{"id":27316,"date":"2024-01-07T13:00:08","date_gmt":"2024-01-07T13:00:08","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27316"},"modified":"2024-07-01T01:41:24","modified_gmt":"2024-07-01T01:41:24","slug":"%e6%97%b6%e7%a9%ba%e5%8f%8c%e6%9b%b2%e6%97%8b%e8%bd%ac","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e6%97%b6%e7%a9%ba%e5%8f%8c%e6%9b%b2%e6%97%8b%e8%bd%ac\/","title":{"rendered":"\u65f6\u7a7a\u53cc\u66f2\u65cb\u8f6c"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u65f6\u7a7a\u53cc\u66f2\u65cb\u8f6c<\/h1>\n<p class=\"eq\"><em><strong>\u6458\u8981\uff1a<\/strong><br \/>\n\u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u56de\u987e\u5982\u4f55\u5c06\u6d1b\u4f26\u5179\u53d8\u6362\u91cd\u65b0\u89e3\u91ca\u4e3a\u65f6\u7a7a\u65cb\u8f6c\u53d8\u6362\u3002\u6211\u4eec\u5c06\u5f00\u59cb\u68c0\u67e5\u56db\u7ef4\u95f5\u53ef\u592b\u65af\u57fa\u7a7a\u95f4\u4e2d\u7684\u65cb\u8f6c\uff0c\u533a\u5206\u7eaf\u7a7a\u95f4\u65cb\u8f6c\u548c\u6d89\u53ca\u65f6\u7a7a\u8f74\u7684\u65cb\u8f6c\u3002<\/br><\/em><\/p>\n<p><\/center><\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5b8c\u6210\u672c\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a<\/p>\n<ol>\n<li><strong>\u7406\u89e3<\/strong>\u95f5\u53ef\u592b\u65af\u57fa\u65f6\u7a7a\u4e2d\u7684\u65cb\u8f6c\u53d8\u6362\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u6d1b\u4f26\u5179\u53d8\u6362\u4f5c\u4e3a\u65f6\u7a7a\u65cb\u8f6c\u3002<\/li>\n<\/ol>\n<p><center><\/p>\n<p><strong>\u76ee\u5f55<\/strong><br \/>\n<a href=\"#0\"><strong>\u7b80\u4ecb<\/strong><\/a><br \/>\n<a href=\"#1\"><strong>\u95f5\u53ef\u592b\u65af\u57fa\u65f6\u7a7a\u4e2d\u7684\u65cb\u8f6c<\/strong><\/a><br \/>\n<a href=\"#2\">\u7eaf\u7a7a\u95f4\u65cb\u8f6c<\/a><br \/>\n<a href=\"#3\">\u4e09\u7ef4\u65cb\u8f6c\u7684\u77e9\u9635\u63a8\u5e7f<\/a><br \/>\n<a href=\"#4\">\u5177\u6709\u65f6\u7a7a\u5750\u6807\u7684\u4e8b\u4ef6\u7684\u7a7a\u95f4\u65cb\u8f6c<\/a><br \/>\n<a href=\"#5\"><strong>\u65f6\u7a7a\u53cc\u66f2\u65cb\u8f6c<\/strong><\/a><br \/>\n<a href=\"#6\">\u5f15\u5165\u901f\u5ea6\u53c2\u6570<\/a><br \/>\n<a href=\"#7\">\u5c06\u65f6\u7a7a\u65cb\u8f6c\u516c\u5f0f\u5316\u4e3a\u53cc\u66f2\u65cb\u8f6c<\/a><br \/>\n<a href=\"#8\"><strong>\u7ed3\u8bba<\/strong><\/a>\n<\/p>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/PCB-XC3XwQE?si=rBjMJhQEZ8O2wBLg\" title=\"YouTube\u89c6\u9891\u64ad\u653e\u5668\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><br \/>\n<\/center>\n<\/div>\n<p><a name=\"0\"><\/a><\/p>\n<h2>\u7b80\u4ecb<\/h2>\n<p style=\"text-align:justify;\">\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u8be6\u7ec6\u68c0\u67e5\u4e86\u6d1b\u4f26\u5179\u53d8\u6362\u7684\u5f62\u5f0f\uff0c\u5373\u89c2\u5bdf\u5230\u7684\u95f5\u53ef\u592b\u65af\u57fa\u65f6\u7a7a\u4e2d\u7684\u4e00\u4e2a\u7279\u5b9a\u4e8b\u4ef6\u7684\u5750\u6807\u5982\u4f55\u4ece\u4e0d\u540c\u7684\u60ef\u6027\u53c2\u8003\u7cfb\u4e2d\u6539\u53d8\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u4ece\u4e0d\u540c\u7684\u89d2\u5ea6\u6765\u5ba1\u89c6\u8fd9\u4e9b\u53d1\u5c55\uff0c\u5c06\u5b83\u4eec\u89c6\u4e3a\u65f6\u7a7a\u65cb\u8f6c\u53d8\u6362\u3002\u5f88\u5feb\u6211\u4eec\u4f1a\u53d1\u73b0\uff0c\u8fd9\u79cd\u65b9\u6cd5\u5728\u4ee3\u6570\u4e0a\u63d0\u4f9b\u4e86\u4f18\u52bf\uff0c\u901a\u5e38\u7b80\u5316\u4e86\u8ba1\u7b97\uff0c\u7279\u522b\u662f\u5728\u7ec4\u5408\u591a\u4e2a\u8fde\u7eed\u7684\u6d1b\u4f26\u5179\u53d8\u6362\u65f6\u3002<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u95f5\u53ef\u592b\u65af\u57fa\u65f6\u7a7a\u4e2d\u7684\u65cb\u8f6c<\/h2>\n<p