{"id":25610,"date":"2022-07-12T00:00:00","date_gmt":"2022-07-12T00:00:00","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=25610"},"modified":"2024-05-21T09:42:45","modified_gmt":"2024-05-21T09:42:45","slug":"%d8%aa%d8%ad%d9%88%d9%8a%d9%84%d8%a7%d8%aa-%d8%ac%d8%a7%d9%84%d9%8a%d9%84%d9%8a%d9%88-%d9%88%d9%82%d9%8a%d9%88%d8%af%d9%87%d8%a7","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ar\/%d8%aa%d8%ad%d9%88%d9%8a%d9%84%d8%a7%d8%aa-%d8%ac%d8%a7%d9%84%d9%8a%d9%84%d9%8a%d9%88-%d9%88%d9%82%d9%8a%d9%88%d8%af%d9%87%d8%a7\/","title":{"rendered":"\u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648 \u0648\u0642\u064a\u0648\u062f\u0647\u0627"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648 \u0648\u0642\u064a\u0648\u062f\u0647\u0627<\/h1>\n<p class=\"eq\"><em><strong>\u0645\u0644\u062e\u0635:<\/strong><br \/>\n\u062a\u0642\u062a\u0631\u062d \u0645\u0628\u062f\u0623 \u0627\u0644\u0646\u0633\u0628\u064a\u0629 \u0623\u0646 \u0627\u0644\u0645\u0644\u0627\u062d\u0638\u0627\u062a \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0625\u0637\u0627\u0631 \u0627\u0644\u0642\u0635\u0648\u0631\u064a\u060c \u0644\u0643\u0646 \u0628\u0637\u0631\u064a\u0642\u0629 \u062a\u0628\u0642\u0649 \u0641\u064a\u0647\u0627 \u0627\u0644\u0642\u0648\u0627\u0646\u064a\u0646 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a\u0629 \u062b\u0627\u0628\u062a\u0629. \u064a\u0623\u062a\u064a \u0627\u0644\u0646\u0647\u062c \u0627\u0644\u0623\u0648\u0644\u064a \u0648\u0627\u0644\u0628\u062f\u064a\u0647\u064a \u0644\u0647\u0630\u0627 \u0627\u0644\u0645\u0628\u062f\u0623 \u0645\u0646 \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648\u060c \u0627\u0644\u062a\u064a \u062a\u0646\u0645\u0630\u062c \u0643\u064a\u0641 \u062a\u062a\u063a\u064a\u0631 \u0627\u0644\u0645\u0644\u0627\u062d\u0638\u0627\u062a \u0628\u064a\u0646 \u0627\u0644\u0625\u0637\u0627\u0631\u0627\u062a \u0627\u0644\u0645\u0631\u062c\u0639\u064a\u0629 \u0627\u0644\u0642\u0635\u0648\u0631\u064a\u0629 \u0641\u064a \u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629. \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0635\u0641\u060c \u0633\u0646\u062f\u0631\u0633 \u0647\u0630\u0647 \u0627\u0644\u062a\u062d\u0648\u064a\u0644\u0627\u062a \u0648\u062e\u0635\u0627\u0626\u0635\u0647\u0627\u060c \u0648\u0633\u0646\u0631\u0649 \u0623\u064a\u0636\u064b\u0627 \u0643\u064a\u0641 \u062a\u0641\u0634\u0644 \u0639\u0646\u062f \u062a\u0637\u0628\u064a\u0642\u0647\u0627 \u0639\u0644\u0649 \u0638\u0627\u0647\u0631\u0629 \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u0645\u0648\u062c\u0627\u062a.<\/br><\/em><\/p>\n<p><strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645<\/strong><br \/>\n\u0628\u0639\u062f \u0625\u0643\u0645\u0627\u0644 \u0647\u0630\u0627 \u0627\u0644\u0635\u0641\u060c \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0644\u0627\u0628 \u0642\u0627\u062f\u0631\u064a\u0646 \u0639\u0644\u0649:\n<\/p>\n<p><\/center><\/p>\n<ol>\n<li><strong>\u0627\u0644\u062a\u0639\u0631\u0641<\/strong> \u0639\u0644\u0649 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648\u060c \u0628\u0645\u0627 \u0641\u064a \u0630\u0644\u0643 \u0635\u064a\u0627\u063a\u062a\u0647\u0627 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0648\u0627\u0644\u0645\u0628\u0627\u062f\u0626 \u0627\u0644\u0643\u0627\u0645\u0646\u0629 \u0648\u0631\u0627\u0621\u0647\u0627.<\/li>\n<li><strong>\u062a\u062d\u0644\u064a\u0644<\/strong> \u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0641\u0636\u0627\u0621 \u0648\u0627\u0644\u0632\u0645\u0627\u0646 \u0639\u0644\u0649 \u0637\u0631\u064a\u0642\u0629 \u062c\u0627\u0644\u064a\u0644\u064a\u0648 \u0648\u0641\u0635\u0644\u0647\u0627 \u0641\u064a \u0625\u0637\u0627\u0631 \u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629.<\/li>\n<li><strong>\u062a\u0642\u064a\u064a\u0645<\/strong> \u0642\u064a\u0648\u062f \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648 \u0639\u0646\u062f \u062a\u0637\u0628\u064a\u0642\u0647\u0627 \u0639\u0644\u0649 \u0638\u0648\u0627\u0647\u0631 \u0645\u062b\u0644 \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u0645\u0648\u062c\u0627\u062a \u0648\u0623\u0647\u0645\u064a\u062a\u0647\u0627 \u0641\u064a \u0627\u0644\u062a\u0642\u062f\u0645 \u0646\u062d\u0648 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0646\u0633\u0628\u064a\u0629 \u0627\u0644\u062e\u0627\u0635\u0629.