sub> \u3001 (cos 60\u00b0 = 0.5)\u3001\u305d\u306e<span><a href=\"https:\/\/science-hub.click\/?p=18862\">\u6b63\u5f26<\/a><\/span>\u306f<sup>\u221a3<\/sup> \/ <sub>2<\/sub> \u3001 (sin 60 \u00b0 \u2248) 0.866\uff09\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30e6\u30cb\u30bf\u30ea\u56db\u5143\u6570\u3068\u5171\u5f79\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\begin{array}{lll} u &amp;=&amp; \\cos\\frac{\\alpha}{2} + \\sin\\frac{\\alpha}{2}\\cdot \\frac{1}{\\| \\vec{v} \\| }\\vec{v}\\\\ &amp;=&amp; \\cos \\frac{\\pi}{3} + \\sin \\frac{\\pi}{3}\\cdot \\frac{1}{\\sqrt{3}}\\vec{v}\\\\ &amp;=&amp; \\frac{1}{2} + \\frac{\\sqrt{3}}{2}\\cdot \\frac{1}{\\sqrt{3}}\\vec{v}\\\\ &amp;=&amp; \\frac{1}{2} + \\frac{\\sqrt{3}}{2}\\cdot \\frac{\\mathbf{i} + \\mathbf{j} + \\mathbf{k}}{\\sqrt{3}}\\\\ &amp;=&amp; \\frac{1 + \\mathbf{i} + \\mathbf{j} + \\mathbf{k}}{2} \\end{array}} $$<\/div><\/dd><\/dl><p> <i>f<\/i>\u304c\u56de\u8ee2\u95a2\u6570\u306e\u5834\u5408\u3001 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {f(a\\mathbf{i} + b\\mathbf{j} + c\\mathbf{k}) = u (a\\mathbf{i} + b\\mathbf{j} + c\\mathbf{k}) u^{-1}} $$<\/div><\/dd><\/dl><p>\u865a\u6570\u5ea7\u6a19\u306e\u7b26\u53f7\u3092\u5909\u66f4\u3059\u308b\u3060\u3051\u3067\u3001\u5358\u4f4d\u56db\u5143\u6570\u306e\u9006\u6570\u304c\u5f97\u3089\u308c\u308b\u3053\u3068\u3092\u8a3c\u660e\u3067\u304d\u307e\u3059\u3002\u305d\u308c\u306b\u5fdc\u3058\u3066\u3001 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {u^{-1} = \\frac{1- \\mathbf{i} &#8211; \\mathbf{j} &#8211; \\mathbf{k}}{2}} $$<\/div><\/dd><\/dl><p>\u305d\u3057\u3066<\/p><dl><dd><div class=\"math-formual notranslate\">$$ {f(a\\mathbf{i} + b\\mathbf{j} + c\\mathbf{k}) = \\frac{1 + \\mathbf{i} + \\mathbf{j} + \\mathbf{k}}{2} (a\\mathbf{i} + b\\mathbf{j} + c\\mathbf{k}) \\frac{1 &#8211; \\mathbf{i} &#8211; \\mathbf{j} &#8211; \\mathbf{k}}{2}} $$<\/div><\/dd><\/dl><p>\u30af\u30a9\u30fc\u30bf\u30cb\u30aa\u30f3\u3092\u4f7f\u7528\u3057\u305f\u901a\u5e38\u306e\u8a08\u7b97\u898f\u5247\u3092\u9069\u7528\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {f(a\\mathbf{i} + b\\mathbf{j} + c\\mathbf{k}) = c\\mathbf{i} + a\\mathbf{j} + b\\mathbf{k}} $$<\/div><\/dd><\/dl><p>\u4e88\u60f3\u306e\u3068\u304a\u308a\u3001\u56de\u8ee2\u306f<span><a href=\"https:\/\/science-hub.click\/?p=101007\">\u7acb\u65b9\u4f53<\/a><\/span>\u306e\u9802\u70b9\u306e 1 \u3064\u3092\u6301\u3061\u3001\u305d\u306e\u70b9\u3092\u901a\u308b\u6700\u9577\u306e\u5bfe\u89d2\u7dda\u306b\u6cbf\u3063\u3066 120 \u5ea6\u56de\u8ee2\u3059\u308b\u3053\u3068\u3068\u540c\u3058\u3067\u3059\u3002 3 \u3064\u306e\u8ef8\u304c\u3069\u306e\u3088\u3046\u306b\u5186<span><a href=\"https:\/\/science-hub.click\/?p=49311\">\u9806\u5217\u3092<\/a><\/span>\u7d4c\u308b\u304b\u3092\u89b3\u5bdf\u3057\u307e\u3059\u3002<\/p><h4><span>\u5b9f\u969b\u306e\u30af\u30a9\u30fc\u30bf\u30cb\u30aa\u30f3\u8a08\u7b97<\/span><\/h4><p>\u524d\u56de\u306e\u7d50\u679c\u3092\u8a3c\u660e\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002 <i>f<\/i>\u306e\u5f0f\u3092 (2 \u3064\u306e\u30b9\u30c6\u30c3\u30d7\u3067) \u4f5c\u6210\u3057\u3001\u30eb\u30fc\u30eb\u3092\u9069\u7528\u3057\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\begin{alignat}{2} \\mathbf{ij} &amp; = \\mathbf{k}, &amp; \\mathbf{ji} &amp; = \\mathbf{-k}, \\\\ \\mathbf{jk} &amp; = \\mathbf{i}, &amp; \\mathbf{kj} &amp; = \\mathbf{-i}, \\\\ \\mathbf{ki} &amp; = \\mathbf{j}, &amp; \\mathbf{ik} &amp; = \\mathbf{-j}, \\\\ \\mathbf{i}^{2} &amp; = \\mathbf{j}^{2}&amp; = \\mathbf{k}^{2} &amp; = -1 \\end{alignat}} $$<\/div><\/dd><\/dl><p>\u4ee5\u4e0b\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\begin{array}{lll} f(a\\mathbf{i} + b\\mathbf{j} + c\\mathbf{k}) &amp;=&amp; \\frac{1 + \\mathbf{i} + \\mathbf{j} + \\mathbf{k}}{2} (a\\mathbf{i} + b\\mathbf{j} + c\\mathbf{k}) \\frac{1 &#8211; \\mathbf{i} &#8211; \\mathbf{j} &#8211; \\mathbf{k}}{2} \\\\ &amp;&amp;                          (1 &#8211; \\mathbf{i} &#8211; \\mathbf{j} &#8211; \\mathbf{k})\\\\ &amp;=&amp; \\frac{1}{4} ( (a\\mathbf{i} + b\\mathbf{j} + c\\mathbf{k}) +(- a + b\\mathbf{k} &#8211; c\\mathbf{j}) + (-a\\mathbf{k} &#8211; b +c\\mathbf{i}) + (a\\mathbf{j} &#8211; b\\mathbf{i} &#8211; c))\\\\ &amp;&amp;                          (1 &#8211; \\mathbf{i} &#8211; \\mathbf{j} &#8211; \\mathbf{k})\\\\ &amp;=&amp; \\frac{1}{4} ( (-a &#8211; b &#8211; c) + (a &#8211; b+ c) \\mathbf{i} + (a + b &#8211; c) \\mathbf{j} + (-a + b + c) \\mathbf{k})\\\\ &amp;&amp;                          (1 &#8211; \\mathbf{i} &#8211; \\mathbf{j} &#8211; \\mathbf{k})\\\\ &amp;=&amp; \\frac{1}{4} ( ( (-a &#8211; b &#8211; c) + (a &#8211; b + c) \\mathbf{i} + (a + b &#8211; c) \\mathbf{j} + (-a + b + c) \\mathbf{k})\\\\ &amp;&amp;+                       ( (a + b + c) \\mathbf{i} + (a &#8211; b + c) + (a + b &#8211; c) \\mathbf{k} + (a &#8211; b &#8211; c) \\mathbf{j})\\\\ &amp;&amp;+                       ( (a + b + c) \\mathbf{j} + (-a + b &#8211; c) \\mathbf{k} + (a + b &#8211; c) + (-a + b + c) \\mathbf{i})\\\\ &amp;&amp;+                       ( (a + b + c) \\mathbf{k} + (a &#8211; b + c) \\mathbf{j} + (-a &#8211; b + c) \\mathbf{i} + (-a + b + c))\\\\ &amp;=&amp; \\frac{1}{4} ( ( (-a &#8211; b &#8211; c) + (a &#8211; b + c) + (a + b &#8211; c) + (-a + b + c) )\\\\ &amp;&amp;+                       ( (a &#8211; b + c) + (a + b + c) + (-a + b + c) + (-a &#8211; b + c) ) \\mathbf{i}\\\\ &amp;&amp;+                       ( (a + b &#8211; c) + (a &#8211; b &#8211; c) + (a + b + c) + (a &#8211; b + c) ) \\mathbf{j}\\\\ &amp;&amp;+                       ( (-a + b + c) + (a + b &#8211; c) + (-a + b &#8211; c) + (a + b + c) ) \\mathbf{k})\\\\ &amp;=&amp; \\frac{1}{4} (0 + 4c \\mathbf{i} + 4a \\mathbf{j} + 4b \\mathbf{k})\\\\ &amp;=&amp;c\\mathbf{i} + a\\mathbf{j} + b\\mathbf{k} \\end{array}} $$<\/div><\/dd><\/dl><p>\u3053\u308c\u306f\u5b9f\u969b\u306b\u767a\u8868\u3055\u308c\u305f\u7d50\u679c\u3067\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u8a08\u7b97\u3092<span><a href=\"https:\/\/science-hub.click\/?p=64953\">\u624b\u4f5c\u696d<\/a><\/span>\u3067\u884c\u3046\u306e\u306f\u6bd4\u8f03\u7684\u9762\u5012\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u304c\u3001<span><a href=\"https:\/\/science-hub.click\/?p=454\">\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc<\/a><\/span>\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u306f\u3001\u7d50\u5c40\u306e\u3068\u3053\u308d\u3001\u56db\u5143\u6570\u4e57\u7b97\u30eb\u30fc\u30c1\u30f3\u3092 2 \u56de\u547c\u3073\u51fa\u3059\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p><\/div><h2 class=\"ref_link\">\u53c2\u8003\u8cc7\u6599<\/h2><ol><li><a class=\"notranslate\" href=\"https:\/\/en.wikipedia.org\/wiki\/Quaternions_and_spatial_rotation\">Quaternions and spatial rotation \u2013 anglais<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/es.wikipedia.org\/wiki\/Cuaterniones_y_rotaci%C3%B3n_en_el_espacio\">Cuaterniones y rotaci\u00f3n en el espacio \u2013 