style=\"text-align:justify;\">\u8ba9\u6211\u4eec\u5f00\u59cb\u5206\u6790\u5728\u95f5\u53ef\u592b\u65af\u57fa\u65f6\u7a7a\u4e2d\u6267\u884c\u7684\u5404\u79cd\u7a7a\u95f4\u65cb\u8f6c\u3002\u7531\u4e8e\u8fd9\u662f\u4e00\u4e2a\u56db\u7ef4\u7a7a\u95f4\uff0c\u6700\u5b9e\u7528\u7684\u65b9\u6cd5\u662f\u76f8\u5bf9\u4e8e\u7279\u5b9a\u5e73\u9762\u8fdb\u884c\u65cb\u8f6c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u5728<bdi><span class=\"katex-eq\" data-katex-display=\"false\">xy<\/span><\/bdi>\u3001<bdi><span class=\"katex-eq\" data-katex-display=\"false\">xz<\/span><\/bdi>\u548c<bdi><span class=\"katex-eq\" data-katex-display=\"false\">yz<\/span><\/bdi>\u5e73\u9762\u4e0a\u7684\u65cb\u8f6c\uff0c\u4ee5\u53ca\u5728<bdi><span class=\"katex-eq\" data-katex-display=\"false\">xt<\/span><\/bdi>\u3001<bdi><span class=\"katex-eq\" data-katex-display=\"false\">yt<\/span><\/bdi>\u548c<bdi><span class=\"katex-eq\" data-katex-display=\"false\">zt<\/span><\/bdi>\u5e73\u9762\u4e0a\u7684\u65cb\u8f6c\u3002\u5728\u7531\u7a7a\u95f4\u8f74\u7ec4\u6210\u7684\u5e73\u9762\u4e2d\u8fdb\u884c\u7684\u65cb\u8f6c\u662f\u7eaf\u7a7a\u95f4\u65cb\u8f6c\uff0c\u800c\u5728\u7531\u65f6\u7a7a\u8f74\u7ec4\u6210\u7684\u5e73\u9762\u4e2d\u8fdb\u884c\u7684\u65cb\u8f6c\u662f\u65f6\u7a7a\u65cb\u8f6c\u3002\u76ee\u524d\uff0c\u6211\u4eec\u5c06\u4e13\u6ce8\u4e8e\u8be6\u7ec6\u4e86\u89e3\u7eaf\u7a7a\u95f4\u65cb\u8f6c\uff0c\u7136\u540e\u6269\u5c55\u5230\u65f6\u7a7a\u65cb\u8f6c\u3002\n<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h3>\u7eaf\u7a7a\u95f4\u65cb\u8f6c<\/h3>\n<p style=\"text-align:justify;\">\n\u8ba9\u6211\u4eec\u5f00\u59cb\u7814\u7a76\u5728<bdi><span class=\"katex-eq\" data-katex-display=\"false\">xy<\/span><\/bdi>\u5e73\u9762\u4e0a\u7684\u65cb\u8f6c\u3002\u4e3a\u6b64\uff0c\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u70b9\uff0c\u5176\u76f8\u5bf9\u4e8e<bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span><\/bdi>\u548c<bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{y}<\/span><\/bdi>\u8f74\u5b9a\u4e49\u7684\u5750\u6807\u4e3a<bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a,b)<\/span><\/bdi>\u3002\u7136\u540e\uff0c\u6211\u4eec\u6765\u5206\u6790\u5c06\u8fd9\u4e9b\u5750\u6807\u4e0e\u4e00\u4e2a\u65cb\u8f6c\u7684\u53c2\u8003\u7cfb\u89c2\u5bdf\u5230\u7684\u5750\u6807\u8fde\u63a5\u8d77\u6765\u7684\u5173\u7cfb\u3002\u8fd9\u4e2a\u7cfb\u7edf\u7531\u65cb\u8f6c\u4e86\u4e00\u4e2a\u89d2\u5ea6<span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span>\u7684<bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}^\\prime<\/span><\/bdi>\u548c<bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{y}^\\prime<\/span><\/bdi>\u8f74\u5b9a\u4e49\uff0c\u5982\u4e0b\u56fe\u6240\u793a\uff1a\n<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/01\/rotaciontheta.jpg\" alt=\"xy\u5e73\u9762\u4e0a\u65cb\u8f6c\u89d2\u5ea6theta\" width=\"623\" height=\"495\" class=\"aligncenter size-full wp-image-25994 