{"id":27226,"date":"2021-08-19T13:00:18","date_gmt":"2021-08-19T13:00:18","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27226"},"modified":"2024-09-16T12:53:53","modified_gmt":"2024-09-16T12:53:53","slug":"%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ar\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\/","title":{"rendered":"\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0636\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639<\/h1>\n<p><em><strong>\u0627\u0644\u0645\u0644\u062e\u0635:<\/strong><br \/>\n    \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u0646\u0633\u062a\u0639\u0631\u0636 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0636\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639. \u0633\u0646\u0633\u062a\u0643\u0634\u0641 \u0643\u064a\u0641\u064a\u0629 \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0645\u0648\u0636\u0639 \u0643\u062f\u0627\u0644\u0629 \u0644\u0644\u0632\u0645\u0646\u060c \u0648\u0633\u0646\u0645\u064a\u0632 \u0628\u064a\u0646 \u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u0644\u062d\u0638\u064a\u0629 \u0648\u0627\u0644\u0645\u062a\u0648\u0633\u0637\u0629 \u0648\u0643\u0630\u0644\u0643 \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0627\u0644\u0644\u062d\u0638\u064a \u0648\u0627\u0644\u0645\u062a\u0648\u0633\u0637. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u0646\u0633\u062a\u0646\u062a\u062c \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629 \u0630\u0627\u062a \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0627\u0644\u062b\u0627\u0628\u062a\u060c \u0648\u0627\u0644\u062a\u064a \u062a\u0639\u062a\u0628\u0631 \u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u062a\u0646\u0628\u0624 \u0628\u0645\u0648\u0642\u0639 \u0648\u0633\u0631\u0639\u0629 \u0627\u0644\u062c\u0633\u0645.<\/em><\/p>\n<p><\/center><\/p>\n<p style=\"text-align:center;\"><strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645:<\/strong><br \/>\n    \u0628\u0646\u0647\u0627\u064a\u0629 \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0644\u0627\u0628 \u0642\u0627\u062f\u0631\u064a\u0646 \u0639\u0644\u0649:<\/p>\n<ol>\n<li><strong>\u062a\u0630\u0643\u0631<\/strong> \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u0645\u0648\u0636\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0641\u064a \u0627\u0644\u062d\u0631\u0643\u0629.<\/li>\n<li><strong>\u062a\u062d\u0644\u064a\u0644<\/strong> \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0628\u064a\u0646 \u0627\u0644\u062a\u0633\u0627\u0631\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u0645\u0648\u0636\u0639.<\/li>\n<li><strong>\u062a\u0637\u0628\u064a\u0642<\/strong> \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0648\u0627\u0644\u062a\u0643\u0627\u0645\u0644\u0627\u062a \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u0645\u0648\u0636\u0639 \u0645\u0646 \u0627\u0644\u062a\u0633\u0627\u0631\u0639\u060c \u0648\u0627\u0644\u0639\u0643\u0633 \u0628\u0627\u0644\u0639\u0643\u0633.<\/li>\n<li><strong>\u0641\u0647\u0645<\/strong> \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u0644\u062d\u0638\u064a\u0629 \u0648\u0627\u0644\u0645\u062a\u0648\u0633\u0637\u0629\u060c \u0648\u0628\u064a\u0646 \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0627\u0644\u0644\u062d\u0638\u064a \u0648\u0627\u0644\u0645\u062a\u0648\u0633\u0637.<\/li>\n<\/ol>\n<p>    <center><\/p>\n<p><strong>\u0641\u0647\u0631\u0633 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a<\/strong><br \/>\n    <a href=\"#1\">\u0627\u0644\u0645\u0642\u062f\u0645\u0629<\/a><br \/>\n    <a href=\"#2\">\u0627\u0644\u0645\u0648\u0636\u0639\u060c \u0627\u0644\u0641\u0636\u0627\u0621 \u0648\u0627\u0644\u0645\u0631\u0627\u0642\u0628\u0648\u0646<\/a><br \/>\n    <a href=\"#3\">\u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u062e\u0637\u064a\u0629<\/a><br \/>\n    <a href=\"#4\">\u0627\u0644\u062a\u0633\u0627\u0631\u0639<\/a><br \/>\n    <a href=\"#5\">\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629<\/a><br \/>\n    <a href=\"#6\">\u0627\u0644\u062e\u0627\u062a\u0645\u0629<\/a>\n    <\/p>\n<p>    <iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/fjv-qEuPhwU\" title=\"\u0645\u0634\u063a\u0644 \u0641\u064a\u062f\u064a\u0648 YouTube\" 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>\u0627\u0644\u0645\u0642\u062f\u0645\u0629<\/h2>\n<p style=\"text-align: justify;\">\u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062a\u0633\u0627\u0631\u0639\u060c \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u0645\u0648\u0636\u0639 \u0639\u0628\u0631 \u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0632\u0645\u0646\u060c \u0648\u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0645\u0648\u0636\u0639\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062d\u0633\u0627\u0628 \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0639\u0628\u0631 \u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0632\u0645\u0646. \u0647\u0630\u0647 \u0627\u0644\u0643\u0644\u0645\u0627\u062a \u062a\u0644\u062e\u0635 \u0645\u0627 \u0633\u0646\u0633\u062a\u0643\u0634\u0641\u0647 \u0641\u064a \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u0648\u0623\u062d\u062f \u0623\u0647\u062f\u0627\u0641\u0646\u0627 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 \u0647\u0648 \u0641\u0647\u0645 \u0645\u0639\u0627\u0646\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a. \u064a\u0645\u062b\u0644 \u0627\u0644\u062d\u0631\u0643\u0629 \u0634\u0643\u0644\u0627\u064b \u0645\u0646 \u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u062a\u063a\u064a\u0631\u060c \u0648\u0643\u0644 \u0634\u064a\u0621 \u0641\u064a \u0627\u0644\u0637\u0628\u064a\u0639\u0629 \u064a\u062e\u0636\u0639 \u0644\u0644\u062a\u063a\u064a\u064a\u0631. \u0644\u0630\u0644\u0643\u060c \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062a\u063a\u064a\u064a\u0631 \u0648\u062a\u0646\u0648\u0639\u0627\u062a\u0647 \u0647\u0648 \u0623\u062d\u062f \u0627\u0644\u0631\u0643\u0627\u0626\u0632 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621.