espagnol<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/he.wikipedia.org\/wiki\/%D7%A7%D7%95%D7%95%D7%98%D7%A8%D7%A0%D7%99%D7%95%D7%A0%D7%99%D7%9D_%D7%95%D7%A1%D7%99%D7%91%D7%95%D7%91%D7%99%D7%9D_%D7%9E%D7%A8%D7%97%D7%91%D7%99%D7%99%D7%9D\">\u05e7\u05d5\u05d5\u05d8\u05e8\u05e0\u05d9\u05d5\u05e0\u05d9\u05dd \u05d5\u05e1\u05d9\u05d1\u05d5\u05d1\u05d9\u05dd \u05de\u05e8\u05d7\u05d1\u05d9\u05d9\u05dd \u2013 h\u00e9breu<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/it.wikipedia.org\/wiki\/Rotazioni_spaziali_con_i_quaternioni\">Rotazioni spaziali con i quaternioni \u2013 italien<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ko.wikipedia.org\/wiki\/%EC%82%AC%EC%9B%90%EC%88%98%EC%99%80_%ED%9A%8C%EC%A0%84\">\uc0ac\uc6d0\uc218\uc640 \ud68c\uc804 \u2013 cor\u00e9en<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9A%D0%B2%D0%B0%D1%82%D0%B5%D1%80%D0%BD%D0%B8%D0%BE%D0%BD%D1%8B_%D0%B8_%D0%B2%D1%80%D0%B0%D1%89%D0%B5%D0%BD%D0%B8%D0%B5_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%82%D0%B2%D0%B0\">\u041a\u0432\u0430\u0442\u0435\u0440\u043d\u0438\u043e\u043d\u044b \u0438 \u0432\u0440\u0430\u0449\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430 \u2013 russe<\/a><\/li><\/ol><\/div>\n<div class=\"feature-video\">\n <h2>\n  \u7a7a\u9593\u5185\u306e\u56db\u5143\u6570\u3068\u56de\u8ee2 &#8211; \u5b9a\u7fa9\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n <div class=\"video-item\">\n  \n  <figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\n   <div class=\"wp-block-embed__wrapper\">\n    <iframe loading=\"lazy\" title=\"\u56db\u5143\u6570\u3078\u306e\u62db\u5f85\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/J6ja6UYk6X4?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n   <\/div>\n  <\/figure>\n  \n <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5c0e\u5165 \u5358\u4f4d\u56db\u5143\u6570\u306f\u30013 \u6b21\u5143\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u5411\u304d\u3068\u56de\u8ee2\u3092\u8868\u3059\u4fbf\u5229\u306a\u6570\u5b66\u7684\u8868\u8a18\u6cd5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u30aa\u30a4\u30e9\u30fc\u89d2\u3068\u6bd4\u3079\u3066\u3001\u69cb\u6210\u304c\u7c21\u5358\u3067\u3001\u30b8\u30f3\u30d0\u30eb\u306e\u30d6\u30ed\u30c3\u30ad\u30f3\u30b0\u306e\u554f\u984c\u3092\u56de\u907f\u3067\u304d\u307e\u3059\u3002\u56de\u8ee2\u884c\u5217\u3068\u6bd4\u8f03\u3057\u3066\u3001\u6570\u5024\u7684\u306b\u5b89\u5b9a\u3057\u3066\u304a\u308a\u3001\u3088\u308a\u52b9\u7387\u7684 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":105546,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/img.youtube.com\/vi\/J6ja6UYk6X4\/0.jpg","fifu_image_alt":"\u7a7a\u9593\u5185\u306e\u56db\u5143\u6570\u3068\u56de\u8ee2 - \u5b9a\u7fa9","footnotes":""},"categories":[5],"tags":[91664,11,13,14,10,31649,4836,12,8,16,293,15,9],"class_list":["post-105545","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dictionary","tag-cybaeidae","tag-techniques","tag-technologie","tag-news","tag-actualite","tag-quaternions","tag-rotation","tag-dossier","tag-definition","tag-sciences","tag-espace","tag-article","tag-explications"],"_links":{"self":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/105545"}],"collection":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=105545"}],"version-history":[{"count":0,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/105545\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/media\/105546"}],"wp:attachment":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=105545"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=105545"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=105545"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}