{"id":27229,"date":"2021-08-19T13:00:44","date_gmt":"2021-08-19T13:00:44","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27229"},"modified":"2024-09-16T12:59:27","modified_gmt":"2024-09-16T12:59:27","slug":"%e0%a4%b8%e0%a4%bf%e0%a4%a8%e0%a5%87%e0%a4%ae%e0%a5%87%e0%a4%9f%e0%a4%bf%e0%a4%95%e0%a5%8d%e0%a4%b8-%e0%a4%95%e0%a5%87-%e0%a4%b8%e0%a4%bf%e0%a4%a6%e0%a5%8d%e0%a4%a7%e0%a4%be%e0%a4%82%e0%a4%a4","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%bf%e0%a4%a8%e0%a5%87%e0%a4%ae%e0%a5%87%e0%a4%9f%e0%a4%bf%e0%a4%95%e0%a5%8d%e0%a4%b8-%e0%a4%95%e0%a5%87-%e0%a4%b8%e0%a4%bf%e0%a4%a6%e0%a5%8d%e0%a4%a7%e0%a4%be%e0%a4%82%e0%a4%a4\/","title":{"rendered":"\u0938\u093f\u0928\u0947\u092e\u0947\u091f\u093f\u0915\u094d\u0938 \u0915\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924: \u0938\u094d\u0925\u093f\u0924\u093f, \u0935\u0947\u0917 \u0914\u0930 \u0924\u094d\u0935\u0930\u0923"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0917\u0924\u093f\u0915\u0940 \u0915\u0940 \u092e\u0942\u0932\u092d\u0942\u0924 \u092c\u093e\u0924\u0947\u0902: \u0938\u094d\u0925\u093f\u0924\u093f, \u0935\u0947\u0917, \u0914\u0930 \u0924\u094d\u0935\u0930\u0923<\/h1>\n<p><em><strong>\u0938\u093e\u0930\u093e\u0902\u0936:<\/strong><br \/>\n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u0917\u0924\u093f\u0915\u0940 \u0915\u0947 \u092e\u0942\u0932\u092d\u0942\u0924 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947: \u0938\u094d\u0925\u093f\u0924\u093f, \u0935\u0947\u0917 \u0914\u0930 \u0924\u094d\u0935\u0930\u0923\u0964 \u0939\u092e \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u0925 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0948\u0938\u0947 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\u0938\u094d\u0925\u093f\u0924\u093f \u0915\u0947 \u092c\u0940\u091a \u0915\u0947 \u0938\u0902\u092c\u0902\u0927\u0964<\/li>\n<li><strong>\u0932\u093e\u0917\u0942 \u0915\u0930\u0947\u0902<\/strong> \u0924\u094d\u0935\u0930\u0923 \u0938\u0947 \u0935\u0947\u0917 \u0914\u0930 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0905\u0935\u0915\u0932\u091c \u0914\u0930 \u0938\u092e\u093e\u0915\u0932\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917, \u0914\u0930 \u0907\u0938\u0915\u0947 \u0935\u093f\u092a\u0930\u0940\u0924\u0964<\/li>\n<li><strong>\u0938\u092e\u091d\u0947\u0902<\/strong> \u0924\u093e\u0924\u094d\u0915\u093e\u0932\u093f\u0915 \u0914\u0930 \u0914\u0938\u0924 \u0935\u0947\u0917 \u0915\u0947 \u092c\u0940\u091a \u0915\u093e \u0905\u0902\u0924\u0930, \u0914\u0930 \u0924\u093e\u0924\u094d\u0915\u093e\u0932\u093f\u0915 \u0914\u0930 \u0914\u0938\u0924 \u0924\u094d\u0935\u0930\u0923 \u0915\u0947 \u092c\u0940\u091a \u0915\u093e \u0905\u0902\u0924\u0930\u0964<\/li>\n<\/ol>\n<p><center><\/p>\n<p><strong>\u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u0915\u0940 \u0938\u0942\u091a\u0915\u093e\u0902\u0915<\/strong><br \/>\n<a href=\"#1\">\u092a\u0930\u093f\u091a\u092f<\/a><br \/>\n<a href=\"#2\">\u0938\u094d\u0925\u093f\u0924\u093f, \u0938\u094d\u0925\u093e\u0928 \u0914\u0930 \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915<\/a><br \/>\n<a href=\"#3\">\u0935\u0947\u0917 \u0914\u0930 \u0924\u0940\u0935\u094d\u0930\u0924\u093e<\/a><br \/>\n<a href=\"#4\">\u0924\u094d\u0935\u0930\u0923<\/a><br \/>\n<a href=\"#5\">\u0917\u0924\u093f \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923\u0947\u0902<\/a><br \/>\n<a href=\"#5\">\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/a>\n<\/p>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/fjv-qEuPhwU\" title=\"YouTube \u0935\u0940\u0921\u093f\u092f\u094b \u092a\u094d\u0932\u0947\u092f\u0930\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u092a\u0930\u093f\u091a\u092f<\/h2>\n<p style=\"text-align: justify;\">\u0924\u094d\u0935\u0930\u0923 \u0938\u0947, \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0938\u092e\u093e\u0915\u0932\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u0935\u0947\u0917 \u0914\u0930 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u093e \u0938\u0902\u092d\u0935 \u0939\u0948, \u0914\u0930 \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u0947, \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0905\u0935\u0915\u0932\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u0935\u0947\u0917 \u0914\u0930 \u0924\u094d\u0935\u0930\u0923 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u093e \u0938\u0902\u092d\u0935 \u0939\u0948\u0964 \u092f\u0947 \u0936\u092c\u094d\u0926 \u0917\u0924\u093f\u0915\u0940 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0939\u092e\u093e\u0930\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u094b \u0938\u0902\u0915\u094d\u0937\u0947\u092a \u092e\u0947\u0902 