<\/p>\n<p style=\"text-align: justify;\">\u0647\u0646\u0627\u0643 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0639\u0631\u0636\u0629 \u0644\u0644\u062a\u063a\u064a\u064a\u0631: \u0627\u0644\u062c\u062f\u064a\u062f \u064a\u0635\u0628\u062d \u0642\u062f\u064a\u0645\u0627\u064b\u060c \u064a\u0645\u0643\u0646 \u0644\u0644\u0645\u0631\u0621 \u0623\u0646 \u064a\u063a\u064a\u0631 \u0645\u0646 \u0645\u0647\u0646\u0629 \u0625\u0644\u0649 \u0623\u062e\u0631\u0649\u060c \u0645\u0646 \u0627\u0644\u0635\u062d\u0629 \u0625\u0644\u0649 \u0627\u0644\u0645\u0631\u0636 \u0648\u0627\u0644\u0639\u0643\u0633 \u0628\u0627\u0644\u0639\u0643\u0633\u060c \u0648\u0645\u0646 \u0627\u0644\u0646\u0647\u0627\u0631 \u0625\u0644\u0649 \u0627\u0644\u0644\u064a\u0644\u060c \u0648\u063a\u064a\u0631\u0647\u0627. \u0643\u0644 \u0647\u0630\u0647 \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u062a\u063a\u064a\u064a\u0631\u060c \u0644\u0643\u0646 \u0639\u0646\u062f \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u0633\u0646\u0631\u0643\u0632 \u0639\u0644\u0649 \u0646\u0648\u0639 \u0648\u0627\u062d\u062f \u0639\u0644\u0649 \u0648\u062c\u0647 \u0627\u0644\u062e\u0635\u0648\u0635: \u062a\u063a\u064a\u064a\u0631 \u0627\u0644\u0645\u0648\u0636\u0639 \u0623\u0648 \u0627\u0644\u062d\u0631\u0643\u0629. \u0641\u064a \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0631\u0649 \u0646\u0647\u062c\u064a\u0646 \u0645\u062a\u0643\u0627\u0645\u0644\u064a\u0646: \u0623\u062d\u062f\u0647\u0645\u0627 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0623\u0633\u0628\u0627\u0628 \u0627\u0644\u062a\u064a \u062a\u0633\u0628\u0628\u0647 \u0648\u0627\u0644\u0622\u062e\u0631 \u0639\u0644\u0649 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062a\u064a \u062a\u062a\u0643\u0634\u0641 \u0628\u0647\u0627\u060c \u0645\u0645\u0627 \u064a\u0624\u062f\u064a \u0625\u0644\u0649 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0648\u0627\u0644\u062d\u0631\u0643\u0629\u060c \u0648\u0627\u0644\u0644\u062a\u064a\u0646 \u0645\u0639\u0627\u064b \u062a\u0634\u0643\u0644\u0627\u0646 \u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627.<\/p>\n<p style=\"text-align: justify;\">\u0641\u064a \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621\u060c \u0646\u0642\u0648\u0645 \u0628\u0646\u0645\u0630\u062c\u0629 \u0627\u0644\u0641\u0636\u0627\u0621 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a \u0643\u0641\u0636\u0627\u0621 \u0645\u062a\u062c\u0647\u064a \u0644\u062a\u0633\u0647\u064a\u0644 \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0645\u062b\u0644 \u0627\u0644\u0645\u0648\u0636\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639. \u0646\u0633\u062a\u062e\u062f\u0645 \u0639\u0627\u062f\u0629\u064b \u0627\u0644\u0641\u0636\u0627\u0621 \u062b\u0644\u0627\u062b\u064a \u0627\u0644\u0623\u0628\u0639\u0627\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^3<\/span><\/span> \u0644\u0647\u0630\u0627 \u0627\u0644\u063a\u0631\u0636\u060c \u0631\u063a\u0645 \u0623\u0646\u0647 \u0646\u0638\u0631\u064a\u0627\u064b\u060c \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0627\u0644\u0641\u0636\u0627\u0621\u0627\u062a \u0630\u0627\u062a \u0627\u0644\u0623\u0628\u0639\u0627\u062f \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0645\u0646\u0627\u0633\u0628\u0629 \u062d\u0633\u0628 \u0627\u0644\u0633\u064a\u0627\u0642.<\/p>\n<p>    <a name=\"2\"><\/a><\/p>\n<h2>\u0627\u0644\u0645\u0648\u0636\u0639\u060c \u0627\u0644\u0641\u0636\u0627\u0621 \u0648\u0627\u0644\u0645\u0631\u0627\u0642\u0628\u0648\u0646<\/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>\u0644\u0646\u0646\u0638\u0631 \u0625\u0644\u0649 \u062f\u0627\u0644\u0629<\/strong><\/a><\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><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\n    t &amp;\\longmapsto&amp;\\vec{r}(t)\n\n    \\end{array}\n\n    <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0647\u0630\u0647 \u062f\u0627\u0644\u0629 \u062a\u0639\u064a\u0646 \u0645\u0648\u0636\u0639\u064b\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}(t)<\/span><\/span> \u0644\u0643\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t\\in\\mathbb{R}<\/span><\/span>\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0646\u0642\u0648\u0644 \u0625\u0646\u0647\u0627 \u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0648\u0636\u0639 (\u0623\u0648 \u0628\u0628\u0633\u0627\u0637\u0629 \u0627\u0644\u0645\u0648\u0636\u0639). \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0645\u0633\u062a\u0642\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">t<\/span> \u064a\u0633\u0645\u0649 \u00ab\u0627\u0644\u0632\u0645\u0646\u00bb\u060c \u0648\u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u064a\u0642\u0627\u0628\u0644 \u00ab\u0627\u0644\u0628\u0639\u062f\u00bb \u0644\u0644\u0641\u0636\u0627\u0621. \u0627\u0644\u0631\u0645\u0648\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">[T]<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">[L]<\/span> \u062a\u0634\u064a\u0631 \u0625\u0644\u0649 \u0627\u0644\u0623\u0628\u0639\u0627\u062f \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a\u0629 \u0644\u0644\u0632\u0645\u0646 \u0648\u0627\u0644\u0637\u0648\u0644\u060c \u0648\u0639\u0627\u062f\u0629 \u0645\u0627 \u062a\u0642\u0627\u0633 \u0628\u0640 \u00ab\u0627\u0644\u062b\u0648\u0627\u0646\u064a\u00bb \u0648 \u00ab\u0627\u0644\u0623\u0645\u062a\u0627\u0631\u00bb \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a.