{"id":25664,"date":"2022-07-18T00:00:08","date_gmt":"2022-07-18T00:00:08","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=25664"},"modified":"2024-05-21T09:42:22","modified_gmt":"2024-05-21T09:42:22","slug":"%e7%89%b9%e6%ae%8a%e7%9b%b8%e5%af%b9%e8%ae%ba%e4%b8%ad%e7%9a%84%e6%b4%9b%e4%bc%a6%e5%85%b9%e5%8f%98%e6%8d%a2","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e7%89%b9%e6%ae%8a%e7%9b%b8%e5%af%b9%e8%ae%ba%e4%b8%ad%e7%9a%84%e6%b4%9b%e4%bc%a6%e5%85%b9%e5%8f%98%e6%8d%a2\/","title":{"rendered":"\u7279\u6b8a\u76f8\u5bf9\u8bba\u4e2d\u7684\u6d1b\u4f26\u5179\u53d8\u6362"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u6d1b\u4f26\u5179\u53d8\u6362\u4e0e\u72ed\u4e49\u76f8\u5bf9\u8bba<\/h1>\n<p class=\"eq\"><em><strong>\u6458\u8981\uff1a<\/strong><br \/>\n\u6d1b\u4f26\u5179\u53d8\u6362\u5141\u8bb8\u6211\u4eec\u5728\u4e24\u4e2a\u60ef\u6027\u53c2\u7167\u7cfb\u4e4b\u95f4\u8f6c\u6362\u89c2\u5bdf\u5230\u7684\u7a7a\u95f4\u548c\u65f6\u95f4\u5750\u6807\u3002\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u56de\u987e\u6d1b\u4f26\u5179\u53d8\u6362\u5982\u4f55\u4f5c\u4e3a\u8003\u8651\u5149\u901f\u5728\u6240\u6709\u60ef\u6027\u53c2\u7167\u7cfb\u4e2d\u4e3a\u5e38\u6570\u7684\u60c5\u51b5\u4e0b\u4ea7\u751f\u7684\u5750\u6807\u7684\u7ebf\u6027\u53d8\u6362\uff0c\u5e76\u5728\u4e0e\u5149\u901f\u76f8\u6bd4\u8f83\u5c0f\u7684\u901f\u5ea6\u65f6\u8d8b\u5411\u4e8e\u4f3d\u5229\u7565\u53d8\u6362\u3002<\/br><\/em><\/p>\n<p><\/center><\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5728\u5b8c\u6210\u8fd9\u8282\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a<\/p>\n<ol>\n<li><strong>\u8bc6\u522b<\/strong>\u72ed\u4e49\u76f8\u5bf9\u8bba\u7684\u5173\u952e\u6982\u5ff5\uff0c\u5982\u6d1b\u4f26\u5179\u53d8\u6362\u3001\u00bb\u901f\u5ea6\u63d0\u5347\u00bb\u548c\u00bb\u6d1b\u4f26\u5179\u56e0\u5b50\u00bb\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u5149\u901f\u5728\u6240\u6709\u60ef\u6027\u6846\u67b6\u4e2d\u4e3a\u5e38\u6570\u8fd9\u4e00\u539f\u7406\u662f\u5982\u4f55\u5f71\u54cd\u5bf9\u65f6\u95f4\u548c\u7a7a\u95f4\u7684\u611f\u77e5\u7684\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u6d1b\u4f26\u5179\u53d8\u6362\u4e8e\u5177\u4f53\u60c5\u51b5\uff0c\u5982\u60ef\u6027\u6846\u67b6\u4e0e\u5149\u901f\u5728\u4e0d\u540c\u53c2\u7167\u7cfb\u4e2d\u7684\u5173\u7cfb\u3002<\/li>\n<li><strong>\u6574\u5408<\/strong>\u4f3d\u5229\u7565\u53d8\u6362\u548c\u72ed\u4e49\u76f8\u5bf9\u8bba\u7684\u5148\u524d\u77e5\u8bc6\uff0c\u4e86\u89e3\u6d1b\u4f26\u5179\u53d8\u6362\u5982\u4f55\u6982\u62ec\u5e76\u8d8b\u540c\u4e8e\u5b83\u4eec\u3002<\/li>\n<li><strong>\u5206\u89e3<\/strong>\u6d1b\u4f26\u5179\u53d8\u6362\u7684\u57fa\u672c\u7ec4\u6210\u90e8\u5206\uff0c\u5982\u5149\u901f\u7684\u6052\u5b9a\u6027\u548c\u5750\u6807\u53d8\u6362\u7684\u7ebf\u6027\u3002<\/li>\n<\/ol>\n<p><center><\/p>\n<p><strong>\u76ee\u5f55<\/strong><br \/>\n<a href=\"#1\"><strong>\u65b0\u7684\u8003\u8651<\/strong><\/a><br \/>\n<a href=\"#2\"><strong>\u6d1b\u4f26\u5179\u53d8\u6362\u7684\u63a8\u5bfc<\/strong><\/a><br \/>\n<a href=\"#3\">\u5173\u4e8e\u5750\u6807\uff08\u7ebf\u6027\uff09\u53d8\u6362\u7684\u56de\u987e<\/a><br \/>\n<a href=\"#4\">\u5f15\u5165\u5149\u901f\u4f5c\u4e3a\u666e\u904d\u5e38\u6570<\/a><br \/>\n<a href=\"#5\">\u901f\u5ea6\u63d0\u5347\u548c\u6d1b\u4f26\u5179\u56e0\u5b50<\/a><br \/>\n<a href=\"#6\">\u6d1b\u4f26\u5179\u53d8\u6362\u7684\u7efc\u5408<\/a><br \/>\n<a href=\"#7\"><strong>\u6d1b\u4f26\u5179\u53d8\u6362\u4e0e\u4f3d\u5229\u7565\u53d8\u6362\u7684\u6c47\u805a\u4e0e\u6982\u62ec<\/strong><\/a>\n<\/p>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/KQby8yJGTSA\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center>\n<\/div>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u65b0\u7684\u8003\u8651<\/h2>\n<p style=\"text-align:justify;\">\u4f5c\u4e3a\u5728<a href=\"http:\/\/toposuranos.com\/material\/zh\/%e5%85%89%e9%80%9f%e4%b8%8e%e7%94%b5%e7%a3%81%e6%b3%a2\/\" rel=\"noopener\" target=\"_blank\">\u771f\u7a7a\u4e2d\u7535\u78c1\u6ce2\u4f20\u64ad<\/a>\u4e2d\u6240\u89c1\u7684\u7ed3\u679c\uff0c\u5728\u72ed\u4e49\u76f8\u5bf9\u8bba\u4e2d\uff0c\u6211\u4eec\u5c06\u5149\u901f<span class=\"katex-eq\" data-katex-display=\"false\">&lt;bdi&gt;c&lt;\/bdi&gt;<\/span>\u5bf9\u6240\u6709\u60ef\u6027\u53c2\u7167\u7cfb\u90fd\u662f\u76f8\u540c\u7684\u8fd9\u4e00\u4e8b\u5b9e\u4f5c\u4e3a\u4e00\u4e2a\u539f\u5219\u3002\u4f46\u8fd9\u6837\u7684\u5047\u8bbe\u5e76\u975e\u6ca1\u6709\u4ee3\u4ef7\uff0c\u56e0\u4e3a\u5b83\u5e26\u6765\u4e86\u4ee5\u4e0b\u542b\u4e49\uff1a<\/p>\n<ol>\n<li>\u5fc5\u987b\u653e\u5f03\u4f7f\u7528\u4f3d\u5229\u7565\u53d8\u6362\u4f5c\u4e3a\u5c06\u4e00\u4e2a\u60ef\u6027\u6846\u67b6\u4e2d\u7684\u89c2\u5bdf\u8f6c\u6362\u4e3a\u53e6\u4e00\u4e2a\u6846\u67b6\u4e2d\u7684\u6709\u6548\u624b\u6bb5\u3002<\/li>\n<li>\u5fc5\u987b\u629b\u5f03\u76f4\u89c2\u7684\u89c2\u5ff5\uff0c\u5373\u65f6\u95f4\u5bf9\u6240\u6709\u60ef\u6027\u53c2\u7167\u7cfb\u90fd\u4ee5\u76f8\u540c\u65b9\u5f0f\u6d41\u901d\u3002<\/li>\n<\/ol>\n<p style=\"text-align:justify;\">\u6b63\u662f\u901a\u8fc7\u8fd9\u4e9b\u8003\u8651\uff0c\u6211\u4eec\u5f97\u5230\u4e86<strong>\u6d1b\u4f26\u5179\u53d8\u6362\uff0c<\/strong>\u5b83\u4f5c\u4e3a\u4f3d\u5229\u7565\u53d8\u6362\u7684\u4fee\u6b63\u548c\u6982\u62ec\uff0c\u5e76\u4e14\u540c\u6837\u9002\u7528\u4e8e\u7535\u78c1\u7406\u8bba\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u6d1b\u4f26\u5179\u53d8\u6362\u7684\u63a8\u5bfc<\/h2>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u5173\u4e8e\u5750\u6807\uff08\u7ebf\u6027\uff09\u53d8\u6362\u7684\u56de\u987e<\/h3>\n<p