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0914\u0930 \u0939\u092e\u093e\u0930\u0947 \u092e\u0941\u0916\u094d\u092f \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u090f\u0915 \u0907\u0928 \u0936\u092c\u094d\u0926\u094b\u0902 \u0915\u0947 \u0905\u0930\u094d\u0925 \u0915\u094b \u0938\u092e\u091d\u0928\u093e \u0939\u094b\u0917\u093e\u0964 \u0917\u0924\u093f \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u093e \u090f\u0915 \u0930\u0942\u092a \u0926\u0930\u094d\u0936\u093e\u0924\u0940 \u0939\u0948, \u0914\u0930 \u092a\u094d\u0930\u0915\u0943\u0924\u093f \u092e\u0947\u0902 \u0938\u092c \u0915\u0941\u091b \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u0905\u0927\u0940\u0928 \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f, \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0914\u0930 \u0907\u0938\u0915\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u092a\u094d\u0930\u0915\u093e\u0930\u094b\u0902 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u092d\u094c\u0924\u093f\u0915\u0940 \u0915\u0947 \u092e\u0941\u0916\u094d\u092f \u0906\u0927\u093e\u0930\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u090f\u0915 \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928\u0936\u0940\u0932\u0924\u093e \u0915\u0947 \u0915\u0908 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948\u0902: \u0928\u092f\u093e \u092a\u0941\u0930\u093e\u0928\u093e \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948, \u0915\u094b\u0908 \u0935\u094d\u092f\u0915\u094d\u0924\u093f \u090f\u0915 \u092a\u0947\u0936\u093e 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\u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902, \u091c\u094b \u092e\u093f\u0932\u0915\u0930 \u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915\u0940 \u092c\u0928\u093e\u0924\u0940 \u0939\u0948\u0902\u0964<\/p>\n<p style=\"text-align: justify;\">\u092d\u094c\u0924\u093f\u0915\u0940 \u092e\u0947\u0902, \u0939\u092e \u0938\u094d\u0925\u093f\u0924\u093f, \u0935\u0947\u0917, \u0914\u0930 \u0924\u094d\u0935\u0930\u0923 \u091c\u0948\u0938\u0947 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u0947 \u0917\u0923\u093f\u0924\u0940\u092f \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u094b \u0938\u0930\u0932 \u092c\u0928\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092d\u094c\u0924\u093f\u0915 \u0938\u094d\u0925\u093e\u0928 \u0915\u094b \u090f\u0915 \u0938\u0926\u093f\u0936 \u0938\u094d\u0925\u093e\u0928 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092e\u0949\u0921\u0932 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0924\u0903, \u0939\u092e \u0907\u0938 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f \u0915\u0947 \u0932\u093f\u090f \u0924\u094d\u0930\u093f-\u0906\u092f\u093e\u092e\u0940 \u0938\u094d\u0925\u093e\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^3<\/span><\/span> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0939\u093e\u0932\u093e\u0902\u0915\u093f \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u092e\u0947\u0902, \u0915\u093f\u0938\u0940 \u092d\u0940 \u0906\u092f\u093e\u092e \u0915\u0947 \u0938\u094d\u0925\u093e\u0928 \u0938\u0902\u0926\u0930\u094d\u092d \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0938\u094d\u0925\u093f\u0924\u093f, \u0938\u094d\u0925\u093e\u0928 \u0914\u0930 \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=fjv-qEuPhwU&amp;t=257s\" target=\"_blank\" rel=\"noopener\"><strong>\u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u090f\u0915 \u092b\u0932\u0928 \u0939\u0948<\/strong><\/a><\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rll}\n\n\\vec{r}:\\mathbb{R}[T]&amp;\\longrightarrow&amp;\\mathbb{R}^n[L] \\\\\n\nt &amp;\\longmapsto&amp;\\vec{r}(t)\n\n\\end{array}\n\n<\/span>\n<p style=\"text-align: justify;\">\u092f\u0939 \u090f\u0915 \u092b\u0932\u0928 \u0939\u0948 \u091c\u094b \u0939\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t\\in\\mathbb{R}<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}(t)<\/span><\/span> \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948, \u0914\u0930 \u0907\u0938\u0932\u093f\u090f, \u0939\u092e \u0915\u0939\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092f\u0939 \u090f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u092b\u0932\u0928 \u0939\u0948 (\u092f\u093e \u092c\u0938 \u0938\u094d\u0925\u093f\u0924\u093f)\u0964 \u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u091a\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">t<\/span> \u0915\u094b \u00ab\u0938\u092e\u092f\u00bb \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0938\u094d\u0925\u093e\u0928 \u0915\u0947 \u00ab\u0906\u092f\u093e\u092e\u00bb \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u092a\u094d\u0930\u0924\u0940\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">[T]<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">[L]<\/span> \u0938\u092e\u092f \u0914\u0930 \u0932\u0902\u092c\u093e\u0908 \u0915\u0947 \u092d\u094c\u0924\u093f\u0915 \u0906\u092f\u093e\u092e\u094b\u0902 \u0915\u094b \u0938\u0902\u0926\u0930\u094d\u092d\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u0906\u092e\u0924\u094c\u0930 \u092a\u0930 \u00ab\u0938\u0947\u0915\u0902\u0921\u00bb \u0914\u0930 \u00ab\u092e\u0940\u091f\u0930\u00bb \u092e\u0947\u0902 \u092e\u093e\u092a\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0902\u0964<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-gCSXLVh_JEI\/YQhm3e26l2I\/AAAAAAAAFXs\/fBu5WvV1PiIhGDkTUZfSAR4EMQqUFneoACLcBGAsYHQ\/s0\/posici%25C3%25B3n%2Ben%2Bel%2Bespacio%2B3D.PNG\" width=\"400\" height=\"300\" alt=\"\u092e\u0942\u0932 \u0917\u0924\u093f\u0915\u0940: \u0924\u094d\u0930\u093f-\u0906\u092f\u093e\u092e\u0940 \u0938\u094d\u0925\u093e\u0928 \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0924\u093f, \u092e\u0942\u0932 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-gCSXLVh_JEI\/YQhm3e26l2I\/AAAAAAAAFXs\/fBu5WvV1PiIhGDkTUZfSAR4EMQqUFneoACLcBGAsYHQ\/s0\/posici%25C3%25B3n%2Ben%2Bel%2Bespacio%2B3D.PNG\" width=\"400\" height=\"300\" alt=\"\u092e\u0942\u0932 \u0917\u0924\u093f\u0915\u0940: \u0924\u094d\u0930\u093f-\u0906\u092f\u093e\u092e\u0940 \u0938\u094d\u0925\u093e\u0928 \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0924\u093f, \u092e\u0942\u0932 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">\u0938\u094d\u0925\u093f\u0924\u093f, \u0915\u093f\u0938\u0940 \u092d\u0940 \u092d\u094c\u0924\u093f\u0915 \u0930\u093e\u0936\u093f \u0915\u0940 \u0924\u0930\u0939, \u090f\u0915 \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915 \u0926\u094d\u0935\u093e\u0930\u093e \u092e\u093e\u092a\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u0947 \u092e\u0947\u0930\u0947 \u0926\u094d\u0935\u093e\u0930\u093e \u0926\u093f\u090f \u0917\u090f \u0935\u093f\u0935\u0930\u0923 \u092e\u0947\u0902, \u092e\u0948\u0902\u0928\u0947 \u092f\u0939 \u0938\u092e\u091d \u0932\u093f\u092f\u093e \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915 \u0915\u0947 \u092a\u093e\u0938 \u0936\u0942\u0928\u094d\u092f \u0938\u0926\u093f\u0936 \u0915\u0940 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0939\u0948\u0902, <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{0}<\/span>\u0964 \u092f\u0926\u093f \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}<\/span> \u0915\u0947 \u092a\u093e\u0938 \u0938\u0926\u093f\u0936 <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}<\/span> \u0915\u0940 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0939\u0948\u0902 \u0914\u0930 \u092c\u093f\u0902\u0926\u0941 \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}^\\prime<\/span><\/span> \u0939\u0948\u0902, \u0924\u094b <strong>\u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915 \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0938\u094d\u0925\u093f\u0924\u093f<\/strong> \u0939\u094b\u0917\u0940:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}_\\mathcal{O} = \\vec{r} - \\vec{r}^\\prime<\/span><\/span><\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-NV6VA_yStVo\/YQhpIOk5yCI\/AAAAAAAAFX0\/YW9xYYXY9h0DTnLfkNA0H7deQPkFqsbogCLcBGAsYHQ\/s0\/posicion%2Bdesde%2Bel%2Bobservador.PNG\" width=\"500\" height=\"300\" alt=\"\u092e\u0942\u0932 \u0917\u0924\u093f\u0915\u0940: \u090f\u0915 \u0906\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u0947\u0930\u0940 \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0938\u094d\u0925\u093f\u0924\u093f\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-NV6VA_yStVo\/YQhpIOk5yCI\/AAAAAAAAFX0\/YW9xYYXY9h0DTnLfkNA0H7deQPkFqsbogCLcBGAsYHQ\/s0\/posicion%2Bdesde%2Bel%2Bobservador.PNG\" width=\"500\" height=\"300\" alt=\"\u092e\u0942\u0932 \u0917\u0924\u093f\u0915\u0940: \u090f\u0915 \u0906\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u0947\u0930\u0940 \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0938\u094d\u0925\u093f\u0924\u093f\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">\u0938\u094d\u0925\u093e\u0928 \u0938\u092d\u0940 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u0915\u093e \u0938\u0947\u091f \u0939\u0948, \u092f\u0939 \u0915\u093f\u0938\u0940 \u092d\u0940 \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915 \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0938\u092d\u0940 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u0915\u093e \u092d\u0940 \u0938\u0947\u091f \u0939\u0948\u0964 \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u092e\u092f \u0915\u093e \u090f\u0915 \u092b\u0932\u0928 \u0939\u0948 \u0914\u0930 \u0907\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u00ab\u092c\u093f\u0902\u0926\u0941 \u0935\u0938\u094d\u0924\u0941\u00bb \u0915\u0939\u0932\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u0906\u0926\u0930\u094d\u0936 \u0935\u0938\u094d\u0924\u0941 \u0915\u093e \u0939\u0930 \u0938\u092e\u092f <span class=\"katex-eq\" data-katex-display=\"false\">t<\/span> \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0924 \u0939\u094b\u0928\u0947 \u0935\u093e\u0932\u0947 \u0938\u094d\u0925\u093e\u0928 \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u092c\u093f\u0902\u0926\u0941 \u0935\u0938\u094d\u0924\u0941 \u090f\u0915 \u0906\u0926\u0930\u094d\u0936\u0940\u0915\u0930\u0923 \u0939\u0948, \u092f\u0939 \u0935\u0939 \u0939\u0948 \u091c\u094b \u090f\u0915 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0935\u0938\u094d\u0924\u0941 \u0938\u0947 \u0924\u092c \u092c\u091a\u0924\u093e \u0939\u0948 \u091c\u092c \u0939\u092e \u0909\u0938\u0947 \u0938\u092d\u0940 \u0917\u0941\u0923\u094b\u0902 \u0938\u0947 \u092e\u0941\u0915\u094d\u0924 \u0915\u0930 \u0926\u0947\u0924\u0947 \u0939\u0948\u0902, \u0906\u0915\u093e\u0930 \u0914\u0930 \u0930\u0942\u092a \u0938\u0939\u093f\u0924, \u0915\u0947\u0935\u0932 \u00ab\u0938\u094d\u0925\u093e\u0928 \u091c\u094b \u0935\u0939 \u0938\u094d\u0925\u093e\u0928 \u092a\u0930 \u0932\u0947\u0924\u093e \u0939\u0948\u00bb \u0915\u094b \u092c\u0928\u093e\u090f \u0930\u0916\u0924\u0947 \u0939\u0941\u090f\u0964<\/p>\n<p style=\"text-align: justify;\">\u0938\u094d\u0925\u093f\u0924\u093f \u0906\u092e\u0924\u094c\u0930 \u092a\u0930 \u090f\u0915 \u0938\u0926\u093f\u0936 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0938\u0926\u093f\u0936\u094b\u0902 \u092e\u0947\u0902 \u0926\u094b \u0924\u0924\u094d\u0935 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902: \u092a\u0930\u093f\u092e\u093e\u0923 \u0914\u0930 \u0926\u093f\u0936\u093e\u0964 \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915 \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u0923 \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915 \u0938\u0947 \u0926\u0942\u0930\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948 \u0914\u0930 \u0907\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">dist_\\mathcal{O}(t)=\\|\\vec{r}_\\mathcal{O}(t)\\|<\/span> \u0926\u094d\u0935\u093e\u0930\u093e \u0926\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u0907\u0938 \u092c\u093f\u0902\u0926\u0941 \u0938\u0947, <strong><a href=\"https:\/\/www.youtube.com\/watch?v=FEPfoAfPsFY&#038;list=PL_C8rbeFjqAVaR_sgLJRBvMm5t6E1GxGI\" rel=\"noopener\" target=\"_blank\">\u0905\u0935\u0915\u0932\u0928<\/a> \u0914\u0930 <a href=\"https:\/\/www.youtube.com\/watch?v=4wSTxA7zY9k&#038;list=PL_C8rbeFjqAUU5ClOkZMRJbiefHDeXGI2\" rel=\"noopener\" target=\"_blank\">\u0938\u092e\u093e\u0915\u0932\u0928<\/a> \u0915\u0947 \u092a\u093e\u0920\u094d\u092f\u0915\u094d\u0930\u092e<\/strong> \u0915\u0940 \u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u092e\u0947\u0902 \u092e\u0939\u093e\u0930\u0924 \u0939\u093e\u0938\u093f\u0932 \u0915\u0930\u0928\u093e \u0905\u0924\u094d\u092f\u0927\u093f\u0915 \u0905\u0928\u0941\u0936\u0902\u0938\u093f\u0924 \u0939\u0948\u0964<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u0924\u0940\u0935\u094d\u0930\u0924\u093e \u0914\u0930 \u0935\u0947\u0917<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=fjv-qEuPhwU&amp;t=1232s\" target=\"_blank\" rel=\"noopener\"><strong>\u092f\u0926\u093f \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0905\u0935\u0915\u0932\u0928\u0940\u092f \u0939\u0948,<\/strong><\/a> \u0924\u094b \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}<\/span> \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0935\u0947\u0917 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{v}_\\mathcal{O}(t)<\/span><\/span> \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{v}_\\mathcal{O}(t) =\\displaystyle \\lim_{\\Delta t \\to 0}\\frac{\\vec{r}_\\mathcal{O}(t+\\Delta t) - \\vec{r}_\\mathcal{O}(t)}{\\Delta t} = \\frac{d\\vec{r}_\\mathcal{O}(t)}{dt} <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0938\u0930\u0932 \u0936\u092c\u094d\u0926\u094b\u0902 \u092e\u0947\u0902: \u0935\u0947\u0917 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u093e \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u0925 \u0905\u0935\u0915\u0932\u091c \u0939\u0948 \u0914\u0930 \u092f\u0939 \u0939\u092e\u0947\u0902 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0938\u094d\u0925\u093f\u0924\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u094d\u0937\u0923 <span class=\"katex-eq\" data-katex-display=\"false\">t<\/span> \u092e\u0947\u0902 \u0915\u0948\u0938\u0947 \u092c\u0926\u0932\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u0935\u0947\u0917 \u0915\u0947 \u0926\u094b \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902: \u0924\u093e\u0924\u094d\u0915\u093e\u0932\u093f\u0915 \u0914\u0930 \u0914\u0938\u0924\u0964 \u0924\u093e\u0924\u094d\u0915\u093e\u0932\u093f\u0915 \u0935\u0947\u0917 \u0905\u092d\u0940 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0925\u093e, \u0914\u0938\u0924 \u0935\u0947\u0917 \u0938\u0940\u092e\u093e \u0915\u0940 \u0917\u0923\u0928\u093e \u091b\u094b\u0921\u093c\u0915\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0938\u092e\u092f\u093e\u0902\u0924\u0930\u093e\u0932 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta t<\/span><\/span> \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u092a\u0930 \u0914\u0938\u0924 \u0935\u0947\u0917 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left&lt; \\vec{v}_{\\mathcal{O},\\Delta t}(\\overline{t}) \\right&gt;<\/span><\/span> \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left&lt; \\vec{v}_{\\mathcal{O},\\Delta t}(\\overline{t}) \\right&gt; = \\displaystyle \\frac{\\vec{r}_\\mathcal{O}(t+\\Delta t) - \\vec{r}_\\mathcal{O}(t)}{\\Delta t}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u091c\u0939\u093e\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">\\overline{t}<\/span> \u0915\u093f\u0938\u0940 \u092d\u0940 \u0915\u094d\u0937\u0923 \u092e\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">[t,t+\\Delta t]<\/span> \u092e\u0947\u0902 \u0928\u093f\u0939\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u0924\u093e\u0924\u094d\u0915\u093e\u0932\u093f\u0915 \u092f\u093e \u0914\u0938\u0924 \u0935\u0947\u0917 \u0938\u0947 \u0924\u0940\u0935\u094d\u0930\u0924\u093e \u0915\u094b \u0909\u0938\u0915\u0940 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092a\u0930\u093f\u092e\u093e\u0923 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}<\/span> \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0924\u0940\u0935\u094d\u0930\u0924\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_\\mathcal{O}(t)=\\|\\vec{v}_\\mathcal{O}(t)\\|<\/span><\/span> \u0939\u094b\u0924\u0940 \u0939\u0948, \u0914\u0930 \u0914\u0938\u0924 \u0924\u0940\u0935\u094d\u0930\u0924\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left&lt; {v}_{\\mathcal{O},\\Delta t}(\\overline{t}) \\right&gt; = \\|\\left&lt; \\vec{v}_{\\mathcal{O},\\Delta t}(\\overline{t}) \\right&gt;\\|<\/span><\/span> \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u0924\u0940\u0935\u094d\u0930\u0924\u093e \u0914\u0930 \u0935\u0947\u0917 \u0932\u0902\u092c\u093e\u0908 \u0915\u0947 \u0907\u0915\u093e\u0908\u092f\u094b\u0902 \u092a\u0930 \u0938\u092e\u092f \u0915\u0947 \u0907\u0915\u093e\u0908\u092f\u094b\u0902 \u092e\u0947\u0902 \u092e\u093e\u092a\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0902, <span class=\"katex-eq\" data-katex-display=\"false\">[L\/T]<\/span>, \u091c\u094b \u0906\u092e\u0924\u094c\u0930 \u092a\u0930 \u00ab\u092e\u0940\u091f\u0930 \u092a\u094d\u0930\u0924\u093f \u0938\u0947\u0915\u0902\u0921\u00bb \u0939\u094b\u0924\u0940 \u0939\u0948\u0902\u0964<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u0924\u094d\u0935\u0930\u0923<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=fjv-qEuPhwU&amp;t=1522s\" target=\"_blank\" rel=\"noopener\"><strong>\u0935\u0947\u0917 \u0915\u0947 \u0938\u092e\u093e\u0928,<\/strong><\/a> \u0905\u0917\u0930 \u092f\u0939 \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0905\u0935\u0915\u0932\u0928\u0940\u092f \u0939\u0948, \u0924\u094b \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}<\/span> \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0924\u094d\u0935\u0930\u0923 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{a}_\\mathcal{O}(t)<\/span><\/span> \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{a}_\\mathcal{O}(t)= \\displaystyle \\lim_{\\Delta t \\to 0}\\frac{\\vec{v}_\\mathcal{O}(t+\\Delta t) - \\vec{v}_\\mathcal{O}(t)}{\\Delta t} = \\frac{d\\vec{v}_\\mathcal{O}(t)}{dt}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0924\u094d\u0935\u0930\u0923 \u0935\u0947\u0917 \u0915\u093e \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u0925 \u0905\u0935\u0915\u0932\u091c \u0939\u0948 \u0914\u0930 \u092a\u0930\u093f\u0923\u093e\u092e\u0938\u094d\u0935\u0930\u0942\u092a \u092f\u0939 \u0939\u092e\u0947\u0902 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0935\u0947\u0917 \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u0925 \u0915\u0948\u0938\u0947 \u092c\u0926\u0932\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u0924\u0940\u0935\u094d\u0930\u0924\u093e \u0915\u0947 \u0938\u092e\u093e\u0928, \u0924\u093e\u0924\u094d\u0915\u093e\u0932\u093f\u0915 \u0914\u0930 \u0914\u0938\u0924 \u0924\u094d\u0935\u0930\u0923 \u092d\u0940 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0924\u093e\u0924\u094d\u0915\u093e\u0932\u093f\u0915 \u0924\u094d\u0935\u0930\u0923 \u091c\u094b \u0939\u092e\u0928\u0947 \u0905\u092d\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u093f\u092f\u093e \u0939\u0948, \u0914\u0938\u0924 \u0924\u094d\u0935\u0930\u0923 \u0938\u0940\u092e\u093e \u0915\u0940 \u0917\u0923\u0928\u093e \u091b\u094b\u0921\u093c\u0915\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0938\u092e\u092f\u093e\u0902\u0924\u0930\u093e\u0932 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta t<\/span><\/span> \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u092a\u0930 \u0914\u0938\u0924 \u0924\u094d\u0935\u0930\u0923 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left&lt;\\vec{a}_{\\mathcal{O},\\Delta t}\\right&gt;<\/span><\/span> \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left&lt; \\vec{a}_{\\mathcal{O},\\Delta t}(\\overline{t}) \\right&gt; = \\displaystyle \\frac{\\vec{v}_\\mathcal{O}(t+\\Delta t) - \\vec{v}_\\mathcal{O}(t)}{\\Delta t}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0924\u094d\u0935\u0930\u0923 \u0932\u0902\u092c\u093e\u0908 \u092a\u0930 \u0938\u092e\u092f \u0915\u0947 \u0935\u0930\u094d\u0917 \u0915\u0947 \u0907\u0915\u093e\u0908\u092f\u094b\u0902 \u092e\u0947\u0902 \u092e\u093e\u092a\u093e \u091c\u093e\u0924\u093e \u0939\u0948, <span class=\"katex-eq\" data-katex-display=\"false\">[L\/T^2]<\/span>, \u091c\u094b \u0906\u092e\u0924\u094c\u0930 \u092a\u0930 \u00ab\u092e\u0940\u091f\u0930 \u092a\u094d\u0930\u0924\u093f \u0938\u0947\u0915\u0902\u0921 \u0935\u0930\u094d\u0917\u00bb \u0939\u094b\u0924\u0940 \u0939\u0948\u0902\u0964<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u0917\u0924\u093f \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923\u0947\u0902<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=fjv-qEuPhwU&amp;t=1588s\" target=\"_blank\" rel=\"noopener\"><strong>\u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u090f\u0915 \u092c\u093f\u0902\u0926\u0941 \u0935\u0938\u094d\u0924\u0941 \u0939\u0948<\/strong><\/a> \u091c\u094b \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}<\/span> \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0938\u094d\u0925\u093f\u0930 \u0924\u094d\u0935\u0930\u0923 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{a}_\\mathcal{O}(t) = \\vec{a}_0<\/span><\/span> \u0915\u0947 \u0938\u093e\u0925 \u091a\u0932 \u0930\u0939\u0940 \u0939\u0948\u0964 \u092f\u0926\u093f \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u0947 \u0935\u0947\u0917 \u0914\u0930 \u0924\u094d\u0935\u0930\u0923 \u0915\u093e \u0905\u0935\u0915\u0932\u091c \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u093e \u0938\u0902\u092d\u0935 \u0939\u0948, \u0924\u094b \u0924\u094d\u0935\u0930\u0923 \u0938\u0947 \u0935\u0947\u0917 \u0914\u0930 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u093e \u0938\u092e\u093e\u0915\u0932\u0928 \u0915\u0930\u0915\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u0924\u0930\u0939 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u094b \u0917\u0924\u093f \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923\u0947\u0902 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u0907\u0902\u091f\u093f\u0917\u094d\u0930\u0947\u091f\u093f\u0902\u0917 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{a}_\\mathcal{O}(t) = \\vec{a}_0<\/span><\/span>, \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{v}_\\mathcal{O}(t) = \\displaystyle \\int \\vec{a}_\\mathcal{O}(t) dt = \\int \\vec{a}_0 dt = \\vec{a}_0 t + \\vec{v}_0 <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0914\u0930 \u092b\u093f\u0930 \u0938\u0947 \u0938\u092e\u093e\u0915\u0932\u0928 \u0915\u0930\u0915\u0947, \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}_\\mathcal{O}(t) = \\displaystyle \\int \\vec{v}_\\mathcal{O}(t) dt = \\int \\vec{a}_0t + \\vec{v}_0 dt = \\displaystyle \\frac{1}{2}\\vec{a}_0 t^2 + \\vec{v}_0t+\\vec{r}_0 <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u092f\u0939\u093e\u0902, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{v}_0<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}_0<\/span><\/span> \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915, \u0938\u094d\u0925\u093f\u0924\u093f \u0914\u0930 \u0935\u0947\u0917 \u0915\u0947 \u0938\u092e\u093e\u0915\u0932\u0928 \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 \u0939\u0948\u0902, \u091c\u094b \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}<\/span> \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u0914\u0930 \u0935\u0947\u0917 \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902\u0964 \u0938\u0902\u0915\u094d\u0937\u0947\u092a \u092e\u0947\u0902, \u0917\u0924\u093f \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923\u0947\u0902 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\vec{a}_\\mathcal{O}(t) =&amp; \\vec{a}_0 \\\\\n\n\\vec{v}_\\mathcal{O}(t) =&amp;  \\vec{a}_0t+\\vec{v}_0 \\\\\n\n\\vec{r}_\\mathcal{O}(t) =&amp; \\displaystyle \\frac{1}{2}\\vec{a}_0t^2 + \\vec{v}_0t + \\vec{r}_0\n\n\\end{array}\n\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0907\u0928 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947, \u0915\u093f\u0938\u0940 \u092d\u0940 \u0935\u0938\u094d\u0924\u0941 \u0915\u0947 \u0938\u094d\u0925\u093f\u0930 \u0924\u094d\u0935\u0930\u0923 \u0915\u0947 \u0938\u093e\u0925 \u091a\u0932\u0928\u0947 \u0935\u093e\u0932\u0940 \u0917\u0924\u093f \u0915\u093e \u092a\u0942\u0930\u094d\u0923 \u0930\u0942\u092a \u0938\u0947 \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0928\u093e \u0938\u0902\u092d\u0935 \u0939\u0948\u0964 \u092f\u0939 \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u0924\u094d\u0935\u0930\u0923 \u0938\u0947 \u0935\u0947\u0917 \u0914\u0930 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u093e \u0938\u092e\u093e\u0915\u0932\u0928 \u0915\u0930\u0915\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u0914\u0930 \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u0947 \u0935\u0947\u0917 \u0914\u0930 \u0924\u094d\u0935\u0930\u0923 \u0915\u093e \u0905\u0935\u0915\u0932\u091c \u0915\u0930\u0915\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902 \u0915\u093f \u092f\u0947 \u0938\u0926\u093f\u0936 \u0938\u092e\u0940\u0915\u0930\u0923\u0947\u0902 \u0939\u0948\u0902, \u0914\u0930 \u0907\u0938\u0932\u093f\u090f, \u0909\u0928\u094d\u0939\u0947\u0902 \u0909\u0928\u0915\u0947 \u0918\u091f\u0915\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u092f\u0926\u093f \u0939\u092e \u090f\u0915 \u0924\u094d\u0930\u093f-\u0906\u092f\u093e\u092e\u0940 \u0938\u094d\u0925\u093e\u0928 \u092e\u0947\u0902 \u0917\u0924\u093f \u0915\u093e \u092e\u0949\u0921\u0932 \u0915\u0930 \u0930\u0939\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u0915\u094d\u0937 \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0940\u0915\u0930\u0923\u0947\u0902 \u092e\u093f\u0932\u0924\u0940 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\vec{a}_\\mathcal{O}(t) &amp;= (a_x(t), a_y(t), a_z(t))\\\\\n\n\\vec{v}_\\mathcal{O}(t) &amp;= (v_x(t), v_y(t), v_z(t))\\\\\n\n\\vec{r}_\\mathcal{O}(t) &amp;= (x(t), y(t), z(t))\\\\\n\n\\vec{a}_0 &amp;= (a_{0x}, a_{0y}, a_{0z})\\\\\n\n\\vec{v}_0 &amp;= (v_{0x}, v_{0y}, v_{0z})\\\\\n\n\\vec{r}_0 &amp;= (x_{0}, y_{0}, z_{0})\\\\\n\n\\end{array}\n\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, 9 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u093e \u0938\u0947\u091f \u092c\u0928\u0924\u093e \u0939\u0948, \u090f\u0915 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u0915\u094d\u0937 \u0915\u0947 \u0932\u093f\u090f\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> \u0905\u0915\u094d\u0937 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0939\u094b\u0917\u093e:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\na_x(t) &amp; = a_{0x}\\\\\n\nv_x(t) &amp; = a_{0x}t + v_{0x} \\\\\n\nx(t) &amp; = \\displaystyle \\frac{1}{2}a_{0x}t^2 + v_{0x}t + x_0\n\n\\end{array}\n\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0906\u092e\u0924\u094c\u0930 \u092a\u0930, <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{z}<\/span> \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u090a\u0902\u091a\u093e\u0908 \u0915\u0947 \u0932\u093f\u090f \u0906\u0930\u0915\u094d\u0937\u093f\u0924 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u092f\u0939 \u092e\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">a_{0z}=-g \\approx -9.81[m\/s^2];<\/span> \u0905\u0930\u094d\u0925\u093e\u0924, \u0907\u0938 \u0905\u0915\u094d\u0937 \u092e\u0947\u0902 \u0924\u094d\u0935\u0930\u0923 \u0915\u094b \u092a\u0943\u0925\u094d\u0935\u0940 \u0915\u0947 \u0917\u0941\u0930\u0941\u0924\u094d\u0935\u093e\u0915\u0930\u094d\u0937\u0923 \u0926\u094d\u0935\u093e\u0930\u093e \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0924\u094d\u0935\u0930\u0923 \u0938\u0947 \u091c\u094b\u0921\u093c\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u092e\u0947\u0902 \u0936\u093e\u092e\u093f\u0932 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0924\u093e\u0915\u093f \u092e\u0941\u0915\u094d\u0924 \u0917\u093f\u0930\u093e\u0935\u091f \u092f\u093e \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u0947 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u091c\u0948\u0938\u0947 \u0918\u091f\u0928\u093e\u0913\u0902 \u0915\u093e \u092e\u0949\u0921\u0932\u093f\u0902\u0917 