<\/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=\"\u0627\u0644\u062d\u0631\u0643\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629: \u0627\u0644\u0645\u0648\u0636\u0639 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0623\u0635\u0644 \u0641\u064a \u0641\u0636\u0627\u0621 \u062b\u0644\u0627\u062b\u064a \u0627\u0644\u0623\u0628\u0639\u0627\u062f\" 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=\"\u0627\u0644\u062d\u0631\u0643\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629: \u0627\u0644\u0645\u0648\u0636\u0639 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0623\u0635\u0644 \u0641\u064a \u0641\u0636\u0627\u0621 \u062b\u0644\u0627\u062b\u064a \u0627\u0644\u0623\u0628\u0639\u0627\u062f\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">\u0627\u0644\u0645\u0648\u0636\u0639\u060c \u0645\u062b\u0644 \u0623\u064a \u0643\u0645\u064a\u0629 \u0641\u064a\u0632\u064a\u0627\u0626\u064a\u0629\u060c \u064a\u062a\u0645 \u0642\u064a\u0627\u0633\u0647 \u0628\u0648\u0627\u0633\u0637\u0629 \u0645\u0631\u0627\u0642\u0628. \u0641\u064a \u0627\u0644\u0648\u0635\u0641 \u0627\u0644\u0630\u064a \u0642\u062f\u0645\u062a\u0647 \u0639\u0646 \u0627\u0644\u0645\u0648\u0636\u0639\u060c \u0627\u0641\u062a\u0631\u0636\u062a \u0636\u0645\u0646\u064a\u0627\u064b \u0623\u0646 \u0627\u0644\u0645\u0631\u0627\u0642\u0628 \u0644\u062f\u064a\u0647 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0635\u0641\u0631\u064a\u060c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{0}<\/span><\/span>. \u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u062f\u0649 \u0627\u0644\u0645\u0631\u0627\u0642\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}<\/span> \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}<\/span> \u0648\u0643\u0627\u0646 \u0644\u0644\u062c\u0633\u0645 \u0627\u0644\u0646\u0642\u0637\u0629 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}^\\prime,<\/span><\/span> \u0641\u0625\u0646 <strong>\u0627\u0644\u0645\u0648\u0636\u0639 \u0627\u0644\u0646\u0633\u0628\u064a \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u0631\u0627\u0642\u0628<\/strong> \u0633\u064a\u0643\u0648\u0646:<\/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=\"\u0627\u0644\u062d\u0631\u0643\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629: \u0627\u0644\u0645\u0648\u0636\u0639 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0645\u0631\u0627\u0642\u0628 \u0639\u0634\u0648\u0627\u0626\u064a\" 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=\"\u0627\u0644\u062d\u0631\u0643\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629: \u0627\u0644\u0645\u0648\u0636\u0639 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0645\u0631\u0627\u0642\u0628 \u0639\u0634\u0648\u0627\u0626\u064a\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">\u0627\u0644\u0641\u0636\u0627\u0621 \u0647\u0648 \u0645\u062c\u0645\u0648\u0639\u0629 \u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0648\u0627\u0636\u0639 \u0627\u0644\u0645\u0645\u0643\u0646\u0629\u060c \u0648\u0647\u0648 \u0623\u064a\u0636\u0627\u064b \u0645\u062c\u0645\u0648\u0639\u0629 \u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0648\u0627\u0636\u0639 \u0627\u0644\u0645\u0645\u0643\u0646\u0629 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0623\u064a \u0645\u0631\u0627\u0642\u0628. \u0627\u0644\u0645\u0648\u0636\u0639 \u0647\u0648 \u062f\u0627\u0644\u0629 \u0644\u0644\u0632\u0645\u0646 \u0648\u064a\u0633\u062a\u062e\u062f\u0645 \u0644\u062a\u0645\u062b\u064a\u0644 \u0645\u0643\u0627\u0646 \u0627\u0644\u062c\u0633\u0645 \u0627\u0644\u0645\u062b\u0627\u0644\u064a \u0627\u0644\u0645\u0633\u0645\u0649 \u00ab\u0627\u0644\u062c\u0633\u0645 \u0627\u0644\u0646\u0642\u0637\u0629\u00bb \u0641\u064a \u0643\u0644 \u0644\u062d\u0638\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">t<\/span>. \u0627\u0644\u062c\u0633\u0645 \u0627\u0644\u0646\u0642\u0637\u0629 \u0647\u0648 \u0645\u062b\u0627\u0644 \u0645\u062b\u0627\u0644\u064a\u060c \u0647\u0648 \u0645\u0627 \u064a\u062a\u0628\u0642\u0649 \u0645\u0646 \u0627\u0644\u062c\u0633\u0645 \u0627\u0644\u062d\u0642\u064a\u0642\u064a \u0639\u0646\u062f\u0645\u0627 \u0646\u062a\u062e\u0644\u0635 \u0645\u0646 \u062c\u0645\u064a\u0639 \u062e\u0635\u0627\u0626\u0635\u0647\u060c \u0628\u0645\u0627 \u0641\u064a \u0630\u0644\u0643 \u0627\u0644\u062d\u062c\u0645 \u0648\u0627\u0644\u0634\u0643\u0644\u060c \u0645\u0639 \u0627\u0644\u0627\u062d\u062a\u0641\u0627\u0638 \u0641\u0642\u0637 \u0628\u0640 \u00ab\u0627\u0644\u0645\u0643\u0627\u0646 \u0627\u0644\u0630\u064a \u064a\u0634\u063a\u0644\u0647 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621\u00bb.<\/p>\n<p style=\"text-align: justify;\">\u0627\u0644\u0645\u0648\u0636\u0639 \u0639\u0627\u062f\u0629\u064b \u0645\u0627 \u064a\u0643\u0648\u0646 \u0645\u062a\u062c\u0647\u064b\u0627. \u064a\u062a\u0643\u0648\u0646 \u0627\u0644\u0645\u062a\u062c\u0647 \u0645\u0646 \u0639\u0646\u0635\u0631\u064a\u0646: \u0627\u0644\u0645\u0642\u062f\u0627\u0631 \u0648\u0627\u0644\u0627\u062a\u062c\u0627\u0647. \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0645\u0648\u0636\u0639 \u0627\u0644\u0646\u0633\u0628\u064a \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u0631\u0627\u0642\u0628 \u0647\u0648 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0625\u0644\u0649 \u0627\u0644\u0645\u0631\u0627\u0642\u0628\u060c \u0648\u064a\u0639\u0637\u0649 \u0628\u0640 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dist_\\mathcal{O}(t)=\\|\\vec{r}_\\mathcal{O}(t)\\|.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629\u060c \u064a\u0648\u0635\u0649 \u0628\u0634\u062f\u0629 \u0628\u0625\u062a\u0642\u0627\u0646 \u0645\u062d\u062a\u0648\u0649 \u062f\u0648\u0631\u0629 <strong>\u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062a\u0643\u0627\u0645\u0644 <a href=\"https:\/\/www.youtube.com\/watch?v=FEPfoAfPsFY&#038;list=PL_C8rbeFjqAVaR_sgLJRBvMm5t6E1GxGI\" rel=\"noopener\" target=\"_blank\">\u0627\u0644\u062a\u0641\u0627\u0636\u0644<\/a> \u0648 <a href=\"https:\/\/www.youtube.com\/watch?v=4wSTxA7zY9k&#038;list=PL_C8rbeFjqAUU5ClOkZMRJbiefHDeXGI2\" rel=\"noopener\" target=\"_blank\">\u0627\u0644\u062a\u0643\u0627\u0645\u0644.<\/a><\/strong><\/p>\n<p>    <a name=\"3\"><\/a><\/p>\n<h2>\u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u062e\u0637\u064a\u0629<\/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>\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u0648\u0636\u0639 \u0642\u0627\u0628\u0644\u0627\u064b \u0644\u0644\u062a\u0641\u0627\u0636\u0644 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0632\u0645\u0646\u060c<\/strong><\/a> \u0641\u0625\u0646\u0647 \u064a\u0645\u0643\u0646 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u0646\u0633\u0628\u064a\u0629 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u0631\u0627\u0642\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}<\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{v}_\\mathcal{O}(t),<\/span><\/span> \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a:<\/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;\">\u0628\u0639\u0628\u0627\u0631\u0627\u062a \u0628\u0633\u064a\u0637\u0629: \u0627\u0644\u0633\u0631\u0639\u0629 \u0647\u064a \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0632\u0645\u0646\u064a\u0629 \u0644\u0644\u0645\u0648\u0636\u0639 \u0648\u062a\u062e\u0628\u0631\u0646\u0627 \u0643\u064a\u0641 \u064a\u062a\u063a\u064a\u0631 \u0627\u0644\u0645\u0648\u0636\u0639 \u0641\u064a \u0643\u0644 \u0644\u062d\u0638\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">t<\/span>.