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/01\/rotaciontheta.jpg\" alt=\"xy\u5e73\u9762\u4e0a\u65cb\u8f6c\u89d2\u5ea6theta\" width=\"623\" height=\"495\" class=\"aligncenter size-full wp-image-25994 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/01\/rotaciontheta.jpg 623w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/01\/rotaciontheta-300x238.jpg 300w\" sizes=\"(max-width: 623px) 100vw, 623px\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align:justify;\">\n\u4e3a\u4e86\u83b7\u5f97\u4ece\u6bcf\u4e2a\u7cfb\u7edf\u6d4b\u91cf\u7684\u5750\u6807<bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a,b)<\/span><\/bdi>\u548c<bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a^\\prime,b^\\prime)<\/span><\/bdi>\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u6307\u5bfc\u7ebf\uff1a\n<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/01\/rotacion-conlineasguia.png\" alt=\"\u83b7\u53d6\u65cb\u8f6c\u7cfb\u7edf\u4e4b\u95f4\u5173\u7cfb\u7684\u6307\u5bfc\u7ebf\" width=\"827\" height=\"620\" class=\"aligncenter size-full wp-image-25998 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/01\/rotacion-conlineasguia.png\" alt=\"\u83b7\u53d6\u65cb\u8f6c\u7cfb\u7edf\u4e4b\u95f4\u5173\u7cfb\u7684\u6307\u5bfc\u7ebf\" width=\"827\" height=\"620\" class=\"aligncenter size-full wp-image-25998 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/01\/rotacion-conlineasguia.png 827w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/01\/rotacion-conlineasguia-300x225.png 300w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/01\/rotacion-conlineasguia-768x576.png 768w\" sizes=\"(max-width: 827px) 100vw, 827px\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align:justify;\">\n\u56e0\u6b64\uff0c\u73b0\u5728\u5f88\u5bb9\u6613\u83b7\u5f97\u8f6c\u6362\u65b9\u7a0b\n<\/p>\n<p><bdi><\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\begin{array}{rcl} a^\\prime &amp; = &amp; \\phantom{-}a\\cos(\\theta) + b\\sin(\\theta) \\\\ b^\\prime &amp; = &amp; -a \\sin(\\theta) + b \\cos(\\theta)\n\n\\end{array} <\/span>\n<p><\/bdi><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u4e09\u7ef4\u65cb\u8f6c\u7684\u77e9\u9635\u63a8\u5e7f<\/h3>\n<p style=\"text-align:justify;\">\n\u8fd9\u79cd\u65b9\u7a0b\u7ec4\u53ef\u4ee5\u66f4\u65b9\u4fbf\u5730\u8868\u793a\u4e3a\u77e9\u9635\u5f62\u5f0f\u3002\n<\/p>\n<p><bdi><\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\left(\\begin{array}{r} a^\\prime \\\\ b^\\prime \\end{array}\\right) = \\left(\\begin{array}{cc} \\cos(\\theta) &amp; \\sin(\\theta) \\\\ -\\sin(\\theta) &amp; \\cos(\\theta)\\end{array}\\right) \\left(\\begin{array}{r} a \\\\ b \\end{array}\\right) <\/span>\n<p><\/bdi><\/p>\n<p style=\"text-align:justify;\">\u8fd9\u662f\u65b9\u4fbf\u7684\uff0c\u56e0\u4e3a\u4ece\u8fd9\u91cc\u5f88\u5bb9\u6613\u63a8\u5e7f\u5230\u66f4\u5927\u7684\u7ef4\u5ea6\u3002\u4f8b\u5982\uff0c\u4e00\u4e2a\u5728<bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span><\/bdi>\u3001<span