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0947\u0964<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/h2>\n<p style=\"text-align: justify;\">\n    \u0907\u0938 \u0917\u0924\u093f\u0915\u0940 \u0915\u0940 \u092e\u0942\u0932\u092d\u0942\u0924 \u092f\u093e\u0924\u094d\u0930\u093e \u092e\u0947\u0902, \u0939\u092e\u0928\u0947 \u092f\u0939 \u0926\u0947\u0916\u093e \u0915\u093f \u0917\u0923\u093f\u0924 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0939\u092e \u092d\u094c\u0924\u093f\u0915 \u0938\u094d\u0925\u093e\u0928 \u092e\u0947\u0902 \u0917\u0924\u093f \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0914\u0930 \u0938\u092e\u091d \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u093e \u090f\u0915 \u0938\u0926\u093f\u0936 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930\u0928\u0947 \u0938\u0947 \u0932\u0947\u0915\u0930 \u0938\u092e\u092f\u093e\u0902\u0924\u0930\u093e\u0932 \u0915\u0947 \u0938\u092e\u093e\u0915\u0932\u0928 \u0914\u0930 \u0905\u0935\u0915\u0932\u0928 \u0924\u0915, \u0939\u092e\u0928\u0947 \u092f\u0939 \u0926\u0947\u0916\u093e \u0915\u093f \u092f\u0947 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u090f\u0902 \u0915\u0948\u0938\u0947 \u091c\u0941\u0921\u093c\u0947 \u0939\u0941\u090f \u0939\u0948\u0902 \u0914\u0930 \u0917\u0924\u093f \u0915\u0947 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u092e\u0947\u0902 \u0932\u093e\u0917\u0942 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902\u0964\n<\/p>\n<p style=\"text-align: justify;\">\n    \u0917\u0924\u093f\u0915\u0940, \u091c\u094b \u092c\u093f\u0928\u093e \u0917\u0924\u093f \u0915\u0947 \u0915\u093e\u0930\u0923\u094b\u0902 \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u093f\u090f \u0917\u0924\u093f \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0924\u0940 \u0939\u0948, \u0939\u092e\u0947\u0902 \u0935\u0938\u094d\u0924\u0941\u0913\u0902 \u0915\u0940 \u0936\u0941\u0926\u094d\u0927 \u0914\u0930 \u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u0938\u0941\u0902\u0926\u0930 \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964 \u0905\u0935\u0915\u0932\u0928 \u0914\u0930 \u0938\u092e\u093e\u0915\u0932\u0928 \u0915\u0940 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947, \u0939\u092e \u0917\u0924\u093f \u0915\u0947 \u092a\u0948\u091f\u0930\u094d\u0928 \u0915\u094b \u0938\u092e\u091d \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u092d\u0935\u093f\u0937\u094d\u092f \u0915\u0940 \u0926\u093f\u0936\u093e\u0913\u0902 \u0915\u0940 \u092d\u0935\u093f\u0937\u094d\u092f\u0935\u093e\u0923\u0940 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u092d\u094c\u0924\u093f\u0915\u0940 \u0914\u0930 \u0905\u092d\u093f\u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915\u0940 \u0915\u0947 \u0915\u0908 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u094b\u0902 \u092e\u0947\u0902 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948\u0964\n<\/p>\n<p style=\"text-align: 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\u0938\u0948\u0926\u094d\u0927\u093e\u0902\u0924\u093f\u0915 \u0905\u092d\u094d\u092f\u093e\u0938 \u0928\u0939\u0940\u0902 \u0939\u0948, \u092c\u0932\u094d\u0915\u093f \u092f\u0939 \u092d\u094c\u0924\u093f\u0915 \u0926\u0941\u0928\u093f\u092f\u093e \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0914\u0930 \u0909\u0938\u0947 \u0938\u0902\u091a\u093e\u0932\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u090f\u0915 \u092e\u094c\u0932\u093f\u0915 \u0909\u092a\u0915\u0930\u0923 \u0939\u0948\u0964<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0917\u0924\u093f\u0915\u0940 \u0915\u0940 \u092e\u0942\u0932\u092d\u0942\u0924 \u092c\u093e\u0924\u0947\u0902: \u0938\u094d\u0925\u093f\u0924\u093f, \u0935\u0947\u0917, \u0914\u0930 \u0924\u094d\u0935\u0930\u0923 \u0938\u093e\u0930\u093e\u0902\u0936: \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u0917\u0924\u093f\u0915\u0940 \u0915\u0947 \u092e\u0942\u0932\u092d\u0942\u0924 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947: \u0938\u094d\u0925\u093f\u0924\u093f, \u0935\u0947\u0917 \u0914\u0930 \u0924\u094d\u0935\u0930\u0923\u0964 \u0939\u092e \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u0925 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902, \u0907\u0938 \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0947\u0902\u0917\u0947, \u0938\u093e\u0925 \u0939\u0940 \u0924\u093e\u0924\u094d\u0915\u093e\u0932\u093f\u0915 \u0914\u0930 \u0914\u0938\u0924 \u0935\u0947\u0917 \u0914\u0930 \u0924\u094d\u0935\u0930\u0923 \u0915\u0947 \u092c\u0940\u091a \u0905\u0902\u0924\u0930 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u0939\u092e \u0938\u094d\u0925\u093f\u0930 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