<\/p>\n<p style=\"text-align: justify;\">\u0647\u0646\u0627\u0643 \u0646\u0648\u0639\u0627\u0646 \u0645\u0646 \u0627\u0644\u0633\u0631\u0639\u0627\u062a: \u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u0644\u062d\u0638\u064a\u0629 \u0648\u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u0645\u062a\u0648\u0633\u0637\u0629. \u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u0644\u062d\u0638\u064a\u0629 \u0647\u064a \u0627\u0644\u062a\u064a \u0642\u062f\u0645\u0646\u0627\u0647\u0627 \u0644\u0644\u062a\u0648\u060c \u0641\u064a \u062d\u064a\u0646 \u064a\u062a\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u0645\u062a\u0648\u0633\u0637\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0625\u0647\u0645\u0627\u0644 \u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629. \u064a\u064f\u0639\u0631\u0641 \u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u0633\u0631\u0639\u0629 \u0639\u0644\u0649 \u0627\u0644\u0641\u062a\u0631\u0629 \u0627\u0644\u0632\u0645\u0646\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u0637\u0648\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta t,<\/span><\/span> \u0628\u0640 <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> \u0648\u064a\u062a\u0645 \u062a\u0639\u0631\u064a\u0641\u0647 \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a:<\/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;\">\u062d\u064a\u062b \u0623\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">\\overline{t}<\/span> \u0647\u0648 \u0623\u064a \u0644\u062d\u0638\u0629 \u0636\u0645\u0646 \u0627\u0644\u0641\u0627\u0635\u0644 \u0627\u0644\u0632\u0645\u0646\u064a <span class=\"katex-eq\" data-katex-display=\"false\">[t,t+\\Delta t].<\/span>\n<p style=\"text-align: justify;\">\u0645\u0646 \u0627\u0644\u0633\u0631\u0639\u0629 (\u0633\u0648\u0627\u0621 \u0643\u0627\u0646\u062a \u0644\u062d\u0638\u064a\u0629 \u0623\u0648 \u0645\u062a\u0648\u0633\u0637\u0629) \u064a\u0645\u0643\u0646 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u062e\u0637\u064a\u0629 \u0628\u0627\u0639\u062a\u0628\u0627\u0631\u0647\u0627 \u0627\u0644\u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0645\u0642\u0627\u0628\u0644 \u0644\u0647\u0627. \u062a\u064f\u0639\u0631\u0641 \u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u062e\u0637\u064a\u0629 \u0627\u0644\u0646\u0633\u0628\u064a\u0629 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u0631\u0627\u0642\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}<\/span> \u0628\u0640 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_\\mathcal{O}(t)=\\|\\vec{v}_\\mathcal{O}(t)\\|,<\/span><\/span> \u0648\u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u062e\u0637\u064a\u0629 \u0628\u0640 <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><\/p>\n<p style=\"text-align: justify;\">\u064a\u062a\u0645 \u0642\u064a\u0627\u0633 \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u062e\u0637\u064a\u0629 \u0628\u0648\u062d\u062f\u0627\u062a \u0627\u0644\u0637\u0648\u0644 \u0639\u0644\u0649 \u0648\u062d\u062f\u0627\u062a \u0627\u0644\u0632\u0645\u0646\u060c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[L\/T]<\/span><\/span>\u060c \u0648\u0639\u0627\u062f\u0629 \u0645\u0627 \u062a\u064f\u0639\u0628\u0631 \u0639\u0646 \u0647\u0630\u0647 \u0627\u0644\u0648\u062d\u062f\u0629 \u0628\u0640 \u00ab\u0645\u062a\u0631 \u0641\u064a \u0627\u0644\u062b\u0627\u0646\u064a\u0629\u00bb.<\/p>\n<p>    <a name=\"4\"><\/a><\/p>\n<h2>\u0627\u0644\u062a\u0633\u0627\u0631\u0639<\/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>\u0648\u0628\u0627\u0644\u0645\u062b\u0644\u060c \u0645\u062b\u0644 \u0627\u0644\u0633\u0631\u0639\u0629\u060c<\/strong><\/a> \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0642\u0627\u0628\u0644\u0627\u064b \u0644\u0644\u062a\u0641\u0627\u0636\u0644 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0632\u0645\u0646\u060c \u0641\u0625\u0646\u0647 \u064a\u0645\u0643\u0646 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0627\u0644\u0646\u0633\u0628\u064a \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u0631\u0627\u0642\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}<\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{a}_\\mathcal{O}(t),<\/span><\/span> \u0643\u0645\u0627 \u064a\u0644\u064a:<\/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;\">\u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0647\u0648 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0632\u0645\u0646\u064a\u0629 \u0644\u0644\u0633\u0631\u0639\u0629 \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u064a\u062e\u0628\u0631\u0646\u0627 \u0643\u064a\u0641 \u064a\u062a\u063a\u064a\u0631 \u0627\u0644\u0633\u0631\u0639\u0629 \u0645\u0639 \u0645\u0631\u0648\u0631 \u0627\u0644\u0632\u0645\u0646.