style=\"text-align:justify;\">\u8003\u8651\u4e24\u4e2a\u60ef\u6027\u53c2\u8003\u7cfb<span class=\"katex-eq\" data-katex-display=\"false\">S<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span>\uff0c\u5b83\u4eec\u5904\u4e8e\u6807\u51c6\u914d\u7f6e\uff0c\u5373\u7b2c\u4e8c\u4e2a\u539f\u70b9\u4ee5\u6052\u5b9a\u901f\u5ea6<span class=\"katex-eq\" data-katex-display=\"false\">\\vec{v}_0 = v_{x_0}\\hat{x}<\/span>\u76f8\u5bf9\u4e8e\u7b2c\u4e00\u4e2a\u539f\u70b9\u8fd0\u52a8\u3002\u4e0b\u9762\u5c06\u8bc1\u660e\uff0c\u5982\u679c\u4ece\u4e24\u4e2a\u60ef\u6027\u7cfb\u7edf<span class=\"katex-eq\" data-katex-display=\"false\">S<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span>\u89c2\u5bdf\u5230\u7684\u4e8b\u4ef6\u5750\u6807\u901a\u8fc7\u7ebf\u6027\u53d8\u6362\uff08\u5982\u5728<a href=\"http:\/\/toposuranos.com\/material\/zh\/%e7%89%b9%e6%ae%8a%e7%9b%b8%e5%af%b9%e6%80%a7%e5%8e%9f%e7%90%86\/\" rel=\"noopener\" target=\"_blank\">\u76f8\u5bf9\u6027\u539f\u7406<\/a>\u4e2d\u63d0\u5230\u7684\uff0c\u7279\u522b\u662f<a href=\"http:\/\/toposuranos.com\/material\/zh\/%e7%89%b9%e6%ae%8a%e7%9b%b8%e5%af%b9%e6%80%a7%e5%8e%9f%e7%90%86\/#eq2\" rel=\"noopener\" target=\"_blank\">\u8fd9\u4e2a\u8868\u8fbe\u5f0f<\/a>\uff09\u76f8\u5173\uff0c\u5e76\u4e14\u63a5\u53d7\u5149\u901f\u5728\u6240\u6709\u60ef\u6027\u53c2\u8003\u7cfb\u4e2d\u90fd\u76f8\u540c\u7684\u4e8b\u5b9e\uff0c\u90a3\u4e48\u5750\u6807\u53d8\u6362\u6070\u597d\u5bf9\u5e94\u4e8e\u6211\u4eec\u7a0d\u540e\u5c06\u83b7\u5f97\u7684\u6d1b\u4f26\u5179\u53d8\u6362\u3002<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio.png\" alt=\"\" width=\"1374\" height=\"741\" class=\"aligncenter size-full wp-image-25502 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio.png\" alt=\"\" width=\"1374\" height=\"741\" class=\"aligncenter size-full wp-image-25502 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio.png 1374w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio-300x162.png 300w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio-1024x552.png 1024w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio-768x414.png 768w\" sizes=\"(max-width: 1374px) 100vw, 1374px\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align:justify;\">\u539f\u5219\u4e0a\uff0c\u4ece<span class=\"katex-eq\" data-katex-display=\"false\">S<\/span>\u89c2\u5bdf\u5230\u7684\u4e8b\u4ef6\u7684\u5750\u6807<span class=\"katex-eq\" data-katex-display=\"false\">(t,x)<\/span>\uff0c\u4ee5\u53ca\u4ece\u76f8\u5bf9\u4e8e<span class=\"katex-eq\" data-katex-display=\"false\">S<\/span>\u4ee5\u901f\u5ea6<span class=\"katex-eq\" data-katex-display=\"false\">v_{v}=v_{x_0}\\hat{x}<\/span>\u79fb\u52a8\u7684<span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span>\u89c2\u5bdf\u5230\u7684\u540c\u4e00\u4e8b\u4ef6\u7684\u5750\u6807<span