class=\"katex-eq\" data-katex-display=\"false\">\\hat{y}<\/span>\u548c<bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{z}<\/span><\/bdi>\u8f74\u5b9a\u4e49\u7684\u7cfb\u7edf\u4e2d\u7684\u70b9\uff0c\u5176\u5750\u6807\u4e3a<bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a,b,c)<\/span><\/bdi>\uff0c\u4ece\u53e6\u4e00\u4e2a\u7cfb\u7edf\u4e2d\u89c2\u5bdf\u5230\u7684\uff0c\u8be5\u7cfb\u7edf\u7531\u65cb\u8f6c\u4e86\u4e00\u4e2a\u89d2\u5ea6<span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span>\u76f8\u5bf9\u4e8e<bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}\\hat{y}<\/span><\/bdi>\u5e73\u9762\u7684\u8f74\u5b9a\u4e49\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n<p><bdi><\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\left(\\begin{array}{r} a^\\prime \\\\ b^\\prime \\\\ c^\\prime \\end{array}\\right) = \\left(\\begin{array}{ccc} \\cos(\\theta) &amp; \\sin(\\theta) &amp; 0 \\\\ -\\sin(\\theta) &amp; \\cos(\\theta) &amp; 0 \\\\ 0 &amp; 0 &amp; 1\\end{array}\\right) \\left(\\begin{array}{r} a \\\\ b \\\\ c\\end{array}\\right) <\/span>\n<p><\/bdi><\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/01\/sistemarotadoxy3d.png\" alt=\"\u7a7a\u95f4\u65cb\u8f6c\" width=\"725\" height=\"597\" class=\"aligncenter size-full wp-image-26014 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/01\/sistemarotadoxy3d.png\" alt=\"\u7a7a\u95f4\u65cb\u8f6c\" width=\"725\" height=\"597\" class=\"aligncenter size-full wp-image-26014 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/01\/sistemarotadoxy3d.png 725w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/01\/sistemarotadoxy3d-300x247.png 300w\" sizes=\"(max-width: 725px) 100vw, 725px\" \/><\/noscript><\/p>\n<p style=\"text-align:justify;\">\u7531\u6b64\uff0c\u6211\u4eec\u5f97\u5230\u4e86\u6bcf\u4e2a\u7a7a\u95f4\u5e73\u9762\u7684\u4e0d\u540c\u65cb\u8f6c\u53d8\u6362\u77e9\u9635\u3002<\/p>\n<p><bdi><\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\begin{array}{rll} R_{xy}(\\theta)= &amp; \\left(\\begin{array}{ccc} \\cos(\\theta) &amp; \\sin(\\theta) &amp; 0 \\\\ -\\sin(\\theta) &amp; \\cos(\\theta) &amp; 0 \\\\ 0 &amp; 0 &amp; 1\\end{array}\\right) &amp; \\begin{array}{l} \\text{\u5728}xy \\text{\u5e73\u9762\u4e0a\u65cb\u8f6c\u4e00\u4e2a\u89d2\u5ea6} \\theta \\end{array} \\\\ \\\\ R_{yz}(\\theta)= &amp; \\left(\\begin{array}{ccc} 1 &amp; 0 &amp; 0 \\\\ 0 &amp; \\cos(\\theta) &amp; \\sin(\\theta) \\\\ 0 &amp; -\\sin(\\theta) &amp; \\cos(\\theta)\\end{array}\\right) &amp; \\begin{array}{l} \\text{\u5728}yz \\text{\u5e73\u9762\u4e0a\u65cb\u8f6c\u4e00\u4e2a\u89d2\u5ea6} \\theta \\end{array} \\\\ \\\\ R_{xz}(\\theta)= &amp; \\left(\\begin{array}{ccc} \\cos(\\theta) &amp; 0 &amp; \\sin(\\theta) \\\\ 0 &amp; 1 &amp; 0 \\\\ -\\sin(\\theta) &amp; 0 &amp; \\cos(\\theta)\\end{array}\\right) &amp; \\begin{array}{l} \\text{\u5728}xz \\text{\u5e73\u9762\u4e0a\u65cb\u8f6c\u4e00\u4e2a\u89d2\u5ea6} \\theta \\end{array} \\end{array} <\/span>\n<p><\/bdi><\/p>\n<p style=\"text-align:justify;\">\u8981\u8ba1\u7b97\u8fd9\u4e9b\u65cb\u8f6c\u53d8\u6362\u7684\u9006\u53d8\u6362\uff0c\u53ea\u9700\u5c06<span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span>\u66ff\u6362\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">-\\theta<\/span>\u3002<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u5177\u6709\u65f6\u7a7a\u5750\u6807\u7684\u4e8b\u4ef6\u7684\u7a7a\u95f4\u65cb\u8f6c<\/h3>\n<p