<\/li>\n<\/ol>\n<p><center><\/p>\n<p class=\"indx\"><strong>\u0627\u0644\u0641\u0647\u0631\u0633<\/strong><br \/>\n<a href=\"#1\"><strong>\u0635\u064a\u0627\u063a\u0629 \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648<\/strong><\/a><br \/>\n<a href=\"#2\">\u0627\u0644\u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u0639\u0643\u0633\u064a<\/a><br \/>\n<a href=\"#3\">\u0627\u0644\u0632\u0645\u0646 \u0627\u0644\u0645\u0637\u0644\u0642 \u0648\u062c\u0645\u0639 \u0627\u0644\u0633\u0631\u0639\u0627\u062a<\/a><br \/>\n<a href=\"#4\">\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0641\u0636\u0627\u0621 \u0648\u0627\u0644\u0632\u0645\u0627\u0646 \u0639\u0644\u0649 \u0637\u0631\u064a\u0642\u0629 \u062c\u0627\u0644\u064a\u0644\u064a\u0648<\/a><br \/>\n<a href=\"#5\"><strong>\u0646\u0633\u0628\u064a\u0629 \u062c\u0627\u0644\u064a\u0644\u064a\u0648 \u0648\u0627\u0644\u0642\u0648\u0627\u0646\u064a\u0646 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a\u0629<\/strong><\/a><br \/>\n<a href=\"#6\">\u062a\u0637\u0628\u064a\u0642\u0647\u0627 \u0639\u0644\u0649 \u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0646\u064a\u0648\u062a\u0646<\/a><br \/>\n<a href=\"#7\">\u062a\u0637\u0628\u064a\u0642\u0647\u0627 \u0639\u0644\u0649 \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u0645\u0648\u062c\u0627\u062a<\/a><br \/>\n<a href=\"#8\">\u0645\u0627 \u0647\u0648 \u062a\u0623\u062b\u064a\u0631 \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648 \u0639\u0644\u0649 \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u0645\u0648\u062c\u0627\u062a\u061f<\/a><\/p>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/ku-9nbTSaJg?si=1dmuCtjzBPUy14v_\" title=\"\u0645\u0634\u063a\u0644 \u0641\u064a\u062f\u064a\u0648 \u064a\u0648\u062a\u064a\u0648\u0628\" 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=\"1\"><\/a><\/p>\n<h2>\u0635\u064a\u0627\u063a\u0629 \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648<\/h2>\n<p style=\"text-align:justify;\">\u062a\u0642\u0648\u0645 \u0641\u064a\u0632\u064a\u0627\u0621 \u0646\u064a\u0648\u062a\u0646 \u0639\u0644\u0649 \u0645\u0628\u062f\u0623 \u0627\u0644\u0646\u0633\u0628\u064a\u0629 \u0627\u0644\u0630\u064a \u064a\u062a\u0645 \u0646\u0645\u0630\u062c\u062a\u0647 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648\u060c \u062d\u064a\u062b \u064a\u062a\u0645 \u062a\u0623\u0633\u064a\u0633 \u0627\u0644\u0648\u0642\u062a \u0643\u0625\u062d\u062f\u0627\u062b\u064a \u0639\u0627\u0644\u0645\u064a \u0644\u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0631\u0627\u0642\u0628\u064a\u0646 \u0627\u0644\u0642\u0635\u0648\u0631\u064a\u064a\u0646\u061b \u0623\u064a: <span class=\"katex-eq\" data-katex-display=\"false\">t=t^\\prime<\/span>. \u062a\u062d\u062a \u0647\u0630\u0627 \u0627\u0644\u0628\u064a\u0627\u0646\u060c \u062a\u0623\u062e\u0630 \u0627\u0644\u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u062e\u0637\u064a \u0627\u0644\u0630\u064a \u064a\u0631\u0628\u0637 \u0627\u0644\u0645\u0644\u0627\u062d\u0638\u0627\u062a \u0645\u0646 \u0625\u0637\u0627\u0631\u064a\u0646 \u0645\u0631\u062c\u0639\u064a\u064a\u0646 \u0642\u0635\u0648\u0631\u064a\u064a\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span> \u0627\u0644\u0645\u0631\u0627\u062c\u0639\u0629 \u0641\u064a \u0627\u0644\u0635\u0641 \u062d\u0648\u0644 <a href=\"http:\/\/toposuranos.com\/material\/es\/el-principio-de-relatividad-especial\/?fbclid=IwAR2_lpF1hyUlbSzFQ5B5OQpPu1Vhc_20zTGu8D4pxKPsSvzZRvLSzPdwQXU\" rel=\"noopener\" target=\"_blank\">\u0645\u0628\u062f\u0623 \u0627\u0644\u0646\u0633\u0628\u064a\u0629 \u0627\u0644\u062e\u0627\u0635\u0629<\/a> \u0634\u0643\u0644 \u0627\u0644\u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u062e\u0637\u064a:<\/p>\n<p><a name=\"eq1\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\nt^\\prime &amp;= At + Bx,\\\\ x^\\prime &amp;= Dt + Ex,\\\\ y^\\prime &amp;= y, \\\\ z^\\prime &amp;=z,\n\n\\end{array}<\/span> <strong>[1]<\/strong><\/p>\n<p style=\"text-align:justify;\">\u064a\u0623\u062e\u0630 \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u062a\u0627\u0644\u064a \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0625\u0637\u0627\u0631\u0627\u062a \u0627\u0644\u0642\u0635\u0648\u0631\u064a\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span> \u0641\u064a \u062a\u0643\u0648\u064a\u0646 \u0642\u064a\u0627\u0633\u064a \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span> \u064a\u062a\u062d\u0631\u0643 \u0628\u0633\u0631\u0639\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">v_{ss^\\prime_x}\\hat{x}<\/span> \u0646\u0633\u0628\u0629\u064b \u0625\u0644\u0649 <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span>\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=\"\u062a\u062d\u0648\u064a\u0644\u0627\u062a \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a\" 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=\"\u062a\u062d\u0648\u064a\u0644\u0627\u062a \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a\" width=\"1374\" height=\"741\" class=\"aligncenter size-full wp-image-25502 lazyload\" srcset=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio.png 1374w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio-300x162.png 300w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio-1024x552.png 1024w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio-768x414.png 768w\" sizes=\"(max-width: 1374px) 100vw, 1374px\" \/><\/noscript><\/center><\/p>\n<p><a name=\"eq2\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rlr}\n\n{}t^\\prime &amp;= t  \\\\ x^\\prime &amp;= x - v_{ss^\\prime_x}t \\\\ y^\\prime &amp;= y \\\\ z^\\prime &amp;= z\n\n\\end{array}\n\n<\/span> <strong>[2]<\/strong><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h3>\u0627\u0644\u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u0639\u0643\u0633\u064a<\/h3>\n<p style=\"text-align:justify;\">\u0645\u0646 \u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u062a\u0645\u0627\u062b\u0644 \u0627\u0644\u062c\u0628\u0631\u064a\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0643\u062a\u0627\u0628\u0629 \u0627\u0644\u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u0639\u0643\u0633\u064a:<\/p>\n<p><a name=\"eq3\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\nt &amp;= t^\\prime \\\\ x &amp;= x^\\prime + v_{ss^\\prime_x}t \\\\ y &amp;= y^\\prime \\\\ z &amp;= z^\\prime \\end{array}\n\n<\/span> <strong>[3]<\/strong><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u0627\u0644\u0632\u0645\u0646 \u0627\u0644\u0645\u0637\u0644\u0642 \u0648\u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0633\u0631\u0639\u0627\u062a<\/h3>\n<p style=\"text-align:justify;\">\u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0623\u0648\u0644\u0649 \u0644\u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648 (\u0625\u0645\u0627 [2] \u0623\u0648 [3])\u060c \u064a\u062a\u0636\u062d \u0623\u0646 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a \u0627\u0644\u0632\u0645\u0646\u064a \u0644\u062d\u062f\u062b \u0645\u0627 \u0644\u0627 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0625\u0637\u0627\u0631 \u0627\u0644\u0630\u064a \u064a\u062a\u0645 \u0645\u0644\u0627\u062d\u0638\u062a\u0647 \u0645\u0646\u0647\u060c \u0628\u064a\u0646\u0645\u0627 \u064a\u0633\u0645\u062d \u0627\u0644\u062b\u0627\u0646\u064a \u0628\u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0645\u0627 \u064a\u064f\u0641\u0647\u0645 \u0639\u0627\u062f\u0629\u064b \u0628\u0640 \u00ab\u0627\u0644\u062d\u0633 \u0627\u0644\u0633\u0644\u064a\u0645\u00bb \u0627\u0644\u0645\u0631\u062a\u0628\u0637 \u0628\u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0633\u0631\u0639\u0627\u062a. \u0625\u0630\u0627 \u062a\u062d\u0631\u0643\u062a \u062c\u0633\u064a\u0645\u0629 \u0628\u0633\u0631\u0639\u0629 \u062b\u0627\u0628\u062a\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">v_{ss^\\prime_x}<\/span> \u0639\u0644\u0649 \u0637\u0648\u0644 \u0645\u062d\u0648\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> \u0644\u0640 <span class=\"katex-eq\" data-katex-display=\"false\">S,<\/span> \u0641\u0625\u0646 \u0633\u0631\u0639\u062a\u0647\u0627 \u0641\u064a <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span> \u062a\u064f\u062d\u062f\u062f \u0628\u0648\u0627\u0633\u0637\u0629<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle v^\\prime_x = \\frac{dx^\\prime}{dt^\\prime} = \\frac{dx^\\prime}{dt} = \\frac{d}{dt}\\left(x - v_{ss^\\prime_x} t \\right) = v_x - v_{ss^\\prime_x}<\/span>\n<p style=\"text-align:justify;\">\u0627\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0639\u0628\u0627\u0631\u0629 \u0627\u0644\u0623\u062e\u064a\u0631\u0629 \u064a\u0638\u0647\u0631 \u0623\u0646 \u062a\u0633\u0627\u0631\u0639 \u0623\u064a \u062c\u0633\u064a\u0645 \u0647\u0648 \u0646\u0641\u0633\u0647 \u0641\u064a <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> \u0648\u0641\u064a <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span>\u060c \u0623\u064a: <span class=\"katex-eq\" data-katex-display=\"false\">dv^\\prime_x\/dt^\\prime = dv_x\/dt<\/span>.<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u0647\u0646\u062f\u0633\u0629 \u062c\u0627\u0644\u064a\u0644\u064a\u0648 \u0644\u0644\u0641\u0636\u0627\u0621 \u0648\u0627\u0644\u0632\u0645\u0627\u0646<\/h3>\n<p style=\"text-align:justify;\">\u0625\u0630\u0627 \u0627\u0639\u062a\u0628\u0631\u0646\u0627 \u062d\u062f\u062b\u064a\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u0644\u0647\u0645\u0627 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a <span class=\"katex-eq\" data-katex-display=\"false\">(t_A,x_A,y_A,z_A)<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">(t_B,x_B,y_B,z_B),<\/span> \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a. \u0645\u0646 \u0627\u0644\u0633\u0647\u0644 \u0631\u0624\u064a\u0629 \u0623\u0646 \u0627\u0644\u0643\u0645\u064a\u0627\u062a <span class=\"katex-eq\" data-katex-display=\"false\">\\Delta t = t_B - t_A<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">\\Delta r^2 = \\Delta x^2 + \\Delta y^2 + \\Delta z^2<\/span> \u0647\u064a \u0645\u0646\u0641\u0635\u0644\u0629 \u063a\u064a\u0631 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062a\u063a\u064a\u064a\u0631 \u062a\u062d\u062a \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648\u060c \u0645\u0645\u0627 \u064a\u0642\u0648\u062f\u0646\u0627 \u0625\u0644\u0649 \u0627\u0639\u062a\u0628\u0627\u0631 \u0627\u0644\u0641\u0636\u0627\u0621 \u0648\u0627\u0644\u0632\u0645\u0627\u0646 \u0643\u0643\u064a\u0627\u0646\u0627\u062a \u0645\u0646\u0641\u0635\u0644\u0629. \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c <span class=\"katex-eq\" data-katex-display=\"false\">\\Delta r^2<\/span> \u064a\u0634\u064a\u0631 \u0625\u0644\u0649 \u0623\u0646 \u0647\u0630\u0647 \u0647\u064a \u062e\u0627\u0635\u064a\u0629 \u0647\u0646\u062f\u0633\u064a\u0629 \u0644\u0644\u0641\u0636\u0627\u0621 \u0646\u0641\u0633\u0647. \u0646\u062d\u0646 \u0646\u062a\u0639\u0631\u0641 \u0639\u0644\u0649 <span class=\"katex-eq\" data-katex-display=\"false\">\\Delta r^2<\/span> \u0643\u0645\u0631\u0628\u0639 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u0623\u062d\u062f\u0627\u062b \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a. \u0647\u0630\u0627 \u064a\u062d\u062f\u062f \u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0641\u0636\u0627\u0621 \u0648\u0627\u0644\u0632\u0645\u0627\u0646 \u0641\u064a \u0633\u064a\u0627\u0642 \u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0646\u064a\u0648\u062a\u0646.<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u0646\u0633\u0628\u064a\u0629 \u062c\u0627\u0644\u064a\u0644\u064a\u0648 \u0648\u0627\u0644\u0642\u0648\u0627\u0646\u064a\u0646 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a\u0629<\/h2>\n<p><a name=\"6\"><\/a><\/p>\n<h3>\u0627\u0644\u062a\u0637\u0628\u064a\u0642 \u0639\u0644\u0649 \u062f\u064a\u0646\u0627\u0645\u064a\u0643\u064a\u0627\u062a \u0646\u064a\u0648\u062a\u0646<\/h3>\n<p style=\"text-align:justify;\">\u0641\u064a \u0627\u0644\u0642\u0633\u0645 \u0627\u0644\u0633\u0627\u0628\u0642\u060c \u0631\u0623\u064a\u0646\u0627 \u0623\u0646\u0647 \u0641\u064a \u0633\u064a\u0627\u0642 \u0641\u064a\u0632\u064a\u0627\u0621 \u0646\u064a\u0648\u062a\u0646\u060c \u0633\u064a\u0644\u0627\u062d\u0638 \u0623\u064a \u0625\u0637\u0627\u0631\u0627\u0646 \u0642\u0635\u0648\u0631\u064a\u0627\u0646 \u0645\u062e\u062a\u0644\u0641\u0627\u0646 \u062f\u0627\u0626\u0645\u064b\u0627 \u0646\u0641\u0633 \u0627\u0644\u062a\u0633\u0627\u0631\u0639. \u0647\u0630\u0627\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u062b\u0627\u0646\u064a \u0644\u0646\u064a\u0648\u062a\u0646\u060c \u064a\u0639\u0646\u064a \u0623\u0646 \u062c\u0645\u064a\u0639 \u0627\u0644\u0625\u0637\u0627\u0631\u0627\u062a \u0627\u0644\u0642\u0635\u0648\u0631\u064a\u0629 \u0633\u062a\u0644\u0627\u062d\u0638 \u062f\u0627\u0626\u0645\u064b\u0627 \u0646\u0641\u0633 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u064a\u0627\u062a. \u0623\u064a:<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle F_x = m\\frac{dv_x}{dt}= m\\frac{dv^\\prime_x}{dt^\\prime} = F^\\prime_x.