class=\"katex-eq\" data-katex-display=\"false\">(t^\\prime, x^\\prime)<\/span>\uff0c\u901a\u8fc7\u4ee5\u4e0b\u7ebf\u6027\u53d8\u6362\u76f8\u5173\u8054\uff1a<\/p>\n<p><a name=\"eq1\"><\/a><a name=\"eq2\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\begin{array}{llr} t^\\prime &amp;= At + Bx, &amp; [1]\\\\ x^\\prime &amp;= Dt + Ex &amp; [2]  \\end{array} <\/span>\n<p style=\"text-align:justify;\" >\u5176\u4e2d<span class=\"katex-eq\" data-katex-display=\"false\">A, B, C<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">D<\/span>\u662f\u5f85\u89e3\u7684\u5e38\u6570\uff0c\u4e3a\u4e86\u7b80\u5316\u95ee\u9898\uff0c\u6211\u4eec\u7701\u7565\u4e86\uff08\u4e0d\u5931\u4e00\u822c\u6027\uff09\u5750\u6807<span class=\"katex-eq\" data-katex-display=\"false\">y<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">z<\/span>\u3002<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u5c06\u5149\u901f\u5f15\u5165\u4f5c\u4e3a\u4e00\u4e2a\u666e\u904d\u5e38\u6570<\/h3>\n<p style=\"text-align:justify;\">\u8fd9\u4e9b\u5e38\u6570<span class=\"katex-eq\" data-katex-display=\"false\">A, B, D<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">E<\/span>\u53ef\u4ee5\u6839\u636e\u8fd9\u4e9b\u65b0\u7684\u8003\u8651\u6765\u786e\u5b9a\uff0c\u9996\u5148\u8981\u6ce8\u610f\u7684\u662f\uff0c\u901a\u8fc7<a href=\"#eq1\">[1]<\/a>\u548c<a href=\"#eq2\">[2]<\/a>\u8868\u8fbe\u7684\u5750\u6807\u53d8\u6362\u5fc5\u987b\u59cb\u7ec8\u6709\u6548\uff0c\u56e0\u6b64\uff0c\u5b83\u4eec\u5fc5\u987b\u5728\u6bcf\u4e00\u4e2a\u7279\u6b8a\u60c5\u51b5\u4e0b\u90fd\u6709\u6548\uff0c\u800c\u8fd9\u4e9b\u7279\u6b8a\u60c5\u51b5\u5c06\u5728\u4e0b\u9762\u5217\u51fa\u4ee5\u63a2\u8ba8\u5b83\u4eec\u7684\u5f62\u5f0f\uff1a<\/p>\n<ul>\n<li>\n<p><strong>\u8003\u8651\u4e8b\u4ef6\u4ee5\u5149\u901f\u8fd0\u52a8\uff1a<\/strong>\u5982\u679c\u4e8b\u4ef6\u5728<span class=\"katex-eq\" data-katex-display=\"false\">S<\/span>\u89c2\u5bdf\u5230\u7684\u5750\u6807\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">(t,x)<\/span>\uff0c\u5728<span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span>\u89c2\u5bdf\u5230\u7684\u5750\u6807\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">(t^\\prime, x^\\prime)<\/span>\uff0c\u90a3\u4e48\u5b83\u4eec\u5fc5\u987b\u6ee1\u8db3\u5173\u7cfb\uff1a<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\frac{x^2}{t^2} = c^2 = \\frac{{x^\\prime}^2}{{t^\\prime}^2}.