style=\"text-align:justify;\">\n\u7c7b\u4f3c\u4e8e\u5982\u4f55\u4ece\u4e8c\u7ef4\u63a8\u5e7f\u5230\u4e09\u7ef4\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5176\u6269\u5c55\u5230\u56db\u7ef4\u3002\u4e3a\u4e86\u4e0e\u72ed\u4e49\u76f8\u5bf9\u8bba\u7684\u8bed\u8a00\u4fdd\u6301\u4e00\u81f4\uff0c\u7406\u89e3\u6bcf\u4e2a\u5750\u6807\u7684\u542b\u4e49\u662f\u91cd\u8981\u7684\u3002\u901a\u5e38\uff0c\u65f6\u7a7a\u5750\u6807\u8868\u793a\u5982\u4e0b\uff1a\n<\/p>\n<p><bdi><\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">x^\\mu = (x^0, x^1, x^2, x^3) = (ct, x, y, z)<\/span>\n<p><\/bdi><\/p>\n<p style=\"text-align:justify;\">\n\u5728\u8fd9\u91cc\uff0c\u4e0a\u6807\u4e0d\u8868\u793a\u5e42\uff0c\u800c\u662f\u6307\u6bcf\u4e2a\u5750\u6807\u7684\u7279\u5f81\u3002\u4e0a\u6807\u4e3a0\u7684\u5750\u6807\u8868\u793a\u65f6\u95f4\u7ef4\u5ea6\uff0c\u800c\u4e0a\u6807\u4e3a1\u30012\u548c3\u7684\u5750\u6807\u5bf9\u5e94\u7a7a\u95f4\u7ef4\u5ea6\u3002\u8003\u8651\u5230\u8fd9\u4e00\u70b9\uff0c\u95f5\u53ef\u592b\u65af\u57fa\u65f6\u7a7a\u4e2d\u7684\u7eaf\u7a7a\u95f4\u65cb\u8f6c\u901a\u8fc7\u4ee5\u4e0b\u5173\u7cfb\u63cf\u8ff0\uff1a<\/p>\n<p><bdi><\/p>\n<p style=\"text-align:center;\"><strong>\u5173\u4e8exy\u5e73\u9762\u7684\u65cb\u8f6c\uff1a<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\n\\underbrace{\\left(\\begin{array}{r}\n\nx^{\\prime 0} \\\\ x^{\\prime 1} \\\\ x^{\\prime 2} \\\\ x^{\\prime 3} \\end{array}\\right)}_{\\large{x^{\\prime \\mu}}} = \\underbrace{\\left(\\begin{array}{cccc}\n\n1 &amp; 0 &amp; 0 &amp; 0 \\\\ 0 &amp; \\cos(\\theta) &amp; \\sin(\\theta) &amp; 0 \\\\ 0 &amp; -\\sin(\\theta) &amp; \\cos(\\theta) &amp; 0 \\\\ 0 &amp; 0 &amp; 0 &amp; 1 \\end{array}\\right)}_{\\large{{R_{xy}(\\theta)^\\mu}_\\nu}} \\underbrace{\\left(\\begin{array}{c} x^0 \\\\ x^1 \\\\ x^2 \\\\ x^3 \\end{array}\\right)}_{\\large{x^{\\nu}}} <\/span>\n<p><\/bdi><\/p>\n<p><bdi><\/p>\n<p style=\"text-align:center;\"><strong>\u5173\u4e8eyz\u5e73\u9762\u7684\u65cb\u8f6c\uff1a<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\n\\underbrace{\\left(\\begin{array}{c}\n\nx^{\\prime 0} \\\\ x^{\\prime 1} \\\\ x^{\\prime 2} \\\\ x^{\\prime 3} \\end{array}\\right)}_{\\large{x^{\\prime \\mu}}} = \\underbrace{\\left(\\begin{array}{cccc} 1 &amp; 0 &amp; 0 &amp; 0 \\\\\n\n{} 0 &amp; 1 &amp; 0 &amp; 0 \\\\ 0 &amp; 0 &amp; \\cos(\\theta) &amp; \\sin(\\theta) \\\\ 0 &amp; 0 &amp; -\\sin(\\theta) &amp; \\cos(\\theta) \\end{array}\\right)}_{\\large{{R_{yz}(\\theta)^\\mu}_\\nu}} \\underbrace{\\left(\\begin{array}{r} x^0 \\\\ x^1 \\\\ x^2 \\\\ x^3 \\end{array}\\right)}_{\\large{x^{\\nu}}} <\/span>\n<p><\/bdi><\/p>\n<p><bdi><\/p>\n<p style=\"text-align:center;\"><strong>\u5173\u4e8exz\u5e73\u9762\u7684\u65cb\u8f6c\uff1a<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\n\\underbrace{\\left(\\begin{array}{c} x^{\\prime 0} \\\\ {}x^{\\prime 1} \\\\ x^{\\prime 2} \\\\ x^{\\prime 3} \\end{array}\\right)}_{\\large{x^{\\prime \\mu}}} = \\underbrace{\\left(\\begin{array}{cccc} 1 &amp; 0 &amp; 0 &amp; 0 \\\\ 0 &amp; \\cos(\\theta) &amp; 0 &amp; \\sin(\\theta) \\\\ 0 &amp; 0 &amp; 1 &amp; 0 \\\\ 0 &amp; -\\sin(\\theta) &amp; 0 &amp; \\cos(\\theta) \\end{array}\\right)}_{\\large{{R_{xz}(\\theta)^\\mu}_\\nu}} \\underbrace{\\left(\\begin{array}{r} x^0 \\\\ {} x^1 \\\\ x^2 \\\\ x^3 \\end{array}\\right)}_{\\large{x^{\\nu}}} <\/span>\n<p><\/bdi><\/p>\n<p