<\/p>\n<p style=\"text-align: justify;\">\u0628\u0627\u0644\u0645\u062b\u0644 \u0645\u0639 \u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u062e\u0637\u064a\u0629\u060c \u0647\u0646\u0627\u0643 \u062a\u0633\u0627\u0631\u0639 \u0644\u062d\u0638\u064a \u0648\u062a\u0633\u0627\u0631\u0639 \u0645\u062a\u0648\u0633\u0637. \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0627\u0644\u0644\u062d\u0638\u064a \u0647\u0648 \u0627\u0644\u0630\u064a \u0642\u0645\u0646\u0627 \u0628\u0645\u0631\u0627\u062c\u0639\u062a\u0647 \u0644\u0644\u062a\u0648\u060c \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0627\u0644\u0645\u062a\u0648\u0633\u0637 \u064a\u062a\u0645 \u062d\u0633\u0627\u0628\u0647 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0625\u0647\u0645\u0627\u0644 \u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629. \u064a\u064f\u0639\u0631\u0641 \u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0639\u0644\u0649 \u0627\u0644\u0641\u062a\u0631\u0629 \u0627\u0644\u0632\u0645\u0646\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u0637\u0648\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta t,<\/span><\/span> \u0628\u0640 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left&lt;\\vec{a}_{\\mathcal{O},\\Delta t}\\right&gt;,<\/span><\/span> \u0648\u064a\u062a\u0645 \u062a\u0639\u0631\u064a\u0641\u0647 \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a:<\/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;\">\u064a\u062a\u0645 \u0642\u064a\u0627\u0633 \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0628\u0648\u062d\u062f\u0627\u062a \u0627\u0644\u0637\u0648\u0644 \u0639\u0644\u0649 \u0645\u0631\u0628\u0639 \u0648\u062d\u062f\u0627\u062a \u0627\u0644\u0632\u0645\u0646\u060c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[L\/T^2]<\/span><\/span>\u060c \u0648\u0639\u0627\u062f\u0629 \u0645\u0627 \u062a\u064f\u0639\u0628\u0631 \u0639\u0646 \u0647\u0630\u0647 \u0627\u0644\u0648\u062d\u062f\u0629 \u0628\u0640 \u00ab\u0645\u062a\u0631 \u0641\u064a \u0627\u0644\u062b\u0627\u0646\u064a\u0629 \u0627\u0644\u0645\u0631\u0628\u0639\u0629\u00bb.<\/p>\n<p>    <a name=\"5\"><\/a><\/p>\n<h2>\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629<\/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>\u0644\u0646\u0641\u062a\u0631\u0636 \u0623\u0646\u0646\u0627 \u0644\u062f\u064a\u0646\u0627 \u062c\u0633\u0645 \u0646\u0642\u0637\u064a<\/strong><\/a> \u064a\u062a\u062d\u0631\u0643 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u0631\u0627\u0642\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}<\/span> \u0628\u062a\u0633\u0627\u0631\u0639 \u062b\u0627\u0628\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{a}_\\mathcal{O}(t) = \\vec{a}_0<\/span><\/span>. \u0625\u0630\u0627 \u0643\u0627\u0646 \u0645\u0646 \u0627\u0644\u0645\u0645\u0643\u0646 \u0627\u0634\u062a\u0642\u0627\u0642 \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0645\u0646 \u0627\u0644\u0645\u0648\u0636\u0639\u060c \u0641\u0625\u0646\u0647 \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u0645\u0648\u0636\u0639 \u0639\u0646 \u0637\u0631\u064a\u0642 \u062a\u0643\u0627\u0645\u0644 \u0627\u0644\u062a\u0633\u0627\u0631\u0639. \u062a\u064f\u0639\u0631\u0641 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u062a\u064a \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0628\u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0628\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629.<\/p>\n<p style=\"text-align: justify;\">\u0628\u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0644\u0640 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{a}_\\mathcal{O}(t) = \\vec{a}_0<\/span><\/span> \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:<\/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;\">\u0648\u0628\u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0645\u0631\u0629 \u0623\u062e\u0631\u0649 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649<\/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;\">\u0647\u0646\u0627\u060c \u0627\u0644\u062b\u0648\u0627\u0628\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{v}_0<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}_0<\/span><\/span> \u0647\u064a \u062b\u0648\u0627\u0628\u062a \u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0648\u062a\u0645\u062b\u0644 \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u0645\u0648\u0636\u0639 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u064a\u0646 \u0644\u0644\u062c\u0633\u0645 \u0627\u0644\u0646\u0642\u0637\u0629 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u0631\u0627\u0642\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}<\/span>. \u0648\u0628\u0627\u062e\u062a\u0635\u0627\u0631\u060c \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629 \u0647\u064a:<\/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;\">\u0645\u0646 \u062e\u0644\u0627\u0644 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a\u060c \u064a\u0645\u0643\u0646 \u0648\u0635\u0641 \u062d\u0631\u0643\u0629 \u0623\u064a \u062c\u0633\u0645 \u0646\u0642\u0637\u064a \u064a\u062a\u062d\u0631\u0643 \u0628\u062a\u0633\u0627\u0631\u0639 \u062b\u0627\u0628\u062a \u0628\u0634\u0643\u0644 \u0643\u0627\u0645\u0644. \u0648\u0647\u0630\u0627 \u064a\u0648\u0636\u062d \u0623\u0646\u0647 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0643\u0627\u0645\u0644 \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u0645\u0648\u0636\u0639\u060c \u0648\u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0634\u062a\u0642\u0627\u0642 \u0627\u0644\u0645\u0648\u0636\u0639 \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639.<\/p>\n<p style=\"text-align: justify;\">\u0644\u0627\u062d\u0638 \u0623\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u064a \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u062a\u062c\u0647\u064a\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u064a\u0645\u0643\u0646 \u0641\u0635\u0644\u0647\u0627 \u0625\u0644\u0649 \u0645\u0643\u0648\u0646\u0627\u062a\u0647\u0627. \u0625\u0630\u0627 \u0643\u0646\u0627 \u0646\u0645\u062b\u0644 \u062d\u0631\u0643\u0629 \u0641\u064a \u0641\u0636\u0627\u0621 \u062b\u0644\u0627\u062b\u064a \u0627\u0644\u0623\u0628\u0639\u0627\u062f\u060c \u0641\u0625\u0646\u0646\u0627 \u0633\u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0643\u0644 \u0645\u0643\u0648\u0646 \u0645\u0641\u0635\u0648\u0644 \u0628\u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/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;\">\u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u064a\u062a\u0645 \u0625\u0646\u0634\u0627\u0621 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 9 \u0645\u0639\u0627\u062f\u0644\u0627\u062a\u060c \u0648\u0627\u062d\u062f\u0629 \u0644\u0643\u0644 \u0645\u062d\u0648\u0631 \u0625\u062d\u062f\u0627\u062b\u064a. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u062d\u0648\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span>\u060c \u0633\u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n    \\begin{array}{rl}\n\n    a_x(t) &amp; = a_{0x}\\\\\n\n    v_x(t) &amp; = a_{0x}t + v_{0x} \\\\\n\n    x(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;\">\u0639\u0627\u062f\u0629\u060c \u064a\u062a\u0645 \u062d\u062c\u0632 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{z}<\/span> \u0644\u0644\u0627\u0631\u062a\u0641\u0627\u0639\u060c \u0644\u0630\u0644\u0643 \u064a\u064f\u0641\u062a\u0631\u0636 \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a_{0z}=-g \\approx -9.81[m\/s^2];<\/span><\/span> \u0623\u064a \u0623\u0646 \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u062d\u0648\u0631 \u0645\u0631\u062a\u0628\u0637 \u0628\u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0627\u0644\u0646\u0627\u062a\u062c \u0639\u0646 \u062c\u0627\u0630\u0628\u064a\u0629 \u0627\u0644\u0623\u0631\u0636. \u064a\u062a\u0645 \u062a\u0636\u0645\u064a\u0646 \u0630\u0644\u0643 \u0641\u064a \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0644\u0646\u0645\u0630\u062c\u0629 \u0627\u0644\u0638\u0648\u0627\u0647\u0631 \u0645\u062b\u0644 \u0627\u0644\u0633\u0642\u0648\u0637 \u0627\u0644\u062d\u0631 \u0623\u0648 \u0625\u0637\u0644\u0627\u0642 \u0627\u0644\u0645\u0642\u0630\u0648\u0641\u0627\u062a.<\/p>\n<p>    <a name=\"6\"><\/a><\/p>\n<h2>\u0627\u0644\u062e\u0627\u062a\u0645\u0629<\/h2>\n<p style=\"text-align: justify;\">\n        \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0631\u062d\u0644\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u0627\u0633\u062a\u0643\u0634\u0641\u0646\u0627 \u0643\u064a\u0641 \u062a\u064f\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0644\u0648\u0635\u0641 \u0648\u0641\u0647\u0645 \u0627\u0644\u062d\u0631\u0643\u0629 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a. \u0645\u0646 \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0645\u0648\u0636\u0639 \u0643\u0645\u062a\u062c\u0647 \u0641\u064a \u0641\u0636\u0627\u0621 \u0630\u064a \u0623\u0628\u0639\u0627\u062f \u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u0625\u0644\u0649 \u0627\u0634\u062a\u0642\u0627\u0642 \u0648\u062a\u0643\u0627\u0645\u0644 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0629 \u0644\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u0633\u0631\u0639\u0629\u060c \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0648\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u0631\u0623\u064a\u0646\u0627 \u0643\u064a\u0641 \u062a\u062a\u0634\u0627\u0628\u0643 \u0647\u0630\u0647 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0648\u062a\u0637\u0628\u0642 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062d\u0631\u0643\u0629.\n    <\/p>\n<p style=\"text-align: justify;\">\n        \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u0645\u0646 \u062e\u0644\u0627\u0644 \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062d\u0631\u0643\u0629 \u062f\u0648\u0646 \u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u0623\u0633\u0628\u0627\u0628 \u0627\u0644\u062a\u064a \u062a\u064f\u0646\u062a\u062c\u0647\u0627\u060c \u062a\u0642\u062f\u0645 \u0644\u0646\u0627 \u0631\u0624\u064a\u0629 \u0646\u0642\u064a\u0629 \u0648\u0623\u0646\u064a\u0642\u0629 \u0631\u064a\u0627\u0636\u064a\u0627\u064b \u0644\u062d\u0631\u0643\u0629 \u0627\u0644\u0623\u062c\u0633\u0627\u0645 \u0627\u0644\u0646\u0642\u0637\u064a\u0629. \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0623\u062f\u0648\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062a\u0643\u0627\u0645\u0644\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0641\u0643 \u0623\u0646\u0645\u0627\u0637 \u0627\u0644\u062d\u0631\u0643\u0629 \u0648\u0627\u0644\u062a\u0646\u0628\u0624 \u0628\u0645\u0633\u0627\u0631\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0628\u0644\u060c \u0648\u0647\u0648 \u0623\u0645\u0631 \u0623\u0633\u0627\u0633\u064a \u0641\u064a \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0648\u0627\u0644\u0647\u0646\u062f\u0633\u0629.\n    <\/p>\n<p style=\"text-align: justify;\">\n        \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0641\u0625\u0646 \u062a\u0636\u0645\u064a\u0646 \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0627\u0644\u0646\u0627\u062a\u062c \u0639\u0646 \u0627\u0644\u062c\u0627\u0630\u0628\u064a\u0629 \u0641\u064a \u0645\u0639\u0627\u062f\u0644\u0627\u062a\u0646\u0627 \u0633\u064a\u0624\u062f\u064a \u0628\u0646\u0627 \u0625\u0644\u0649 \u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0623\u0643\u062b\u0631 \u062a\u062d\u062f\u064a\u062f\u064b\u0627\u060c \u0645\u062b\u0644 \u0627\u0644\u0633\u0642\u0648\u0637 \u0627\u0644\u062d\u0631 \u0648\u0625\u0637\u0644\u0627\u0642 \u0627\u0644\u0645\u0642\u0630\u0648\u0641\u0627\u062a\u060c \u0645\u0645\u0627 \u064a\u062b\u0628\u062a \u0623\u0647\u0645\u064a\u0629 \u0648\u0625\u0645\u0643\u0627\u0646\u064a\u0629 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u062d\u0631\u0643\u0629 \u0641\u064a \u0639\u0627\u0644\u0645\u0646\u0627 \u0627\u0644\u064a\u0648\u0645\u064a. \u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062d\u0631\u0643\u0629 \u0644\u064a\u0633\u062a \u0645\u062c\u0631\u062f \u062a\u0645\u0631\u064a\u0646 \u0646\u0638\u0631\u064a\u060c \u0628\u0644 \u0647\u064a \u0623\u062f\u0627\u0629 \u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0641\u0647\u0645 \u0648\u0627\u0644\u062a\u0644\u0627\u0639\u0628 \u0628\u0627\u0644\u0639\u0627\u0644\u0645 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a \u0645\u0646 \u062d\u0648\u0644\u0646\u0627.\n    <\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0636\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0627\u0644\u0645\u0644\u062e\u0635: \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u0646\u0633\u062a\u0639\u0631\u0636 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0636\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639. \u0633\u0646\u0633\u062a\u0643\u0634\u0641 \u0643\u064a\u0641\u064a\u0629 \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0645\u0648\u0636\u0639 \u0643\u062f\u0627\u0644\u0629 \u0644\u0644\u0632\u0645\u0646\u060c \u0648\u0633\u0646\u0645\u064a\u0632 \u0628\u064a\u0646 \u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u0644\u062d\u0638\u064a\u0629 \u0648\u0627\u0644\u0645\u062a\u0648\u0633\u0637\u0629 \u0648\u0643\u0630\u0644\u0643 \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0627\u0644\u0644\u062d\u0638\u064a \u0648\u0627\u0644\u0645\u062a\u0648\u0633\u0637. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u0646\u0633\u062a\u0646\u062a\u062c \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629 \u0630\u0627\u062a \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0627\u0644\u062b\u0627\u0628\u062a\u060c \u0648\u0627\u0644\u062a\u064a \u062a\u0639\u062a\u0628\u0631 \u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u062a\u0646\u0628\u0624 \u0628\u0645\u0648\u0642\u0639 \u0648\u0633\u0631\u0639\u0629 \u0627\u0644\u062c\u0633\u0645. \u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645: \u0628\u0646\u0647\u0627\u064a\u0629 \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0644\u0627\u0628 \u0642\u0627\u062f\u0631\u064a\u0646 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28506,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":85,"footnotes":""},"categories":[657,641],"tags":[],"class_list":["post-27226","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-657","category-641"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0645\u0646 \u062e\u0644\u0627\u0644 \u0647\u0630\u0647 \u0627\u0644\u062f\u0631\u0633\u060c \u0633\u062a\u0641\u0647\u0645 \u0628\u0634\u0643\u0644 \u0639\u0645\u064a\u0642 \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u0628\u0645\u0631\u0627\u062c\u0639\u0629 \u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629\u060c \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/ar\/\u0623\u0633\u0627\u0633\u064a\u0627\u062a-\u0627\u0644\u062d\u0631\u0643\u0629-\u0627\u0644\u0645\u0648\u0642\u0639\u060c-\u0627\u0644\u0633\u0631\u0639\u0629-\u0648\u0627\u0644\u062a\u0633\u0627\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639\" \/>\n<meta property=\"og:description\" content=\"\u0645\u0646 \u062e\u0644\u0627\u0644 \u0647\u0630\u0647 \u0627\u0644\u062f\u0631\u0633\u060c \u0633\u062a\u0641\u0647\u0645 \u0628\u0634\u0643\u0644 \u0639\u0645\u064a\u0642 \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u0628\u0645\u0631\u0627\u062c\u0639\u0629 \u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629\u060c \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/ar\/\u0623\u0633\u0627\u0633\u064a\u0627\u062a-\u0627\u0644\u062d\u0631\u0643\u0629-\u0627\u0644\u0645\u0648\u0642\u0639\u060c-\u0627\u0644\u0633\u0631\u0639\u0629-\u0648\u0627\u0644\u062a\u0633\u0627\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-08-19T13:00:18+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-09-16T12:53:53+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/08\/cinematica-5.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1792\" \/>\n\t<meta property=\"og:image:height\" content=\"1024\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639\" \/>\n<meta name=\"twitter:description\" content=\"\u0645\u0646 \u062e\u0644\u0627\u0644 \u0647\u0630\u0647 \u0627\u0644\u062f\u0631\u0633\u060c \u0633\u062a\u0641\u0647\u0645 \u0628\u0634\u0643\u0644 \u0639\u0645\u064a\u0642 \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u0628\u0645\u0631\u0627\u062c\u0639\u0629 \u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629\u060c \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639.\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/08\/cinematica-5.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\\\/#article\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639\",\"datePublished\":\"2021-08-19T13:00:18+00:00\",\"dateModified\":\"2024-09-16T12:53:53+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\\\/\"},\"wordCount\":590,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2021\\\/08\\\/cinematica-5.jpg\",\"articleSection\":[\"\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627\",\"\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\\\/\",\"name\":\"\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639 - toposuranos.com\\\/material\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\\\/#primaryimage\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2021\\\/08\\\/cinematica-5.jpg\",\"datePublished\":\"2021-08-19T13:00:18+00:00\",\"dateModified\":\"2024-09-16T12:53:53+00:00\",\"description\":\"\u0645\u0646 \u062e\u0644\u0627\u0644 \u0647\u0630\u0647 \u0627\u0644\u062f\u0631\u0633\u060c \u0633\u062a\u0641\u0647\u0645 \u0628\u0634\u0643\u0644 \u0639\u0645\u064a\u0642 \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u0628\u0645\u0631\u0627\u062c\u0639\u0629 \u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629\u060c \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639.\",\"breadcrumb\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\\\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\\\/#primaryimage\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2021\\\/08\\\/cinematica-5.jpg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2021\\\/08\\\/cinematica-5.jpg\",\"width\":1792,\"height\":1024},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/es\\\/cursos-de-matematica-y-fisica\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639\"}]},{\"@type\":\"WebSite\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#website\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/\",\"name\":\"toposuranos.com\\\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\",\"name\":\"toposuranos.com\\\/material\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\\\/material\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/groups\\\/toposuranos\",\"https:\\\/\\\/x.com\\\/topuranos\",\"https:\\\/\\\/www.youtube.com\\\/channel\\\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\\\/\\\/www.linkedin.com\\\/company\\\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\\\/\\\/toposuranos.com\\\/material\"],\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/author\\\/giorgio-reveco\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639 - toposuranos.com\/material","description":"\u0645\u0646 \u062e\u0644\u0627\u0644 \u0647\u0630\u0647 \u0627\u0644\u062f\u0631\u0633\u060c \u0633\u062a\u0641\u0647\u0645 \u0628\u0634\u0643\u0644 \u0639\u0645\u064a\u0642 \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u0628\u0645\u0631\u0627\u062c\u0639\u0629 \u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629\u060c \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"http:\/\/toposuranos.com\/material\/ar\/\u0623\u0633\u0627\u0633\u064a\u0627\u062a-\u0627\u0644\u062d\u0631\u0643\u0629-\u0627\u0644\u0645\u0648\u0642\u0639\u060c-\u0627\u0644\u0633\u0631\u0639\u0629-\u0648\u0627\u0644\u062a\u0633\u0627\/","og_locale":"es_ES","og_type":"article","og_title":"\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639","og_description":"\u0645\u0646 \u062e\u0644\u0627\u0644 \u0647\u0630\u0647 \u0627\u0644\u062f\u0631\u0633\u060c \u0633\u062a\u0641\u0647\u0645 \u0628\u0634\u0643\u0644 \u0639\u0645\u064a\u0642 \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u0628\u0645\u0631\u0627\u062c\u0639\u0629 \u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629\u060c \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639.","og_url":"http:\/\/toposuranos.com\/material\/ar\/\u0623\u0633\u0627\u0633\u064a\u0627\u062a-\u0627\u0644\u062d\u0631\u0643\u0629-\u0627\u0644\u0645\u0648\u0642\u0639\u060c-\u0627\u0644\u0633\u0631\u0639\u0629-\u0648\u0627\u0644\u062a\u0633\u0627\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-08-19T13:00:18+00:00","article_modified_time":"2024-09-16T12:53:53+00:00","og_image":[{"width":1792,"height":1024,"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/08\/cinematica-5.jpg","type":"image\/jpeg"}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639","twitter_description":"\u0645\u0646 \u062e\u0644\u0627\u0644 \u0647\u0630\u0647 \u0627\u0644\u062f\u0631\u0633\u060c \u0633\u062a\u0641\u0647\u0645 \u0628\u0634\u0643\u0644 \u0639\u0645\u064a\u0642 \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u0628\u0645\u0631\u0627\u062c\u0639\u0629 \u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629\u060c \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639.","twitter_image":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/08\/cinematica-5.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"6 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"http:\/\/toposuranos.com\/material\/ar\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\/#article","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/ar\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\/"},"author":{"name":"giorgio.reveco","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639","datePublished":"2021-08-19T13:00:18+00:00","dateModified":"2024-09-16T12:53:53+00:00","mainEntityOfPage":{"@id":"http:\/\/toposuranos.com\/material\/ar\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\/"},"wordCount":590,"commentCount":0,"publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"http:\/\/toposuranos.com\/material\/ar\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/08\/cinematica-5.jpg","articleSection":["\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627","\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["http:\/\/toposuranos.com\/material\/ar\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\/#respond"]}]},{"@type":"WebPage","@id":"http:\/\/toposuranos.com\/material\/ar\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\/","url":"http:\/\/toposuranos.com\/material\/ar\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\/","name":"\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639 - toposuranos.com\/material","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"http:\/\/toposuranos.com\/material\/ar\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\/#primaryimage"},"image":{"@id":"http:\/\/toposuranos.com\/material\/ar\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/08\/cinematica-5.jpg","datePublished":"2021-08-19T13:00:18+00:00","dateModified":"2024-09-16T12:53:53+00:00","description":"\u0645\u0646 \u062e\u0644\u0627\u0644 \u0647\u0630\u0647 \u0627\u0644\u062f\u0631\u0633\u060c \u0633\u062a\u0641\u0647\u0645 \u0628\u0634\u0643\u0644 \u0639\u0645\u064a\u0642 \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u0628\u0645\u0631\u0627\u062c\u0639\u0629 \u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629\u060c \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639.","breadcrumb":{"@id":"http:\/\/toposuranos.com\/material\/ar\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["http:\/\/toposuranos.com\/material\/ar\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/ar\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\/#primaryimage","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/08\/cinematica-5.jpg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/08\/cinematica-5.jpg","width":1792,"height":1024},{"@type":"BreadcrumbList","@id":"http:\/\/toposuranos.com\/material\/ar\/%d8%a3%d8%b3%d8%a7%d8%b3%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%b1%d9%83%d8%a9-%d8%a7%d9%84%d9%85%d9%88%d9%82%d8%b9%d8%8c-%d8%a7%d9%84%d8%b3%d8%b1%d8%b9%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%b3%d8%a7\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"http:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062d\u0631\u0643\u0629: \u0627\u0644\u0645\u0648\u0642\u0639\u060c \u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0627\u0644\u062a\u0633\u0627\u0631\u0639"}]},{"@type":"WebSite","@id":"http:\/\/toposuranos.com\/material\/#website","url":"http:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"http:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"http:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"http:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/27226","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=27226"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/27226\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/28506"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=27226"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=27226"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=27226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}