<\/span>\n<p>\u4ece\u8fd9\u91cc\u53ef\u4ee5\u63a8\u65ad\u51fa<\/p>\n<p><a name=\"eq3\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">c^2 t^2 - x^2 = c^2{t^\\prime}^2 - {x^\\prime}^2 = 0\\;\\;\\; [3]<\/span>\n<\/li>\n<li>\n<p><strong>\u8003\u8651\u4e8b\u4ef6\u4e0e\u60ef\u6027\u53c2\u8003\u7cfb<span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span>\u4e00\u8d77\u79fb\u52a8\uff1a<\/strong><\/p>\n<p>\u5982\u679c\u4e8b\u4ef6\u4e0e\u60ef\u6027\u53c2\u8003\u7cfb<span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span>\u7684\u539f\u70b9\u5177\u6709\u76f8\u540c\u7684\u5750\u6807\uff0c\u90a3\u4e48\u5c06\u6709<span class=\"katex-eq\" data-katex-display=\"false\">x=v_0 t<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">x^\\prime =0<\/span>\u3002\u56e0\u6b64\uff0c\u6839\u636e\u65b9\u7a0b<a href=\"#eq2\">[2]<\/a>\uff1a<\/p>\n<p><a name=\"eq4\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl} &amp; 0 = Dt + Ev_0 t \\\\ \\equiv &amp; D = -Ev_0\\:\\:\\;[4] \\end{array}<\/span>\n<\/li>\n<li>\n<p><strong>\u6700\u540e\uff0c\u8003\u8651\u4e8b\u4ef6\u4fdd\u6301\u5728\u60ef\u6027\u53c2\u8003\u7cfb<span class=\"katex-eq\" data-katex-display=\"false\">S<\/span>\u7684\u539f\u70b9\u9644\u8fd1\uff1a<\/strong><\/p>\n<p style=\"text-align:justify;\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5c06\u6709<span class=\"katex-eq\" data-katex-display=\"false\">x=0<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">x^\\prime = -v_0 t^\\prime<\/span>\uff0c\u56e0\u6b64\u6839\u636e\u65b9\u7a0b<a href=\"#eq2\">[2]<\/a>\uff1a<\/p>\n<p><a name=\"eq5\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl} &amp;-v_0t^\\prime = Dt\\\\ \\equiv &amp; t= \\displaystyle -\\frac{v_0}{D} t^\\prime\\;\\;\\;[5] \\end{array}<\/span>\n<p style=\"text-align:justify;\">\u7136\u540e\uff0c\u6839\u636e<a href=\"#eq1\">[1]<\/a>\u548c<a href=\"#eq5\">[5]<\/a>\uff1a<\/p>\n<p><a name=\"eq6\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\begin{array}{rl} &amp; t^\\prime = A \\left(\\displaystyle -\\frac{v_0}{D}\\right) t^\\prime + \\underbrace{Bx}_{x=0} \\\\ \\\\ \\equiv &amp; \\displaystyle \\frac{-Av_0}{D} = 1 \\\\ \\\\ \\equiv &amp; D = -Av_0\\;\\;\\;[6] \\end{array}<\/span>\n<\/li>\n<\/ul>\n<p style=\"text-align:justify;\">\u6700\u540e\uff0c\u4ece<a href=\"#eq4\">[4]<\/a>\u548c<a href=\"#eq6\">[6]<\/a>\u5f97\u51fa\uff1a<span class=\"katex-eq\" data-katex-display=\"false\">A = E<\/span>\uff0c\u56e0\u6b64\u7531<a href=\"#eq1\">[1]<\/a>\u548c<a href=\"#eq2\">[2]<\/a>\u7ed9\u51fa\u7684\u65b9\u7a0b\u7ec4\u7b80\u5316\u4e3a\uff1a<\/p>\n<p><a name=\"eq7\"><\/a> <a name=\"eq8\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll} t^\\prime &amp;= At + Bx  &amp;  [7]\\\\ \\\\ x^\\prime &amp;= A(x - v_{x_0} t) &amp; [8] \\end{array}<\/span>\n<p><a name=\"5\"><\/a><\/p>\n<h3>\u901f\u5ea6\u63d0\u5347\u548c\u6d1b\u4f26\u5179\u56e0\u5b50<\/h3>\n<p style=\"text-align:justify;\">\u73b0\u5728\uff0c\u5c06<a href=\"#eq7\">[7]<\/a>\u548c<a