style=\"text-align:justify;\">\u8fd9\u4e9b\u53d8\u6362\u4fdd\u6301\u4e86\u4e0e\u5176\u4e09\u7ef4\u5bf9\u5e94\u7684\u76f8\u540c\u6027\u8d28\u3002<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u65f6\u7a7a\u53cc\u66f2\u65cb\u8f6c<\/h2>\n<p><a name=\"6\"><\/a><\/p>\n<h3>\u5f15\u5165\u901f\u5ea6\u53c2\u6570<\/h3>\n<p style=\"text-align:justify;\">\u901a\u8fc7\u5f15\u5165\u6240\u8c13\u7684<strong>\u901f\u5ea6\u53c2\u6570<\/strong>\u53ef\u4ee5\u5f97\u5230\u6d1b\u4f26\u5179\u53d8\u6362\u4e0e\u7a7a\u95f4\u65cb\u8f6c\u7684\u76f8\u4f3c\u6027\u3002<\/p>\n<p style=\"text-align:center;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_{ss^\\prime_x}= \\text{argtanh}(\\beta_{ss^\\prime_x}).<\/span><\/bdi><\/p>\n<p style=\"text-align:justify;\">\u7531\u4e8e<span class=\"katex-eq\" data-katex-display=\"false\">\\beta_{ss^\\prime_x}\\in]-1,1[<\/span>\uff0c\u56e0\u6b64<span class=\"katex-eq\" data-katex-display=\"false\">\\psi_{ss^\\prime_x}\\in\\mathbb{R}<\/span>\u3002\u6b64\u5916\u6ce8\u610f\u5230\uff0c\u4ece\u4e2d\u53ef\u4ee5\u5f97\u5230<span class=\"katex-eq\" data-katex-display=\"false\">\\gamma_{ss^\\prime_x}=\\cosh(\\psi_{ss^\\prime_x})<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">\\gamma_{ss^\\prime_x} \\beta_{ss^\\prime_x} = \\sinh(\\psi_{ss^\\prime_x})<\/span>\u3002\u8fd9\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u8ba1\u7b97\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align:justify;\">\u663e\u7136<bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_{ss^\\prime_x}= \\text{argtanh}(\\beta_{ss^\\prime_x})<\/span><\/bdi>\u7b49\u4ef7\u4e8e\u8bf4<bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\beta_{ss^\\prime_x} =\\tanh(\\psi_{ss^\\prime_x})<\/span><\/bdi>\uff1b\u56e0\u6b64\uff1a<\/p>\n<p style=\"text-align:center;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl} \\gamma^2_{ss^\\prime_x} &amp;= \\dfrac{1}{1-\\beta^2_{ss^\\prime_x}} \\\\ \\\\ &amp; = \\dfrac{1}{1-\\tanh^2(\\psi_{ss^\\prime_x})} \\\\ \\\\ {} &amp; = \\dfrac{\\cosh^2(\\psi_{ss^\\prime_x})}{\\cosh^2(\\psi_{ss^\\prime_x}) - \\sinh^2(\\psi_{ss^\\prime_x})} \\\\ \\\\ &amp; = \\cosh^2(\\psi_{ss^\\prime_x}) \\end{array}<\/span><\/bdi><\/p>\n<p style=\"text-align:justify;\">\u7531\u4e8e\u4f3d\u9a6c\u56e0\u5b50\u548c\u53cc\u66f2\u4f59\u5f26\u603b\u662f\u5927\u4e8e\u6216\u7b49\u4e8e1\uff0c\u6700\u540e\u53ef\u4ee5\u8bc1\u660e<bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma_{ss^\\prime_x} = \\cosh(\\psi_{ss^\\prime_x})<\/span><\/bdi>\u3002<\/p>\n<p style=\"text-align:justify;\">\u7c7b\u4f3c\u5730\uff0c\u7ee7\u7eed\u4ee5\u524d\u7684\u8ba1\u7b97\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align:center;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma^2_{ss^\\prime_x} \\beta^2_{ss^\\prime_x} = \\cosh^2(\\psi_{ss^\\prime_x}) \\tanh^2(\\psi_{ss^\\prime_x})= \\sinh^2(\\psi_{ss^\\prime_x})<\/span>.<\/bdi><\/p>\n<p style=\"text-align:justify;\">\u56e0\u6b64<bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma_{ss^\\prime_x} \\beta_{ss^\\prime_x} = \\sinh(\\psi_{ss^\\prime_x})<\/span><\/bdi>\u3002<\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u5c06\u65f6\u7a7a\u65cb\u8f6c\u516c\u5f0f\u5316\u4e3a\u53cc\u66f2\u65cb\u8f6c<\/h3>\n<p style=\"text-align:justify;\">\n\u5230\u8fd9\u91cc\uff0c\u6211\u4eec\u73b0\u5728\u53ef\u4ee5\u7528\u901f\u5ea6\u53c2\u6570\u91cd\u65b0\u7f16\u5199\u6d1b\u4f26\u5179\u53d8\u6362\u4e2d\u7684\u901f\u5ea6\u63d0\u5347\u56e0\u5b50\u548c\u4f3d\u9a6c\u56e0\u5b50\u3002\u8003\u8651\u4e24\u4e2a\u60ef\u6027\u7cfb<span