<\/span> <\/p>\n<p style=\"text-align:justify;\">\u062a\u062e\u0628\u0631\u0646\u0627 \u0647\u0630\u0647 \u0627\u0644\u0639\u0628\u0627\u0631\u0629 \u0627\u0644\u0623\u062e\u064a\u0631\u0629 \u0623\u0646 <strong>\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0644\u0627 \u062a\u062a\u063a\u064a\u0631 \u0639\u0646\u062f \u062a\u0646\u0641\u064a\u0630 \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648\u060c<\/strong> \u0648\u0647\u0648 \u0645\u0627 \u064a\u0639\u0627\u062f\u0644 \u0627\u0644\u0642\u0648\u0644 \u0628\u0623\u0646: \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0647\u064a \u0646\u0641\u0633\u0647\u0627 \u0644\u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0631\u0627\u0642\u0628\u064a\u0646 \u0627\u0644\u0642\u0635\u0648\u0631\u064a\u064a\u0646.<\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u0627\u0644\u062a\u0637\u0628\u064a\u0642 \u0639\u0644\u0649 \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u0645\u0648\u062c\u0627\u062a<\/h3>\n<p style=\"text-align:justify;\">\u0628\u064a\u0646\u0645\u0627 \u064a\u064f\u062a\u0648\u0642\u0639 \u0627\u0633\u062a\u0645\u0631\u0627\u0631 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0641\u064a \u0645\u0648\u0627\u062c\u0647\u0629 \u0627\u0644\u062a\u063a\u064a\u064a\u0631\u0627\u062a \u0641\u064a \u0627\u0644\u0645\u0631\u0627\u0642\u0628\u064a\u0646 \u0627\u0644\u0642\u0635\u0648\u0631\u064a\u064a\u0646\u060c \u0623\u0648\u0644\u0627\u064b \u0644\u0623\u0646\u0647 \u0645\u0627 \u0646\u0644\u0627\u062d\u0638\u0647 \u0639\u0646\u062f \u0627\u0644\u062a\u062d\u0631\u0643\u060c \u0648\u062b\u0627\u0646\u064a\u064b\u0627 \u0644\u0623\u0646\u0647 \u0645\u0627 \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u0633\u0627\u0628\u0642\u0629\u060c \u0644\u064a\u0633 \u0647\u0630\u0627 \u0647\u0648 \u0627\u0644\u062d\u0627\u0644 \u062f\u0627\u0626\u0645\u064b\u0627. \u0623\u0628\u0631\u0632 \u062d\u0627\u0644\u0629 \u0644\u0638\u0627\u0647\u0631\u0629 \u0644\u0627 \u062a\u062d\u062a\u0641\u0638 \u062a\u062d\u062a \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648 \u0647\u064a \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u0645\u0648\u062c\u0627\u062a\u061b \u0639\u0645\u0648\u0645\u064b\u0627\u060c \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u064a \u062a\u0646\u0645\u0630\u062c \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u0645\u0648\u062c\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">\\psi<\/span> \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 \u0648\u0627\u0644\u0632\u0645\u0627\u0646 \u0647\u064a \u0641\u064a \u0627\u0644\u0634\u0643\u0644<\/p>\n<p><a name=\"eq4\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\nabla^2 \\psi = \\frac{1}{v_0^2}\\frac{\\partial^2 \\psi}{\\partial t^2}<\/span> <strong>[4]<\/strong><\/p>\n<p style=\"text-align:justify;\">\u062d\u064a\u062b <span class=\"katex-eq\" data-katex-display=\"false\">v_0<\/span> \u0647\u064a \u0633\u0631\u0639\u0629 \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u0645\u0648\u062c\u0629.