href=\"#eq8\">[8]<\/a>\u66ff\u6362\u8fdb<a href=\"#eq3\">[3]<\/a>\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\begin{array}{rl} &amp; c^2 (At +Bx)^2 - A^2 (x - v_{x_0} t)^2 = c^2t^2 - x^2\\\\ \\\\ \\equiv\\; &amp; \\color{blue}{(c^2 A^2) t^2} + \\color{red}{(2c^2 AB)xt} \\color{black} + c^2 B^2 x^2 -  A^2 x^2 + \\color{red} {(2A^2v_{x_0})xt} \\color{black}- \\color{blue}{(A^2 v_{x_0}^2) t^2} \\color{black}= \\color{blue}{(c^2) t^2} \\color{black}- x^2. \\end{array}<\/span>\n<p style=\"text-align:justify;\"><span style=\"color:blue\"><strong>\u4ece\u84dd\u8272\u90e8\u5206\u6211\u4eec\u5f97\u5230\uff1a<\/strong><\/span><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\begin{array}{rl} &amp;c^2 A^2 - A^2 v_{x_0}^2 = c^2 \\\\ \\\\ \\equiv\\;&amp; A^2 (c^2 - v_{x_0}^2) = c^2 \\\\ \\\\ \\equiv\\;&amp; \\displaystyle A^2 = \\frac{c^2}{c^2 - v_{x_0}^2} = \\frac{1}{1 - \\frac{v_{x_0}^2}{c^2}}  \\\\ \\equiv\\;&amp; \\displaystyle A = \\frac{1}{\\sqrt{1 - \\frac{v_{x_0}^2}{c^2}}} \\end{array}<\/span>\n<p><p style=\"text-align:justify;\">\u901a\u5e38\u6211\u4eec\u5c06<span class=\"katex-eq\" data-katex-display=\"false\">A=\\gamma_x<\/span>\uff08\u6d1b\u4f26\u5179\u6536\u7f29\u56e0\u5b50\uff09\u548c<span class=\"katex-eq\" data-katex-display=\"false\">\\beta_x = v_{x_0}\/c<\/span>\uff08\u901f\u5ea6\u63d0\u5347\uff09\uff0c\u6700\u7ec8\u5f62\u5f0f\u4e3a\uff1a<\/p>\n<p><a name=\"eq9\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle A = \\gamma_x = \\frac{1}{\\sqrt{1 - \\beta_x^2}},\\;\\;\\;[9]<\/span>\n<p style=\"text-align:justify;\">\u5c06<a href=\"#eq9\">[9]<\/a>\u66ff\u6362\u8fdb<a href=\"#eq2\">[2]<\/a>\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">x^\\prime = \\gamma_x(x - \\beta_x ct)<\/span>\n<p style=\"text-align:justify;\"><span style=\"color:red\"><strong>\u4ece\u7ea2\u8272\u90e8\u5206\u6211\u4eec\u5f97\u5230\uff1a<\/strong><\/span><\/p>\n<p><a name=\"eq10\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\begin{array}{rll} &amp;2c^2 AB + 2A^2v_{x_{x_0}} = 0&amp; \\\\ \\\\ \\equiv\\;&amp; cB^2 + Av_{x_0} = 0 &amp; \\\\ \\\\ \\equiv\\;&amp; B=\\displaystyle -\\frac{1}{c^2}Av_{x_0} = -\\frac{\\gamma_x v_{x_0}}{c^2}&amp; \\\\ \\\\ \\equiv\\;&amp; B=\\displaystyle -\\frac{\\gamma_x \\beta_x}{c} &amp; [10] \\end{array}<\/span>\n<p style=\"text-align:justify;\">\u56e0\u6b64\uff0c\u5c06<a href=\"#eq9\">[9]<\/a>\u548c<a href=\"#eq10\">[10]<\/a>\u66ff\u6362\u8fdb<a href=\"#eq7\">[7]<\/a>\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl} &amp;t^\\prime =\\displaystyle \\gamma_x t -\\frac{\\gamma_x \\beta_x}{c} \\\\ \\\\ \\equiv\\; &amp;t^\\prime =\\displaystyle \\gamma_x \\left( t -\\frac{\\beta_x x}{c}\\right)\\\\ \\\\ \\equiv\\; &amp;ct^\\prime =\\displaystyle \\gamma_x \\left( ct - \\beta_x x \\right) \\end{array}<\/span>\n<p><a name=\"6\"><\/a><\/p>\n<h3>\u6d1b\u4f26\u5179\u53d8\u6362\u7684\u7efc\u5408<\/h3>\n<p style=\"text-align:justify;\">\u6700\u7ec8\uff0c\u4ece\u7cfb\u7edf<span class=\"katex-eq\" data-katex-display=\"false\">S<\/span>\u5230<span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span>\u7684\u5750\u6807\u53d8\u6362\u7ebf\u6027\u6a21\u578b\u53ef\u4ee5\u7528\u4e0b\u5217\u8868\u8fbe\u5f0f\u8868\u793a\u3002<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}ct^\\prime &amp;=\\gamma_x \\left( ct - \\beta_x x \\right) \\\\ x^\\prime &amp;= \\gamma_x(x - \\beta_x ct) \\end{array}<\/span>\n<p style=\"text-align:justify;\">\u8fd9\u5957\u53d8\u6362\u53ef\u4ee5\u4ee5\u77e9\u9635\u5f62\u5f0f\u8868\u793a\uff1a<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\left(\\begin{matrix}ct^\\prime \\\\ x^\\prime \\\\ y^\\prime \\\\ z^\\prime \\end{matrix}\\right) = \\left( \\begin{matrix}\\gamma_x &amp; -\\gamma_x\\beta_x &amp; 0 &amp; 0 \\\\ -\\gamma_x\\beta_x &amp; \\gamma_x &amp; 0 &amp; 0 \\\\  0 &amp; 0 &amp; 1 &amp; 0 \\\\ 0 &amp; 0 &amp; 0 &amp; 1 \\end{matrix} \\right) \\left(\\begin{matrix} ct \\\\ x \\\\ y \\\\ z \\end{matrix} \\right)\n\n<\/span>\n<p style=\"text-align:justify;\">\u8fd9\u5c31\u662f\u7279\u6b8a\u76f8\u5bf9\u8bba\u4e2d\u6240\u77e5\u7684\u6d1b\u4f26\u5179\u53d8\u6362\u3002<\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h2>\u6d1b\u4f26\u5179\u53d8\u6362\u4e0e\u4f3d\u5229\u7565\u53d8\u6362\u7684\u878d\u5408\u4e0e\u6982\u62ec<\/h2>\n<p style=\"text-align:justify;\">\u5f53\u53c2\u7167\u7cfb\u4e4b\u95f4\u7684\u901f\u5ea6\u8fdc\u5c0f\u4e8e\u5149\u901f\u65f6\uff0c\u6d1b\u4f26\u5179\u53d8\u6362\u5411\u4f3d\u5229\u7565\u53d8\u6362\u7684\u878d\u5408\u53ef\u4ee5\u660e\u663e\u770b\u51fa\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u6709\uff1a<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\"> |v_{x_0}| \\ll c \\longrightarrow \\left\\{\\begin{matrix}\\beta_x = \\frac{v_{x_0}}{c} \\approx 0 \\\\ \\\\ \\gamma_x = \\sqrt{1-\\beta_x} \\approx 1 \\\\ \\\\ \\gamma_x \\beta_x c = v_{x_0} \\gamma_x \\approx v_{x_0} \\end{matrix}\\right.  <\/span>\n<p style=\"text-align:justify;\">\u56e0\u6b64\uff1a<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\left(\\begin{matrix}ct^\\prime \\\\ x^\\prime \\\\ y^\\prime \\\\ z^\\prime \\end{matrix}\\right) = \\left( \\begin{matrix}\\gamma_x &amp; -\\gamma_x\\beta_x &amp; 0 &amp; 0 \\\\ -\\gamma_x\\beta_x &amp; \\gamma_x &amp; 0 &amp; 0 \\\\  0 &amp; 0 &amp; 1 &amp; 0 \\\\ 0 &amp; 0 &amp; 0 &amp; 1 \\end{matrix} \\right) \\left(\\begin{matrix} ct \\\\ x \\\\ y \\\\ z \\end{matrix} \\right) = \\left(\\begin{matrix} \\gamma_x ct  -\\gamma_x \\beta_x x \\\\ -\\gamma_x \\beta_x