{"id":27321,"date":"2024-01-07T13:00:55","date_gmt":"2024-01-07T13:00:55","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27321"},"modified":"2024-07-01T06:52:35","modified_gmt":"2024-07-01T06:52:35","slug":"%e0%a4%b8%e0%a5%8d%e0%a4%aa%e0%a5%87%e0%a4%b8%e0%a4%9f%e0%a4%be%e0%a4%87%e0%a4%ae-%e0%a4%95%e0%a5%87-%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%bf%e0%a4%95","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a5%8d%e0%a4%aa%e0%a5%87%e0%a4%b8%e0%a4%9f%e0%a4%be%e0%a4%87%e0%a4%ae-%e0%a4%95%e0%a5%87-%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%bf%e0%a4%95\/","title":{"rendered":"\u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0915\u0947 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0915\u0947 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928<\/h1>\n<p class=\"eq\"><em><strong>\u0938\u093e\u0930\u093e\u0902\u0936:<\/strong><br \/>\n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f \u0915\u0948\u0938\u0947 \u0932\u0949\u0930\u0947\u0902\u091c\u093c \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0915\u094b \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0930\u094b\u091f\u0947\u0936\u0928 \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0941\u0928\u0903\u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948\u0964 \u0939\u092e 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href=\"#0\"><strong>\u092a\u0930\u093f\u091a\u092f<\/strong><\/a><br \/>\n<a href=\"#1\"><strong>\u092e\u093f\u0902\u0915\u0949\u0935\u094d\u0938\u094d\u0915\u0940 \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u092e\u0947\u0902 \u0930\u094b\u091f\u0947\u0936\u0928<\/strong><\/a><br \/>\n<a href=\"#2\">\u0936\u0941\u0926\u094d\u0927 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928<\/a><br \/>\n<a href=\"#3\">\u0924\u094d\u0930\u093f\u0935\u093f\u092e\u0940\u092f \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0947 \u0932\u093f\u090f \u092e\u0948\u091f\u094d\u0930\u093f\u0915\u094d\u0938 \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0930\u0923<\/a><br \/>\n<a href=\"#4\">\u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0915\u0949\u0930\u094d\u0921\u093f\u0928\u0947\u091f\u094d\u0938 \u0915\u0947 \u0938\u093e\u0925 \u0918\u091f\u0928\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u0938\u094d\u0925\u093e\u0928\u093f\u0915 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title=\"YouTube video player\" 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>\u092a\u0930\u093f\u091a\u092f<\/h2>\n<p style=\"text-align:justify;\">\u0907\u0938 \u092c\u093f\u0902\u0926\u0941 \u0924\u0915, \u0939\u092e\u0928\u0947 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0930\u0942\u092a \u0938\u0947 \u0926\u0947\u0916\u093e \u0939\u0948 \u0915\u093f \u0915\u0948\u0938\u0947 \u0932\u0949\u0930\u0947\u0902\u091c\u093c \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0905\u0930\u094d\u0925\u093e\u0924\u094d \u092e\u093f\u0902\u0915\u0949\u0935\u094d\u0938\u094d\u0915\u0940 \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u092e\u0947\u0902 \u0915\u093f\u0938\u0940 \u0935\u093f\u0936\u0947\u0937 \u0918\u091f\u0928\u093e 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name=\"1\"><\/a><\/p>\n<h2>\u092e\u093f\u0902\u0915\u0949\u0935\u094d\u0938\u094d\u0915\u0940 \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u092e\u0947\u0902 \u0930\u094b\u091f\u0947\u0936\u0928<\/h2>\n<p style=\"text-align:justify;\">\u0906\u0907\u090f \u0939\u092e \u092e\u093f\u0902\u0915\u0949\u0935\u094d\u0938\u094d\u0915\u0940 \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u092e\u0947\u0902 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0940 \u091c\u093e\u0902\u091a \u0915\u0930\u0947\u0902\u0964 \u091a\u0942\u0902\u0915\u093f \u092f\u0939 \u090f\u0915 \u091a\u093e\u0930-\u0906\u092f\u093e\u092e\u0940 \u0938\u094d\u0925\u093e\u0928 \u0939\u0948, \u090f\u0915 \u0935\u093f\u0936\u093f\u0937\u094d\u091f \u0935\u093f\u092e\u093e\u0928 \u0915\u0947 \u0938\u0902\u092c\u0902\u0927 \u092e\u0947\u0902 \u090f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 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\u0935\u093f\u092e\u093e\u0928\u094b\u0902 \u092a\u0930 \u092d\u0940\u0964 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0905\u0915\u094d\u0937\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u092c\u0928\u0947 \u0935\u093f\u092e\u093e\u0928\u094b\u0902 \u092e\u0947\u0902 \u0915\u093f\u090f \u0917\u090f \u0930\u094b\u091f\u0947\u0936\u0928 \u0936\u0941\u0926\u094d\u0927 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u091c\u092c\u0915\u093f \u0938\u094d\u0925\u093e\u0928 \u0914\u0930 \u0938\u092e\u092f \u0915\u0947 \u0905\u0915\u094d\u0937\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u092c\u0928\u0947 \u0935\u093f\u092e\u093e\u0928\u094b\u0902 \u092e\u0947\u0902 \u0915\u093f\u090f \u0917\u090f \u0930\u094b\u091f\u0947\u0936\u0928 \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0930\u094b\u091f\u0947\u0936\u0928 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u092b\u093f\u0932\u0939\u093e\u0932, \u0939\u092e \u0936\u0941\u0926\u094d\u0927 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u092a\u0930 \u0927\u094d\u092f\u093e\u0928 \u0915\u0947\u0902\u0926\u094d\u0930\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947 \u0924\u093e\u0915\u093f \u092c\u093e\u0926 \u092e\u0947\u0902 \u0907\u0938 \u091c\u094d\u091e\u093e\u0928 \u0915\u094b \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0930\u094b\u091f\u0947\u0936\u0928 \u0924\u0915 \u0935\u093f\u0938\u094d\u0924\u093e\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0947\u0964\n<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h3>\u0936\u0941\u0926\u094d\u0927 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928<\/h3>\n<p style=\"text-align:justify;\">\n\u0906\u0907\u090f \u0939\u092e <bdi><span class=\"katex-eq\" data-katex-display=\"false\">xy<\/span><\/bdi> \u0935\u093f\u092e\u093e\u0928 \u092e\u0947\u0902 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0948\u0938\u0947 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0902, \u0907\u0938\u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0939\u092e\u093e\u0930\u0947 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0936\u0941\u0930\u0942 \u0915\u0930\u0947\u0902\u0964 \u0907\u0938\u0915\u0947 \u0932\u093f\u090f, \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 <bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a,b)<\/span><\/bdi> \u0915\u0949\u0930\u094d\u0921\u093f\u0928\u0947\u091f\u094d\u0938 \u0915\u0947 \u0938\u093e\u0925 \u090f\u0915 \u092c\u093f\u0902\u0926\u0941 \u0939\u0948 \u091c\u094b <bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span><\/bdi> \u0914\u0930 <bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{y}<\/span><\/bdi> \u0905\u0915\u094d\u0937\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0947 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u0939\u0948\u0964 \u092b\u093f\u0930, \u0939\u092e \u0909\u0938 \u0938\u0902\u092c\u0902\u0927 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0947\u0902\u0917\u0947 \u091c\u094b \u0907\u0928 \u0915\u0949\u0930\u094d\u0921\u093f\u0928\u0947\u091f\u094d\u0938 \u0915\u094b \u0909\u0938 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0947 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u0926\u0947\u0916\u0947 \u0917\u090f \u0915\u0949\u0930\u094d\u0921\u093f\u0928\u0947\u091f\u094d\u0938 \u0915\u0947 \u0938\u093e\u0925 \u091c\u094b\u0921\u093c\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 <bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}^\\prime<\/span><\/bdi> \u0914\u0930 <bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{y}^\\prime<\/span><\/bdi> \u0905\u0915\u094d\u0937\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u0948, \u091c\u094b \u092e\u0942\u0932 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0947 \u0938\u0902\u092c\u0902\u0927 \u092e\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span> \u0915\u094b\u0923 \u092a\u0930 \u0918\u0942\u092e\u0947 \u0939\u0941\u090f \u0939\u0948\u0902, \u091c\u0948\u0938\u093e \u0915\u093f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u091a\u093f\u0924\u094d\u0930 \u092e\u0947\u0902 \u0926\u093f\u0916\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948:\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=\"Rotaci\u00f3n en un \u00e1ngulo theta del plano xy\" 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=\"Rotaci\u00f3n en un \u00e1ngulo theta del plano xy\" 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\u0939\u0930 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0938\u0947 \u092e\u093e\u092a\u0947 \u0917\u090f \u0915\u0949\u0930\u094d\u0921\u093f\u0928\u0947\u091f\u094d\u0938 <bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a,b)<\/span><\/bdi> \u0914\u0930 <bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a^\\prime,b^\\prime)<\/span><\/bdi> \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u093e \u0906\u0938\u093e\u0928 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948\u0964\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=\"Lineas gu\u00eda para la obtenci\u00f3n de la relaci\u00f3n entre sistemas rotados\" 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=\"Lineas gu\u00eda para la obtenci\u00f3n de la relaci\u00f3n entre sistemas rotados\" 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\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0905\u092c \u0939\u092e\u0947\u0902 \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u093e \u0906\u0938\u093e\u0928 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948\u0964\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) \\end{array} <\/span>\n<p><\/bdi><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u0924\u094d\u0930\u093f\u0935\u093f\u092e\u0940\u092f \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0947 \u0932\u093f\u090f \u092e\u0948\u091f\u094d\u0930\u093f\u0915\u094d\u0938 \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0930\u0923<\/h3>\n<p style=\"text-align:justify;\">\n\u0907\u0928 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u094b \u0905\u0927\u093f\u0915 \u0938\u0941\u0935\u093f\u0927\u093e\u091c\u0928\u0915 \u0930\u0942\u092a \u092e\u0947\u0902 \u092e\u0948\u091f\u094d\u0930\u093f\u0915\u094d\u0938 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964\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;\">\u092f\u0939 \u0938\u0941\u0935\u093f\u0927\u093e\u091c\u0928\u0915 \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092f\u0939\u093e\u0902 \u0938\u0947 \u092c\u0921\u093c\u0940 \u0906\u092f\u093e\u092e\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0930\u0923 \u0915\u0930\u0928\u093e \u0906\u0938\u093e\u0928 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, <bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a,b,c)<\/span><\/bdi> \u0915\u0949\u0930\u094d\u0921\u093f\u0928\u0947\u091f\u094d\u0938 \u0915\u0947 \u0938\u093e\u0925 \u090f\u0915 \u092c\u093f\u0902\u0926\u0941 \u091c\u094b <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{y}<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{z}<\/span> \u0905\u0915\u094d\u0937\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u092e\u0947\u0902 \u0939\u0948, \u0926\u0942\u0938\u0930\u0947 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0938\u0947 \u0926\u0947\u0916\u093e \u0917\u092f\u093e \u0939\u0948 \u091c\u094b <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}^\\prime<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{y}^\\prime<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{z}^\\prime<\/span> \u0905\u0915\u094d\u0937\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u0948, \u091c\u094b \u092e\u0942\u0932 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0947 \u0938\u0902\u092c\u0902\u0927 \u092e\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span> \u0915\u094b\u0923 \u092a\u0930 \u0918\u0942\u092e\u0947 \u0939\u0941\u090f \u0939\u0948\u0902, \u0939\u094b\u0917\u093e:<\/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=\"Rotaciones Espaciales\" 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=\"Rotaciones Espaciales\" 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;\">\u0907\u0938\u0938\u0947, \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0935\u093f\u092e\u093e\u0928 \u0915\u0947 \u0932\u093f\u090f \u0930\u094b\u091f\u0947\u0936\u0928 \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0915\u0940 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u092e\u0948\u091f\u094d\u0930\u093f\u0915\u094d\u0938 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902\u0964<\/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{Rotaci\u00f3n en un \u00e1ngulo }\\theta\\\\ \\text{sobre el plano }xy \\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{Rotaci\u00f3n en un \u00e1ngulo }\\theta\\\\ \\text{sobre el plano }yz \\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{Rotaci\u00f3n en un \u00e1ngulo }\\theta\\\\ \\text{sobre el plano }xz \\end{array} \\end{array} <\/span>\n<p><\/bdi><\/p>\n<p style=\"text-align:justify;\">\u0907\u0928 \u0930\u094b\u091f\u0947\u0936\u0928 \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0915\u0947 \u0935\u093f\u092a\u0930\u0940\u0924 \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, <span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span> \u0915\u094b <span class=\"katex-eq\" data-katex-display=\"false\">-\\theta<\/span> \u0915\u0947 \u0938\u093e\u0925 \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u093e \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0939\u0948\u0964<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0915\u0949\u0930\u094d\u0921\u093f\u0928\u0947\u091f\u094d\u0938 \u0915\u0947 \u0938\u093e\u0925 \u0918\u091f\u0928\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928<\/h3>\n<p style=\"text-align:justify;\">\n\u091c\u0948\u0938\u0947 \u0939\u092e\u0928\u0947 \u0926\u094b \u0938\u0947 \u0924\u0940\u0928 \u0906\u092f\u093e\u092e\u094b\u0902 \u092e\u0947\u0902 \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0930\u0923 \u0915\u093f\u092f\u093e \u0939\u0948, \u0939\u092e \u0907\u0938\u0947 \u091a\u093e\u0930 \u0906\u092f\u093e\u092e\u094b\u0902 \u092e\u0947\u0902 \u092d\u0940 \u0935\u093f\u0938\u094d\u0924\u093e\u0930\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0935\u093f\u0936\u0947\u0937 \u0938\u093e\u092a\u0947\u0915\u094d\u0937\u0924\u093e \u0915\u0940 \u092d\u093e\u0937\u093e \u0915\u0947 \u0938\u093e\u0925 \u0938\u0941\u0938\u0902\u0917\u0924 \u0930\u0939\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u0949\u0930\u094d\u0921\u093f\u0928\u0947\u091f \u0915\u0947 \u0905\u0930\u094d\u0925 \u0915\u094b \u0938\u092e\u091d\u0928\u093e \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948\u0964 \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0924\u0903, \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0915\u0949\u0930\u094d\u0921\u093f\u0928\u0947\u091f\u094d\u0938 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u0940\u0915\u0947 \u0938\u0947 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902:\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\u092f\u0939\u093e\u0902, \u0938\u0941\u092a\u0930\u0938\u094d\u0915\u094d\u0930\u093f\u092a\u094d\u091f \u092a\u094b\u091f\u0947\u0902\u0936\u093f\u092f\u0932 \u0915\u094b \u0928\u0939\u0940\u0902 \u0926\u0930\u094d\u0936\u093e\u0924\u0947 \u0939\u0948\u0902, \u092c\u0932\u094d\u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u0949\u0930\u094d\u0921\u093f\u0928\u0947\u091f \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u0913\u0902 \u0915\u094b \u0907\u0902\u0917\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0938\u0941\u092a\u0930\u0938\u094d\u0915\u094d\u0930\u093f\u092a\u094d\u091f 0 \u0915\u0947 \u0938\u093e\u0925 \u0915\u0949\u0930\u094d\u0921\u093f\u0928\u0947\u091f \u0938\u092e\u092f \u0906\u092f\u093e\u092e \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930\u0924\u093e \u0939\u0948, \u091c\u092c\u0915\u093f \u0938\u0941\u092a\u0930\u0938\u094d\u0915\u094d\u0930\u093f\u092a\u094d\u091f 1, 2 \u0914\u0930 3 \u0915\u0947 \u0938\u093e\u0925 \u0915\u0949\u0930\u094d\u0921\u093f\u0928\u0947\u091f\u094d\u0938 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0906\u092f\u093e\u092e\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938 \u092a\u0930 \u0927\u094d\u092f\u093e\u0928 \u0930\u0916\u0924\u0947 \u0939\u0941\u090f, \u092e\u093f\u0902\u0915\u0949\u0935\u094d\u0938\u094d\u0915\u0940 \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u092e\u0947\u0902 \u0936\u0941\u0926\u094d\u0927 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u092c\u0902\u0927\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0935\u0930\u094d\u0923\u093f\u0924 \u0939\u0948\u0902:<\/p>\n<p><bdi><\/p>\n<p style=\"text-align:center;\"><strong>xy \u0935\u093f\u092e\u093e\u0928 \u0915\u0947 \u0938\u0902\u092c\u0902\u0927 \u092e\u0947\u0902 \u0930\u094b\u091f\u0947\u0936\u0928:<\/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>yz \u0935\u093f\u092e\u093e\u0928 \u0915\u0947 \u0938\u0902\u092c\u0902\u0927 \u092e\u0947\u0902 \u0930\u094b\u091f\u0947\u0936\u0928:<\/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>xz \u0935\u093f\u092e\u093e\u0928 \u0915\u0947 \u0938\u0902\u092c\u0902\u0927 \u092e\u0947\u0902 \u0930\u094b\u091f\u0947\u0936\u0928:<\/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;\">\u0907\u0928 \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0915\u0940 \u0935\u0939\u0940 \u0917\u0941\u0923\u0927\u0930\u094d\u092e \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b \u0909\u0928\u0915\u0940 \u0924\u0940\u0928-\u0906\u092f\u093e\u092e\u0940 \u0938\u092e\u0915\u0915\u094d\u0937 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902\u0964<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0915\u0947 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928<\/h2>\n<p><a name=\"6\"><\/a><\/p>\n<h3>\u0935\u0947\u0917 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 \u0915\u093e \u092a\u0930\u093f\u091a\u092f<\/h3>\n<p style=\"text-align:justify;\">\u0932\u0949\u0930\u0947\u0902\u091c\u093c \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0914\u0930 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0938\u092e\u093e\u0928\u0924\u093e \u0915\u094b \u0939\u092e \u0935\u0947\u0917 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 \u0915\u094b \u092a\u0947\u0936 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/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;\">\u0915\u094d\u092f\u094b\u0902\u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">\\beta_{ss^\\prime_x}\\in]-1,1[<\/span>, \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">\\psi_{ss^\\prime_x}\\in\\mathbb{R}<\/span>\u0964 \u0938\u093e\u0925 \u0939\u0940, \u0928\u094b\u091f \u0915\u0930\u0947\u0902 \u0915\u093f \u0907\u0938\u0938\u0947 \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">\\gamma_{ss^\\prime_x}=\\cosh(\\psi_{ss^\\prime_x})<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\gamma_{ss^\\prime_x} \\beta_{ss^\\prime_x} = \\sinh(\\psi_{ss^\\prime_x})<\/span>\u0964 \u092f\u0939 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0917\u0923\u0928\u093e\u0913\u0902 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:justify;\">\u092f\u0939 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u0915\u093f <bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_{ss^\\prime_x}= \\text{argtanh}(\\beta_{ss^\\prime_x})<\/span><\/bdi> \u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 <bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\beta_{ss^\\prime_x} =\\tanh(\\psi_{ss^\\prime_x})<\/span><\/bdi>; \u0914\u0930 \u0907\u0938\u0932\u093f\u090f: <\/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;\">\u091c\u0948\u0938\u093e \u0915\u093f \u0917\u093e\u092e\u093e \u092b\u0948\u0915\u094d\u091f\u0930 \u0914\u0930 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0915\u094b\u0938\u0947\u0928 \u0926\u094b\u0928\u094b\u0902 \u0939\u092e\u0947\u0936\u093e 1 \u092f\u093e \u0909\u0938\u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u092f\u0939 \u0905\u0902\u0924\u0924\u0903 \u0938\u093e\u092c\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f <bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma_{ss^\\prime_x} = \\cosh(\\psi_{ss^\\prime_x})<\/span><\/bdi>\u0964<\/p>\n<p style=\"text-align:justify;\">\u0907\u0938\u0940 \u0924\u0930\u0939, \u0909\u092a\u0930\u094b\u0915\u094d\u0924 \u0917\u0923\u0928\u093e\u0913\u0902 \u0915\u094b \u091c\u093e\u0930\u0940 \u0930\u0916\u0924\u0947 \u0939\u0941\u090f, \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902:<\/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;\">\u0914\u0930 \u0907\u0938\u0932\u093f\u090f <bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma_{ss^\\prime_x} \\beta_{ss^\\prime_x} = \\sinh(\\psi_{ss^\\prime_x})<\/span><\/bdi>\u0964 <\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u094b \u0938\u0942\u0924\u094d\u0930\u092c\u0926\u094d\u0927 \u0915\u0930\u0928\u093e<\/h3>\n<p style=\"text-align:justify;\">\n\u0905\u092c, \u0939\u092e \u0932\u0949\u0930\u0947\u0902\u091c\u093c \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u092e\u0947\u0902 \u0935\u0947\u0917 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0917\u0924\u093f \u092c\u0942\u0938\u094d\u091f \u0914\u0930 \u0917\u093e\u092e\u093e \u092b\u0948\u0915\u094d\u091f\u0930 \u0915\u094b \u092a\u0941\u0928\u0903\u0932\u093f\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0926\u094b \u091c\u0921\u093c\u0924\u094d\u0935\u0940\u092f \u092a\u094d\u0930\u0923\u093e\u0932\u093f\u092f\u094b\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span> \u0915\u094b \u092e\u093e\u0928\u0924\u0947 \u0939\u0941\u090f, \u091c\u0939\u093e\u0901 \u0926\u0942\u0938\u0930\u0947 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u094b <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0905\u0915\u094d\u0937 \u092a\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\beta_{ss^\\prime_x}<\/span> \u0935\u0947\u0917 \u092c\u0942\u0938\u094d\u091f \u0932\u093e\u0917\u0942 \u0939\u094b\u0924\u093e \u0939\u0948, \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902:\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, \\\\ \\\\ z^\\prime &amp;= z. \\end{array} <\/span><\/bdi><\/p>\n<p style=\"text-align:justify;\">\u0907\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092e\u0948\u091f\u094d\u0930\u093f\u0915\u094d\u0938 \u0938\u094d\u0935\u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><strong>\u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0915\u0947 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 tx \u0935\u093f\u092e\u093e\u0928 \u092a\u0930: <\/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 \\\\ {} 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;\">\u0907\u0938\u0940 \u0924\u0930\u0939, \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0935\u093f\u092e\u093e\u0928 \u092a\u0930 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><strong>\u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0915\u0947 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 ty \u0935\u093f\u092e\u093e\u0928 \u092a\u0930: <\/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>\u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0915\u0947 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 tz \u0935\u093f\u092e\u093e\u0928 \u092a\u0930: <\/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\u0909\u0928\u0915\u0947 \u0938\u094d\u0935\u0930\u0942\u092a \u0914\u0930 \u0917\u0941\u0923\u0927\u0930\u094d\u092e\u094b\u0902 \u0915\u0947 \u0915\u093e\u0930\u0923, \u092f\u0947 \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948\u0902, \u0915\u0947\u0935\u0932 \u0935\u0947 \u0924\u094d\u0930\u093f\u0915\u094b\u0923\u092e\u093f\u0924\u0940\u092f \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0947 \u092c\u091c\u093e\u092f \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0939\u093e\u0932\u093e\u0902\u0915\u093f \u092f\u0947 \u0938\u0916\u094d\u0924 \u0905\u0930\u094d\u0925 \u092e\u0947\u0902 \u0930\u094b\u091f\u0947\u0936\u0928 \u0928\u0939\u0940\u0902 \u0939\u0948\u0902, \u092f\u0947 \u092a\u0939\u0932\u0947 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0940 \u0917\u0908 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0947 \u0938\u093e\u0925 \u0915\u0941\u091b \u0938\u092e\u093e\u0928\u0924\u093e\u090f\u0902 \u0938\u093e\u091d\u093e \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u091c\u0948\u0938\u0947 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0947 \u092e\u093e\u092e\u0932\u0947 \u092e\u0947\u0902 \u0939\u094b\u0924\u093e \u0939\u0948, \u0935\u093f\u092a\u0930\u0940\u0924 \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0935\u0947\u0917 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\psi<\/span> \u0915\u094b <span class=\"katex-eq\" data-katex-display=\"false\">-\\psi<\/span> \u0938\u0947 \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0928 \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0915\u094b \u0915\u092d\u0940-\u0915\u092d\u0940 <strong>\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928<\/strong> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u0935\u0947\u0917 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 \u0915\u094b <strong>\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0915\u094b\u0923<\/strong> \u092d\u0940 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964\n<\/p>\n<p><a name=\"8\"><\/a><\/p>\n<div style=\"background-color:#F3F3F3; padding:20px;\">\n<h2>\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/h2>\n<p style=\"text-align:justify;\">\n        \u0905\u092c \u0924\u0915 \u0939\u092e\u0928\u0947 \u092e\u093f\u0902\u0915\u0949\u0935\u094d\u0938\u094d\u0915\u0940 \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u092e\u0947\u0902 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0947 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0915\u094b \u0917\u0939\u0930\u093e\u0908 \u0938\u0947 \u0938\u092e\u091d\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 \u0932\u0949\u0930\u0947\u0902\u091c\u093c \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0915\u0940 \u092c\u0947\u0939\u0924\u0930 \u0938\u092e\u091d \u092e\u093f\u0932\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938 \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947, \u0939\u092e\u0928\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u094d\u0930\u092e\u0941\u0916 \u092c\u093f\u0902\u0926\u0941 \u0939\u093e\u0938\u093f\u0932 \u0915\u093f\u090f \u0939\u0948\u0902:\n    <\/p>\n<ul>\n<li><strong>\u0932\u0949\u0930\u0947\u0902\u091c\u093c \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0915\u0940 \u092a\u0941\u0928\u0903\u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e<\/strong>: \u0939\u092e\u0928\u0947 \u0932\u0949\u0930\u0947\u0902\u091c\u093c \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0915\u094b \u0915\u0947\u0935\u0932 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u0902\u0926\u0930\u094d\u092d \u092b\u094d\u0930\u0947\u092e\u094b\u0902 \u0915\u0947 \u0915\u093e\u0930\u0923 \u0915\u0949\u0930\u094d\u0921\u093f\u0928\u0947\u091f\u094d\u0938 \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0928\u0939\u0940\u0902, \u092c\u0932\u094d\u0915\u093f \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092d\u0940 \u0926\u0947\u0916\u0928\u0947 \u0914\u0930 \u0938\u092e\u091d\u0928\u0947 \u0915\u0940 \u0915\u0932\u093e \u0938\u0940\u0916\u0940 \u0939\u0948\u0964<\/li>\n<li><strong>\u092e\u093f\u0902\u0915\u0949\u0935\u094d\u0938\u094d\u0915\u0940 \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u092e\u0947\u0902 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0940 \u0938\u092e\u091d<\/strong>: \u0939\u092e\u0928\u0947 \u092e\u093f\u0902\u0915\u0949\u0935\u094d\u0938\u094d\u0915\u0940 \u0915\u0947 \u091a\u093e\u0930-\u0906\u092f\u093e\u092e\u0940 \u0938\u094d\u0925\u093e\u0928 \u0915\u0947 \u092d\u0940\u0924\u0930 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u093e \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u093f\u092f\u093e \u0939\u0948\u0964<\/li>\n<li><strong>\u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0915\u0947 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0940 \u0916\u094b\u091c<\/strong>: \u0905\u0902\u0924\u0924\u0903, \u0939\u092e\u0928\u0947 \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0915\u0947 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0947 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0915\u094b \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u093f\u092f\u093e, \u0914\u0930 \u0907\u0938\u0915\u0940 \u0938\u092e\u093e\u0928\u0924\u093e\u090f\u0902 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0947 \u0938\u093e\u0925 \u091c\u093e\u0902\u091a\u0940\u0964<\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0915\u0947 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 \u0938\u093e\u0930\u093e\u0902\u0936: \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f \u0915\u0948\u0938\u0947 \u0932\u0949\u0930\u0947\u0902\u091c\u093c \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0915\u094b \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0930\u094b\u091f\u0947\u0936\u0928 \u091f\u094d\u0930\u093e\u0902\u0938\u092b\u0949\u0930\u094d\u092e\u0947\u0936\u0928 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0941\u0928\u0903\u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948\u0964 \u0939\u092e \u092e\u093f\u0902\u0915\u0949\u0935\u094d\u0938\u094d\u0915\u0940 \u0915\u0947 \u091a\u093e\u0930-\u0906\u092f\u093e\u092e\u0940 \u0938\u094d\u0925\u093e\u0928 \u092e\u0947\u0902 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0940 \u091c\u093e\u0902\u091a \u0936\u0941\u0930\u0942 \u0915\u0930\u0947\u0902\u0917\u0947, \u0915\u0947\u0935\u0932 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0930\u094b\u091f\u0947\u0936\u0928 \u0914\u0930 \u0909\u0928 \u0930\u094b\u091f\u0947\u0936\u0928 \u0915\u0947 \u092c\u0940\u091a \u0905\u0902\u0924\u0930 \u0915\u0930\u0947\u0902\u0917\u0947 \u091c\u094b \u0938\u094d\u092a\u0947\u0938\u091f\u093e\u0907\u092e \u0905\u0915\u094d\u0937\u094b\u0902 \u0915\u094b \u0936\u093e\u092e\u093f\u0932 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0936\u093f\u0915\u094d\u0937\u0923 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