<\/p>\n<p><a name=\"8\"><\/a><\/p>\n<h4>\u0645\u0627 \u062a\u0623\u062b\u064a\u0631 \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648 \u0639\u0644\u0649 \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u0645\u0648\u062c\u0629\u061f<\/h4>\n<p style=\"text-align:justify;\">\u0644\u0647\u0630\u0627\u060c \u0647\u0646\u0627\u0643 \u0625\u062c\u0627\u0628\u0629 \u0642\u0635\u064a\u0631\u0629 \u0648\u0623\u062e\u0631\u0649 \u0637\u0648\u064a\u0644\u0629. \u0627\u0644\u0625\u062c\u0627\u0628\u0629 \u0627\u0644\u0642\u0635\u064a\u0631\u0629 \u0647\u064a \u0623\u0646 \u00ab\u062d\u062a\u0649 \u0639\u0646\u062f \u0645\u0644\u0627\u062d\u0638\u0629 \u0646\u0641\u0633 \u0627\u0644\u0638\u0627\u0647\u0631\u0629\u060c \u0633\u064a\u0634\u0627\u0647\u062f \u0627\u0644\u0645\u0631\u0627\u0642\u0628\u0648\u0646 \u0627\u0644\u0642\u0635\u0648\u0631\u064a\u0648\u0646 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0648\u0646 &#8216;\u0641\u064a\u0632\u064a\u0627\u0621 \u0645\u062e\u062a\u0644\u0641\u0629'\u00bb. \u0627\u0644\u0625\u062c\u0627\u0628\u0629 \u0627\u0644\u0637\u0648\u064a\u0644\u0629 \u062a\u062a\u0636\u0645\u0646 \u0641\u062d\u0635 \u0643\u064a\u0641\u064a\u0629 \u062a\u063a\u064a\u0631 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u0645\u0648\u062c\u0629 \u0639\u0646\u062f \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u062c\u0627\u0644\u064a\u0644\u064a\u061b \u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u0646\u0623\u062e\u0630 \u0623\u0648\u0644\u0627\u064b \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 [4] \u0648\u0646\u0648\u0633\u0639\u0647\u0627 \u0639\u0644\u0649 \u0643\u0644 \u0645\u0646 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a\u0647\u0627 \u0644\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649:<\/p>\n<p><a name=\"eq5\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\partial ^2 \\psi}{\\partial x^2} + \\frac{\\partial ^2 \\psi}{\\partial y^2} + \\frac{\\partial ^2 \\psi}{\\partial z^2} = \\frac{1}{v_0^2} \\frac{\\partial ^2 \\psi}{\\partial t^2}.<\/span> <strong>[5]<\/strong><\/p>\n<p>\u0645\u0639 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0641\u064a \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0627\u0644\u0622\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0646 <a href=\"#eq3\">[3]<\/a> \u0644\u0625\u0639\u0627\u062f\u0629 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0641\u064a \u0627\u0644\u0625\u0637\u0627\u0631 \u0627\u0644\u0642\u0635\u0648\u0631\u064a \u0627\u0644\u0622\u062e\u0631.<\/p>\n<h5>\u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u0623\u0648\u0644\u0649<\/h5>\n<p style=\"text-align:justify;\">\u0628\u0627\u062a\u0628\u0627\u0639 \u0627\u0644\u062a\u0639\u0628\u064a\u0631\u0627\u062a \u0645\u0646 <a href=\"#eq3\">[3]<\/a> \u0648\u0627\u0634\u062a\u0642\u0627\u0642 \u0643\u0644 \u0645\u062a\u063a\u064a\u0631 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0639\u0637\u0627\u0629\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\partial x^\\prime}{\\partial x} = \\frac{\\partial y^\\prime}{\\partial y}= \\frac{\\partial z^\\prime}{\\partial z}= \\frac{\\partial t^\\prime}{\\partial t}= 1<\/span>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\partial x^\\prime}{\\partial t} = - v_{x_0}<\/span>\n<p style=\"text-align:justify;\">\u0628\u064a\u0646\u0645\u0627 \u064a\u062a\u0645 \u0625\u0644\u063a\u0627\u0621 \u062c\u0645\u064a\u0639 \u0627\u0644\u0622\u062e\u0631\u064a\u0646:<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\partial t^\\prime}{\\partial x} = \\frac{\\partial t^\\prime}{\\partial y} = \\frac{\\partial t^\\prime}{\\partial z} = \\frac{\\partial x^\\prime}{\\partial y} = \\frac{\\partial x^\\prime}{\\partial z} = \\frac{\\partial y^\\prime}{\\partial x} = \\frac{\\partial y^\\prime}{\\partial z} = \\frac{\\partial y^\\prime}{\\partial t} = \\frac{\\partial z^\\prime}{\\partial x} = \\frac{\\partial z^\\prime}{\\partial y} = \\frac{\\partial z^\\prime}{\\partial t} = 0\n\n<\/span>\n<p style=\"text-align:justify;\">\u0645\u0639 \u0647\u0630\u0627 \u0641\u064a \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u0622\u0646 \u062d\u0633\u0627\u0628 \u0645\u0634\u062a\u0642\u0627\u062a <span class=\"katex-eq\" data-katex-display=\"false\">\\psi<\/span> \u0645\u0646 \u062e\u0644\u0627\u0644 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0633\u0644\u0633\u0644\u0629:<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\frac{\\partial \\psi}{\\partial x} = \\frac{\\partial \\psi}{\\partial x^\\prime} \\underbrace{\\frac{\\partial x^\\prime}{\\partial x}}_{=1} + \\frac{\\partial \\psi}{\\partial y^\\prime} \\underbrace{\\frac{\\partial y^\\prime}{\\partial x}}_{=0} +\n\n\\frac{\\partial \\psi}{\\partial z^\\prime} \\underbrace{\\frac{\\partial z^\\prime}{\\partial x}}_{=0} + \\frac{\\partial \\psi}{\\partial t^\\prime} \\underbrace{\\frac{\\partial t^\\prime}{\\partial x}}_{=0} =  \\frac{\\partial \\psi}{\\partial x^\\prime}.