c t + \\gamma_x x \\\\ y \\\\ z \\end{matrix} \\right) \\approx \\left(\\begin{matrix} ct \\\\ -v_{x_0}t + x \\\\ y \\\\ z \\end{matrix}\\right)<\/span>\n<p style=\"text-align:justify;\">\u5373\uff1a<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\begin{array}{rl} t^\\prime &amp;\\approx t \\\\ x^\\prime &amp;\\approx x - v_{x_0}t \\\\ y^\\prime &amp;\\approx y \\\\ z^\\prime &amp;\\approx z \\end{array}\n\n<\/span>\n<p style=\"text-align:justify;\">\u8fd9\u6b63\u597d\u4e0e\u4f3d\u5229\u7565\u53d8\u6362\u76f8\u7b26\u3002\u901a\u8fc7\u6b64\uff0c\u6211\u4eec\u8bc1\u5b9e\u4e86\u6d1b\u4f26\u5179\u53d8\u6362\u4e0d\u4ec5\u662f\u4f3d\u5229\u7565\u53d8\u6362\u5728\u63a5\u8fd1\u5149\u901f\u65f6\u7684\u6982\u62ec\uff0c\u800c\u4e14\u5728\u8fdc\u5c0f\u4e8e\u5149\u901f\u7684\u901f\u5ea6\u65f6\uff0c\u5b83\u4eec\u4f1a\u878d\u5408\u4e3a\u4f3d\u5229\u7565\u53d8\u6362\u3002<\/p>\n<div style=\"background-color:#F3F3F3; padding:20px;\">\n<h2>\u7ed3\u8bba<\/h2>\n<p style=\"text-align:justify;\">\n        \u6211\u4eec\u6df1\u5165\u63a2\u8ba8\u4e86\u6d1b\u4f26\u5179\u53d8\u6362\uff0c\u8fd9\u662f\u7231\u56e0\u65af\u5766\u7279\u6b8a\u76f8\u5bf9\u8bba\u7684\u4e00\u4e2a\u57fa\u672c\u652f\u67f1\u3002\u901a\u8fc7\u4ed4\u7ec6\u5206\u6790\u548c\u89e3\u6790\uff0c\u6211\u4eec\u770b\u5230\u8fd9\u4e9b\u53d8\u6362\u662f\u5982\u4f55\u4ece\u5149\u901f\u5728\u6240\u6709\u60ef\u6027\u53c2\u8003\u7cfb\u4e2d\u6052\u5b9a\u8fd9\u4e00\u5047\u8bbe\u81ea\u7136\u800c\u7136\u5730\u4ea7\u751f\u7684\u3002\u6211\u4eec\u5c55\u793a\u4e86\u6d1b\u4f26\u5179\u53d8\u6362\u7684\u91cd\u8981\u6027\uff0c\u5b83\u4e0d\u4ec5\u662f\u5bf9\u4f3d\u5229\u7565\u53d8\u6362\u7684\u6982\u62ec\u548c\u4fee\u6b63\uff0c\u800c\u4e14\u8fd8\u662f\u7406\u89e3\u76f8\u5bf9\u8bba\u548c\u7535\u78c1\u7406\u8bba\u4e2d\u7269\u7406\u73b0\u8c61\u7684\u57fa\u672c\u6846\u67b6\u3002\n    <\/p>\n<p style=\"text-align:justify;\">\n        \u7406\u89e3\u8fd9\u4e9b\u5185\u5bb9\u5c06\u5e2e\u52a9\u5b66\u751f\u719f\u6089\u73b0\u4ee3\u7269\u7406\u5b66\u7684\u5173\u952e\u6982\u5ff5\uff0c\u5982\u201c\u901f\u5ea6\u63d0\u5347\u201d\u548c\u201c\u6d1b\u4f26\u5179\u56e0\u5b50\u201d\uff0c\u5e76\u5c06\u8fd9\u4e9b\u601d\u60f3\u5e94\u7528\u4e8e\u76f8\u5bf9\u8bba\u9886\u57df\u7684\u5177\u4f53\u60c5\u51b5\u3002\u6b64\u5916\uff0c\u6211\u4eec\u770b\u5230\uff0c\u5728\u8fdc\u5c0f\u4e8e\u5149\u901f\u7684\u901f\u5ea6\u6781\u9650\u4e0b\uff0c\u6d1b\u4f26\u5179\u53d8\u6362\u878d\u5408\u4e3a\u4f3d\u5229\u7565\u53d8\u6362\uff0c\u4ece\u800c\u8bc1\u660e\u4e86\u5b83\u4eec\u5728\u7814\u7a76\u8fd0\u52a8\u7269\u4f53\u52a8\u529b\u5b66\u4e2d\u7684\u901a\u7528\u6027\u548c\u591a\u529f\u80fd\u6027\u3002\n    <\/p>\n<p style=\"text-align:justify;\">\n        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