class=\"katex-eq\" data-katex-display=\"false\">S<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span>\u5728\u6807\u51c6\u914d\u7f6e\u4e2d\uff0c\u5176\u4e2d\u7b2c\u4e8c\u4e2a\u5728<span class=\"katex-eq\" data-katex-display=\"false\">x<\/span>\u8f74\u4e0a\u65bd\u52a0\u4e86\u901f\u5ea6\u63d0\u5347\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">\\beta_{ss^\\prime_x}<\/span>\uff0c\u6709\uff1a\n<\/p>\n<p style=\"text-align:center;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl} ct^\\prime &amp;= \\gamma_{ss^\\prime_x}(ct - \\beta_{ss^\\prime_x} x) \\\\ &amp;= \\gamma_{ss^\\prime_x} ct - \\gamma_{ss^\\prime_x}\\beta_{ss^\\prime_x} x \\\\ &amp;= ct\\cosh(\\psi_{ss^\\prime_x}) - x\\sinh(\\psi_{ss^\\prime_x}), \\\\ \\\\ x^\\prime &amp;= \\gamma_{ss^\\prime_x}(x - \\beta_{ss^\\prime_x} ct) \\\\ &amp;= -\\gamma_{ss^\\prime_x}\\beta_{ss^\\prime_x} ct + \\gamma_{ss^\\prime_x}x \\\\ &amp;= -ct \\sinh(\\psi_{ss^\\prime_x}) + x\\cosh(\\psi_{ss^\\prime_x}), \\\\ \\\\ y^\\prime &amp;= y, \\\\ \\\\\n\nz^\\prime &amp;= z. \\end{array} <\/span><\/bdi><\/p>\n<p style=\"text-align:justify;\">\u8fd9\u79cd\u65b9\u7a0b\u7ec4\u53ef\u4ee5\u8868\u793a\u4e3a\u4ee5\u4e0b\u77e9\u9635\u5f62\u5f0f\uff1a<\/p>\n<p style=\"text-align:center;\"><strong>tx\u5e73\u9762\u4e0a\u7684\u65f6\u7a7a\u53cc\u66f2\u65cb\u8f6c\uff1a<\/strong><\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl} \\underbrace{\\left( \\begin{array}{c} ct^\\prime \\\\ x^\\prime \\\\ y^\\prime \\\\ z^\\prime \\end{array} \\right)}_{\\large{x^{\\prime \\mu}}} &amp;= \\underbrace{\\left( \\begin{array}{cccc} \\cosh(\\psi_{ss^\\prime_x}) &amp; -\\sinh(\\psi_{ss^\\prime_x}) &amp; 0 &amp; 0 \\\\ - \\sinh(\\psi_{ss^\\prime_x}) &amp; \\cosh(\\psi_{ss^\\prime_x}) &amp; 0 &amp; 0 \\\\\n\n{} 0 &amp; 0 &amp; 1 &amp; 0 \\\\ 0 &amp; 0 &amp; 0 &amp; 1 \\end{array}\\right)}_{\\large{{R_{tx}(\\psi_{ss^\\prime_x})^\\mu}_\\nu}} \\underbrace{\\left( \\begin{array}{c} ct \\\\ x \\\\ y \\\\ z \\end{array} \\right)}_{\\large{x^{\\nu}}} \\end{array} <\/span>\n<p style=\"text-align:justify;\">\u7c7b\u4f3c\u5730\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u6bcf\u4e2a\u65f6\u7a7a\u5e73\u9762\u7684\u53cc\u66f2\u65cb\u8f6c\uff1a<\/p>\n<p style=\"text-align:center;\"><strong>ty\u5e73\u9762\u4e0a\u7684\u65f6\u7a7a\u53cc\u66f2\u65cb\u8f6c\uff1a<\/strong><\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl} \\underbrace{\\left( \\begin{array}{c} ct^\\prime \\\\ x^\\prime \\\\ y^\\prime \\\\ z^\\prime \\end{array} \\right)}_{\\large{x^{\\prime \\mu}}} &amp;= \\underbrace{\\left(\\begin{array}{cccc} \\cosh(\\psi_{ss^\\prime_y}) &amp; 0 &amp; -\\sinh(\\psi_{ss^\\prime_y}) &amp; 0 \\\\ 0 &amp; 1 &amp; 0 &amp; 0 \\\\ {} - \\sinh(\\psi_{ss^\\prime_y}) &amp; 0 &amp; \\cosh(\\psi_{ss^\\prime_y}) &amp; 0 \\\\ 0 &amp; 0 &amp; 0 &amp; 1 \\end{array}\\right)}_{\\large{{R_{ty}(\\psi_{ss^\\prime_y})^\\mu}_\\nu}} \\underbrace{\\left( \\begin{array}{c} ct \\\\ x \\\\ y \\\\ z \\end{array} \\right)}_{\\large{x^{\\nu}}} \\end{array} <\/span>\n<p style=\"text-align:center;\"><strong>tz\u5e73\u9762\u4e0a\u7684\u65f6\u7a7a\u53cc\u66f2\u65cb\u8f6c\uff1a<\/strong><\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl} \\underbrace{\\left( \\begin{array}{c} ct^\\prime \\\\ x^\\prime \\\\ y^\\prime \\\\ z^\\prime \\end{array} \\right)}_{\\large{x^{\\prime \\mu}}} &amp;= \\underbrace{\\left( \\begin{array}{cccc} \\cosh(\\psi_{ss^\\prime_z}) &amp; 0 &amp; 0 &amp; -\\sinh(\\psi_{ss^\\prime_z}) \\\\ 0 &amp; 1 &amp; 0 &amp; 0 \\\\ 0 &amp; 0 &amp; 1 &amp; 0 \\\\ {} - \\sinh(\\psi_{ss^\\prime_z}) &amp; 0 &amp; 0 &amp; \\cosh(\\psi_{ss^\\prime_z}) \\end{array}\\right)}_{\\large{{R_{tz}(\\psi_{ss^\\prime_z})^\\mu}_\\nu}} \\underbrace{\\left( \\begin{array}{c} ct \\\\ x \\\\ y \\\\ z \\end{array} \\right)}_{\\large{x^{\\nu}}} \\end{array} <\/span>\n<p style=\"text-align:justify;\">\n\u7531\u4e8e\u5176\u5f62\u5f0f\u548c\u4ee3\u6570\u6027\u8d28\uff0c\u8fd9\u4e9b\u53d8\u6362\u4e0e\u7a7a\u95f4\u65cb\u8f6c\u975e\u5e38\u76f8\u4f3c\uff0c\u53ea\u662f\u4f7f\u7528\u53cc\u66f2\u51fd\u6570\u800c\u4e0d\u662f\u4e09\u89d2\u51fd\u6570\u3002\u867d\u7136\u5b83\u4eec\u4e0d\u662f\u4e25\u683c\u610f\u4e49\u4e0a\u7684\u65cb\u8f6c\uff0c\u4f46\u5b83\u4eec\u4e0e\u4e00\u5f00\u59cb\u5ba1\u67e5\u7684\u65cb\u8f6c\u6709\u4e00\u5b9a\u7684\u76f8\u4f3c\u6027\u3002\u4f8b\u5982\uff0c\u7c7b\u4f3c\u4e8e\u65cb\u8f6c\uff0c\u9006\u53d8\u6362\u901a\u8fc7\u5c06\u76f8\u5e94\u7684\u901f\u5ea6\u53c2\u6570<span class=\"katex-eq\" data-katex-display=\"false\">\\psi<\/span>\u66ff\u6362\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">-\\psi<\/span>\u6765\u83b7\u5f97\u3002\u8fd9\u4e9b\u53d8\u6362\u6709\u65f6\u88ab\u79f0\u4e3a<strong>\u53cc\u66f2\u65cb\u8f6c<\/strong>\uff0c\u901f\u5ea6\u53c2\u6570\u4e5f\u79f0\u4e3a<strong>\u53cc\u66f2\u89d2<\/strong>\u3002\n<\/p>\n<p><a name=\"8\"><\/a><\/p>\n<div style=\"background-color:#F3F3F3; padding:20px;\">\n<h2>\u7ed3\u8bba<\/h2>\n<p style=\"text-align:justify;\">\n        \u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u5df2\u7ecf\u5168\u9762\u8ba8\u8bba\u4e86\u95f5\u53ef\u592b\u65af\u57fa\u65f6\u7a7a\u4e2d\u7684\u65cb\u8f6c\u6982\u5ff5\uff0c\u8fd9\u4f7f\u6211\u4eec\u80fd\u591f\u66f4\u6df1\u5165\u5730\u7406\u89e3\u6d1b\u4f26\u5179\u53d8\u6362\u3002\u901a\u8fc7\u8fd9\u9879\u7814\u7a76\uff0c\u6211\u4eec\u8fbe\u5230\u4e86\u4ee5\u4e0b\u5173\u952e\u70b9\uff1a\n    <\/p>\n<ul>\n<li><strong>\u91cd\u65b0\u89e3\u91ca\u6d1b\u4f26\u5179\u53d8\u6362<\/strong>\uff1a\u6211\u4eec\u5b66\u4f1a\u4e86\u5c06\u6d1b\u4f26\u5179\u53d8\u6362\u4e0d\u4ec5\u89c6\u4e3a\u7531\u4e8e\u4e0d\u540c\u53c2\u8003\u7cfb\u800c\u5f15\u8d77\u7684\u5750\u6807\u53d8\u5316\uff0c\u8fd8\u89c6\u4e3a\u65f6\u7a7a\u65cb\u8f6c\u3002<\/li>\n<li><strong>\u7406\u89e3\u95f5\u53ef\u592b\u65af\u57fa\u65f6\u7a7a\u4e2d\u7684\u65cb\u8f6c<\/strong>\uff1a\u6211\u4eec\u8be6\u7ec6\u68c0\u67e5\u4e86\u56db\u7ef4\u95f5\u53ef\u592b\u65af\u57fa\u7a7a\u95f4\u5185\u7684\u65cb\u8f6c\u3002<\/li>\n<li><strong>\u63a2\u7d22\u65f6\u7a7a\u53cc\u66f2\u65cb\u8f6c<\/strong>\uff1a\u6700\u540e\uff0c\u6211\u4eec\u5f15\u5165\u4e86\u65f6\u7a7a\u53cc\u66f2\u65cb\u8f6c\u7684\u6982\u5ff5\uff0c\u68c0\u67e5\u4e86\u5176\u4e0e\u5e38\u89c4\u7a7a\u95f4\u65cb\u8f6c\u7684\u76f8\u4f3c\u4e4b\u5904\u3002<\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u65f6\u7a7a\u53cc\u66f2\u65cb\u8f6c \u6458\u8981\uff1a 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