<\/span>\n<p>\u0648\u0628\u0627\u0644\u0645\u062b\u0644 \u0644\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0643\u0627\u0646\u064a\u0629 \u0627\u0644\u0623\u062e\u0631\u0649:<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\frac{\\partial \\psi}{\\partial y} =  \\frac{\\partial \\psi}{\\partial y^\\prime}.<\/span>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\frac{\\partial \\psi}{\\partial z} =  \\frac{\\partial \\psi}{\\partial z^\\prime}.<\/span>\n<p style=\"text-align:justify;\">\u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0633\u062a\u0638\u0647\u0631 \u0628\u0639\u0636 \u0627\u0644\u0627\u062e\u062a\u0644\u0627\u0641\u0627\u062a \u0641\u064a \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0632\u0645\u0646\u064a\u0629:<\/p>\n<p id=\"eq\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\displaystyle \\frac{\\partial \\psi}{\\partial t} &amp;= \\displaystyle\\frac{\\partial \\psi}{\\partial x^\\prime}\\underbrace{\\frac{\\partial x^\\prime}{\\partial t}}_{=-v_{x_0}} + \\frac{\\partial \\psi}{\\partial y^\\prime}\\underbrace{\\frac{\\partial y^\\prime}{\\partial t}}_{=0} + \\frac{\\partial \\psi}{\\partial z^\\prime}\\underbrace{\\frac{\\partial z^\\prime}{\\partial t}}_{=0} + \\frac{\\partial \\psi}{\\partial t^\\prime}\\underbrace{\\frac{\\partial t^\\prime}{\\partial t}}_{=1}\\\\ &amp;=\\displaystyle -v_{x_0} \\frac{\\partial \\psi}{\\partial x^\\prime} + \\frac{\\partial \\psi}{\\partial t^\\prime},\n\n\\end{array}\n\n<\/span>\n<h5>\u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u062b\u0627\u0646\u064a\u0629<\/h5>\n<p style=\"text-align:justify;\">\u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u062c\u0632\u0621 \u0627\u0644\u0645\u0643\u0627\u0646\u064a\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631 \u062f\u0648\u0646 \u0635\u0639\u0648\u0628\u0627\u062a \u0643\u0628\u064a\u0631\u0629\u060c \u0648\u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0647\u064a:<\/p>\n<p><a name=\"eq6\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\partial^2 \\psi}{\\partial x^2} = \\frac{\\partial^2 \\psi}{\\partial {x^\\prime}^2}.<\/span> <strong>[6]<\/strong><\/p>\n<p><a name=\"eq7\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\partial^2 \\psi}{\\partial y^2} = \\frac{\\partial^2 \\psi}{\\partial {y^\\prime}^2}<\/span> <strong>[7]<\/strong><\/p>\n<p><a name=\"eq8\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\partial^2 \\psi}{\\partial z^2} = \\frac{\\partial^2 \\psi}{\\partial {z^\\prime}^2}<\/span> <strong>[8]<\/strong><\/p>\n<p style=\"text-align:justify;\">\u0644\u0643\u0646 \u0627\u0644\u062c\u0632\u0621 \u0627\u0644\u0632\u0645\u0646\u064a\u060c \u0643\u0645\u0627 \u0643\u0646\u0627 \u0646\u062a\u0648\u0642\u0639 \u0628\u0627\u0644\u0641\u0639\u0644 \u0645\u0646 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u0623\u0648\u0644\u0649\u060c \u064a\u0638\u0647\u0631 \u0627\u062e\u062a\u0644\u0627\u0641\u0627\u062a \u0643\u0628\u064a\u0631\u0629:<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\displaystyle\\frac{\\partial^2 \\psi}{\\partial t^2} &amp;=\\displaystyle \\frac{\\partial}{\\partial t}\\left( -v_{x_0} \\frac{\\partial \\psi}{\\partial x^\\prime} + \\frac{\\partial \\psi}{\\partial t^\\prime} \\right)\\\\ &amp; \\displaystyle = -v_{x_0} \\frac{\\partial }{\\partial t} \\left(\\frac{\\partial \\psi}{\\partial x^\\prime} \\right) + \\frac{\\partial }{\\partial t} \\left(\\frac{\\partial \\psi}{\\partial t^\\prime} \\right)\\\\ &amp;\\displaystyle = -v_{x_0} \\frac{\\partial }{\\partial x^\\prime} \\left(\\frac{\\partial \\psi}{\\partial t} \\right) + \\frac{\\partial }{\\partial t^\\prime} \\left(\\frac{\\partial \\psi}{\\partial t} \\right)\\\\ &amp;\\displaystyle = -v_{x_0} \\frac{\\partial }{\\partial x^\\prime} \\left(-v_{x_0} \\frac{\\partial \\psi}{\\partial x^\\prime} + \\frac{\\partial \\psi}{\\partial t^\\prime} \\right) + \\frac{\\partial }{\\partial t^\\prime} \\left(-v_{x_0} \\frac{\\partial \\psi}{\\partial x^\\prime} + \\frac{\\partial \\psi}{\\partial t^\\prime} \\right) \\end{array}<\/span>\n<p><a name=\"eq9\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\displaystyle\\frac{\\partial^2 \\psi}{\\partial t^2}  = v_{x_0}^2 \\frac{\\partial^2 \\psi}{\\partial {x^\\prime}^2} - 2v_{x_0}\\frac{\\partial^2 \\psi}{\\partial x^\\prime \\partial t^\\prime} + \\frac{\\partial^2 \\psi}{\\partial {t^\\prime}^2}.<\/span> <strong>[9]<\/strong><\/p>\n<h5>\u062a\u0637\u0628\u064a\u0642 \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648 \u0639\u0644\u0649 \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u0645\u0648\u062c\u0627\u062a<\/h5>\n<p style=\"text-align:justify;\">\u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u064a\u0645\u0643\u0646 \u0625\u062c\u0631\u0627\u0621 \u062a\u062d\u0648\u064a\u0644 \u062c\u0627\u0644\u064a\u0644\u064a\u0648 \u0639\u0644\u0649 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u0645\u0648\u062c\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a [<a href=\"#eq6\">6<\/a>\u060c<a href=\"#eq7\">7<\/a>\u060c<a href=\"#eq8\">8<\/a>] \u0648 [<a href=\"#eq9\">9<\/a>] \u0641\u064a [<a href=\"#eq5\">5<\/a>]\u060c \u0645\u0645\u0627 \u064a\u0646\u062a\u062c \u0639\u0646\u0647:<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\displaystyle \\frac{\\partial^2 \\psi}{\\partial {x^\\prime}^2} + \\frac{\\partial^2 \\psi}{\\partial {y^\\prime}^2} + \\frac{\\partial^2 \\psi}{\\partial {z^\\prime}^2} = \\frac{1}{v_0^2} \\left(\\color{red}{ v_{x_0}^2 \\frac{\\partial^2 \\psi}{\\partial {x^\\prime}^2} - 2v_{x_0}\\frac{\\partial^2 \\psi}{\\partial x^\\prime \\partial t^\\prime}} + \\frac{\\partial^2 \\psi}{\\partial {t^\\prime}^2} \\right).\n\n<\/span> <strong>[10]<\/strong><\/p>\n<p style=\"text-align:justify;\">\u064a\u064f\u0644\u0627\u062d\u0638 \u0623\u0646 \u0634\u0643\u0644 \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u0645\u0648\u062c\u0629 \u0644\u0627 \u064a\u062d\u062a\u0641\u0638 \u0628\u0647 \u062a\u062d\u062a \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648 \u0628\u0633\u0628\u0628 \u0638\u0647\u0648\u0631 \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0625\u0636\u0627\u0641\u064a\u0629 \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u0628\u0627\u0644\u0644\u0648\u0646 \u0627\u0644\u0623\u062d\u0645\u0631. \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646 \u0647\u0630\u0627 \u0644\u0627 \u064a\u0643\u0648\u0646 \u0644\u0647 \u0639\u0648\u0627\u0642\u0628 \u0643\u0628\u064a\u0631\u0629 \u0641\u064a \u0627\u0644\u0648\u0642\u062a \u0627\u0644\u062d\u0627\u0644\u064a\u060c \u0625\u0644\u0627 \u0623\u0646\u0646\u0627 \u0633\u0646\u0631\u0649 \u0641\u064a \u0627\u0644\u062f\u0631\u0648\u0633 \u0627\u0644\u0645\u0633\u062a\u0642\u0628\u0644\u064a\u0629 \u0623\u0646 \u0647\u0630\u0647 \u0647\u064a \u0628\u0627\u0644\u0636\u0628\u0637 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u064a \u00ab\u062a\u0643\u0633\u0631\u00bb\u060c \u0625\u0630\u0627 \u062c\u0627\u0632 \u0627\u0644\u062a\u0639\u0628\u064a\u0631\u060c \u0645\u0639 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629\u060c \u0645\u0645\u0627 \u064a\u0641\u0633\u062d \u0627\u0644\u0645\u062c\u0627\u0644 \u0644\u0644\u0646\u0633\u0628\u064a\u0629 \u0627\u0644\u062e\u0627\u0635\u0629.<\/p>\n<div style=\"background-color:#F3F3F3; padding:20px;\">\n<h2>\u0627\u0644\u062e\u0644\u0627\u0635\u0627\u062a<\/h2>\n<p style=\"text-align:justify;\">\n        \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062c\u0627\u0644\u064a\u0644\u064a\u0648\u060c \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629\u060c \u062a\u0642\u064a\u0645 \u0625\u0637\u0627\u0631\u064b\u0627 \u0644\u0641\u0647\u0645 \u0643\u064a\u0641\u064a\u0629 \u062a\u063a\u064a\u0631 \u0627\u0644\u0645\u0644\u0627\u062d\u0638\u0627\u062a \u0628\u064a\u0646 \u0625\u0637\u0627\u0631\u0627\u062a \u0627\u0644\u0625\u0633\u0646\u0627\u062f \u0627\u0644\u0642\u0635\u0648\u0631\u064a\u0629 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629. \u0645\u0646 \u062e\u0644\u0627\u0644 \u0647\u0630\u0647 \u0627\u0644\u062f\u0631\u0627\u0633\u0629\u060c \u062a\u0639\u0631\u0641\u0646\u0627 \u0639\u0644\u0649 \u0645\u0641\u0647\u0648\u0645 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