{"id":28773,"date":"2024-09-19T17:27:48","date_gmt":"2024-09-19T17:27:48","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28773"},"modified":"2024-09-19T17:32:56","modified_gmt":"2024-09-19T17:32:56","slug":"%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ar\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\/","title":{"rendered":"\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a"},"content":{"rendered":"<h1 style=\"text-align:center;\">\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0641\u064a \u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c<\/h1>\n<p style=\"text-align:center;\"><em><strong>\u0645\u0644\u062e\u0635:<\/strong><\/br>\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u0646\u0631\u0627\u062c\u0639 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0645\u0646 \u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0642\u0646\u064a\u0627\u062a \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a\u060c \u0648\u0645\u0646 \u062e\u0644\u0627\u0644 \u0630\u0644\u0643 \u0633\u0646\u0648\u0636\u062d \u0628\u062a\u0641\u0635\u064a\u0644 \u0643\u064a\u0641\u064a\u0629 \u062a\u0637\u0628\u064a\u0642\u0647\u0627 \u0641\u064a \u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646.<\/em><\/p>\n<hr>\n<p style=\"text-align:center;\"><strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645:<\/strong><br \/>\n\u0639\u0646\u062f \u0627\u0644\u0627\u0646\u062a\u0647\u0627\u0621 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0627\u0644\u0628 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649:<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u0641\u0647\u0645<\/strong> \u0645\u0628\u062f\u0623 \u0647\u0627\u0645\u064a\u0644\u062a\u0648\u0646 \u0644\u0644\u0641\u0639\u0644 \u0627\u0644\u0623\u062f\u0646\u0649<\/li>\n<li><strong>\u0625\u062b\u0628\u0627\u062a<\/strong> \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c<\/li>\n<li><strong>\u062d\u0644<\/strong> \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c.<\/li>\n<\/ol>\n<hr>\n<p style=\"text-align:center;\">\n<strong><u>\u0641\u0647\u0631\u0633 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a<\/u>:<\/strong><br \/>\n<a href=\"#1\">\u0644\u0645\u0627\u0630\u0627 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0641\u064a \u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629\u061f<\/a><br \/>\n<a href=\"#2\">\u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0629<\/a><br \/>\n<a href=\"#3\">\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c<\/a><br \/>\n<a href=\"#4\">\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646<\/a><br \/>\n<a href=\"#5\">\u0645\u0633\u062a\u0648\u062f\u0639 GitHub \u0645\u0639 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0648\u0644\u0641\u0631\u0627\u0645<\/a>\n<\/p>\n<hr>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/JyumifjGzM0\" title=\"\u0645\u0634\u063a\u0644 \u0641\u064a\u062f\u064a\u0648 \u064a\u0648\u062a\u064a\u0648\u0628\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/center><\/p>\n<hr>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0644\u0645\u0627\u0630\u0627 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0641\u064a \u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629\u061f<\/h2>\n<p style=\"text-align:justify;\">\u062a\u0642\u062f\u0645 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0627\u0644\u0646\u064a\u0648\u062a\u0648\u0646\u064a\u0629 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u0645\u0639\u0627\u0644\u062c\u062a\u0647\u0627 \u0628\u0634\u0643\u0644 \u0623\u0643\u062b\u0631 \u0641\u0639\u0627\u0644\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a. \u0647\u0630\u0627 \u0627\u0644\u0646\u0647\u062c \u0623\u0633\u0627\u0633\u064a \u0641\u064a \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0648\u0641\u064a \u0645\u0628\u062f\u0623 \u0627\u0644\u0641\u0639\u0644 \u0627\u0644\u0623\u062f\u0646\u0649 \u0644\u0647\u0627\u0645\u064a\u0644\u062a\u0648\u0646. \u0641\u064a \u062c\u0648\u0647\u0631\u0647\u060c \u064a\u062a\u0643\u0648\u0646 \u0647\u0630\u0627 \u0627\u0644\u0623\u0633\u0644\u0648\u0628 \u0645\u0646 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0633\u0627\u0631\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0632\u064a\u062f \u0623\u0648 \u062a\u0642\u0644\u0644 \u0645\u0646 \u0643\u0645\u064a\u0629 \u0645\u0639\u064a\u0646\u0629. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u064a\u0645\u0643\u0646 \u0627\u0644\u0628\u062d\u062b \u0639\u0646 \u0627\u0644\u0645\u0633\u0627\u0631 \u0628\u064a\u0646 \u0646\u0642\u0637\u062a\u064a\u0646 \u0627\u0644\u0630\u064a \u064a\u0642\u0644\u0644 \u0645\u0646 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0627\u0644\u0645\u0642\u0637\u0648\u0639\u0629 \u0623\u0648 \u0648\u0642\u062a \u0627\u0644\u0633\u0641\u0631. \u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u0647\u0630\u0627 \u0627\u0644\u0646\u0647\u062c \u0647\u0648 \u0645\u0628\u062f\u0623 \u0641\u064a\u0631\u0645\u0627\u060c \u0627\u0644\u0630\u064a \u064a\u0646\u0635 \u0639\u0644\u0649 \u0623\u0646 \u0627\u0644\u0636\u0648\u0621 \u064a\u062a\u0628\u0639 \u062f\u0627\u0626\u0645\u064b\u0627 \u0627\u0644\u0645\u0633\u0627\u0631 \u0627\u0644\u0630\u064a \u064a\u0642\u0644\u0644 \u0645\u0646 \u0648\u0642\u062a \u0627\u0644\u0633\u0641\u0631\u060c \u0645\u0645\u0627 \u064a\u0624\u062f\u064a \u0628\u062f\u0648\u0631\u0647 \u0625\u0644\u0649 <a href=\"http:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%86%d9%83%d8%b3%d8%a7%d8%b1-%d8%a7%d9%84%d8%b6%d9%88%d8%a1-%d9%88%d9%82%d8%a7%d9%86%d9%88%d9%86-%d8%b3%d9%86%d9%8a%d9%84\/\" target=\"_blank\" rel=\"noopener\">\u0642\u0627\u0646\u0648\u0646 \u0633\u0646\u064a\u0644 \u0644\u0627\u0646\u0643\u0633\u0627\u0631 \u0627\u0644\u0636\u0648\u0621<\/a>.<\/p>\n<p style=\"text-align:justify;\">\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0645\u0632\u0627\u064a\u0627 \u0645\u062a\u0639\u062f\u062f\u0629 \u0641\u064a \u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u064a\u0633\u0645\u062d \u0628\u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u062d\u0644\u0648\u0644 \u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u062f\u0642\u064a\u0642\u0629 \u0644\u0644\u0623\u0646\u0638\u0645\u0629 \u0630\u0627\u062a \u0627\u0644\u062a\u0646\u0627\u0638\u0631\u060c \u0648\u062d\u0644\u0648\u0644 \u062a\u0642\u0631\u064a\u0628\u064a\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628\u0627\u062a \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0629 \u0644\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0623\u0643\u062b\u0631 \u062a\u0639\u0642\u064a\u062f\u064b\u0627. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0641\u064a \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u0635\u0639\u0628 \u0641\u064a\u0647\u0627 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0627\u0644\u0642\u0648\u0649 \u0645\u0646 \u062d\u064a\u062b \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629\u060c \u064a\u0648\u0641\u0631 \u0645\u0628\u062f\u0623 \u0627\u0644\u0641\u0639\u0644 \u0627\u0644\u0623\u062f\u0646\u0649 \u0637\u0631\u064a\u0642\u0629 \u0623\u0643\u062b\u0631 \u0643\u0641\u0627\u0621\u0629 \u0644\u062d\u0644 \u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a \u0641\u064a \u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629. \u0628\u0627\u062e\u062a\u0635\u0627\u0631\u060c \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0647\u0648 \u0623\u062f\u0627\u0629 \u0623\u0633\u0627\u0633\u064a\u0629 \u062a\u0648\u0641\u0631 \u0635\u064a\u0627\u063a\u0629 \u0628\u062f\u064a\u0644\u0629 \u0644\u0642\u0648\u0627\u0646\u064a\u0646 \u0646\u064a\u0648\u062a\u0646\u060c \u0648\u062a\u0648\u062d\u064a\u062f \u0642\u0648\u0627\u0646\u064a\u0646 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621\u060c \u0648\u0643\u0641\u0627\u0621\u0629 \u0623\u0643\u0628\u0631 \u0641\u064a \u062d\u0644 \u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a\u060c \u0648\u062f\u0642\u0629 \u0623\u0643\u0628\u0631 \u0641\u064a \u062a\u0648\u0642\u0639 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u062a\u062c\u0631\u064a\u0628\u064a\u0629.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0629<\/h2>\n<p style=\"text-align:justify;\">\u064a\u0631\u0643\u0632 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0639\u0644\u0649 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span><\/span> \u0627\u0644\u062a\u064a \u062a\u0632\u064a\u062f \u0623\u0648 \u062a\u0642\u0644\u0644 \u0645\u0646 \u0642\u064a\u0645\u0629 \u0627\u0644\u062a\u0627\u0628\u0639:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">J(x,y(x))=\\displaystyle \\int_{x_1}^{x_2} f\\left(x,y(x),\\frac{dy(x)}{dx}\\right)dx,<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0645\u0646 \u0623\u062c\u0644 \u0625\u064a\u062c\u0627\u062f \u0642\u064a\u0645\u062a\u0647 \u0627\u0644\u0642\u0635\u0648\u0649 \u0623\u0648 \u0627\u0644\u062f\u0646\u064a\u0627. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629\u060c \u064a\u0639\u062a\u0645\u062f \u0627\u0644\u062a\u0627\u0628\u0639 <span class=\"katex-eq\" data-katex-display=\"false\">J<\/span> \u0639\u0644\u0649 \u0627\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span><\/span> \u0648\u0645\u0634\u062a\u0642\u062a\u0647\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dy(x)\/dx,<\/span><\/span> \u0628\u064a\u0646\u0645\u0627 \u062a\u0638\u0644 \u062d\u062f\u0648\u062f \u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u062b\u0627\u0628\u062a\u0629. \u0644\u062a\u0639\u0638\u064a\u0645 \u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0623\u0648 \u062a\u0635\u063a\u064a\u0631\u0647\u060c \u062a\u064f\u0637\u0628\u0642 \u062a\u063a\u064a\u064a\u0631\u0627\u062a \u0639\u0644\u0649 \u0627\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span><\/span>\u060c \u0628\u0647\u062f\u0641 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u064a \u062a\u062c\u0639\u0644 \u0642\u064a\u0645\u0629 \u0627\u0644\u062a\u0627\u0628\u0639 \u0641\u064a \u062d\u0627\u0644\u0629 \u0642\u0635\u0648\u0649. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0625\u0630\u0627 \u062a\u0645 \u062a\u062d\u0642\u064a\u0642 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u062f\u0646\u0649 \u0645\u0646 \u0627\u0644\u062a\u0643\u0627\u0645\u0644\u060c \u0641\u0625\u0646 \u0623\u064a \u062f\u0627\u0644\u0629 <em>\u062f\u0627\u062e\u0644 \u0645\u062d\u064a\u0637\u0647\u0627<\/em>\u060c \u0628\u063a\u0636 \u0627\u0644\u0646\u0638\u0631 \u0639\u0646 \u0645\u062f\u0649 \u0642\u0631\u0628\u0647\u0627 \u0645\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span><\/span>\u060c \u0633\u062a\u0632\u064a\u062f \u0645\u0646 \u0642\u064a\u0645\u0629 \u0627\u0644\u062a\u0627\u0628\u0639.<\/p>\n<p style=\"text-align:justify;\">\u0644\u062a\u062d\u062f\u064a\u062f \u0645\u0641\u0647\u0648\u0645 <em>\u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u062c\u0627\u0648\u0631\u0629<\/em>\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u062e\u0635\u064a\u0635 \u062a\u0645\u062b\u064a\u0644 \u0628\u0627\u0631\u0627\u0645\u064a\u062a\u0631\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=(\\alpha,x)<\/span><\/span> \u0644\u062c\u0645\u064a\u0639 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u0645\u0643\u0646\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span>\u060c \u0628\u062d\u064a\u062b \u0625\u0630\u0627 \u0643\u0627\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha=0<\/span><\/span>\u060c \u0641\u0625\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y(0,x)=y(x)<\/span><\/span> \u0647\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u064a \u062a\u0632\u064a\u062f \u0623\u0648 \u062a\u0642\u0644\u0644 \u0645\u0646 \u0627\u0644\u062a\u0627\u0628\u0639 <span class=\"katex-eq\" data-katex-display=\"false\">J<\/span>. \u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0647\u0630\u0627 \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\">y(\\alpha, x) = y(x) + \\alpha \\eta(x),<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\eta(x)<\/span><\/span> \u0647\u064a \u062f\u0627\u0644\u0629 \u0645\u0646 \u0627\u0644\u0646\u0648\u0639 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{C}^1<\/span><\/span> \u0648\u062a\u0644\u063a\u064a \u0646\u0641\u0633\u0647\u0627 \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1<\/span><\/span> \u0648<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_2<\/span><\/span>\u060c \u0628\u062d\u064a\u062b \u062a\u0643\u0648\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y(\\alpha,x)<\/span><\/span> \u0627\u0644\u062a\u064a \u062a\u062a\u0636\u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u062a\u063a\u064a\u064a\u0631 \u0645\u0645\u0627\u062b\u0644\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span><\/span> \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 \u0648\u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0644\u0645\u0633\u0627\u0631 \u0627\u0644\u062a\u0643\u0627\u0645\u0644.<\/p>\n<p style=\"text-align:justify;\">\u0639\u0646\u062f \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y(\\alpha,x)<\/span><\/span> \u0627\u0644\u062a\u064a \u062a\u062a\u0636\u0645\u0646 \u0627\u0644\u062a\u063a\u064a\u064a\u0631 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\eta(x)<\/span><\/span> \u0628\u062f\u0644\u0627\u064b \u0645\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span><\/span> \u0641\u064a \u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0627\u0644\u0630\u064a \u064a\u062d\u062f\u062f \u0627\u0644\u062a\u0627\u0628\u0639 <span class=\"katex-eq\" data-katex-display=\"false\">J<\/span>\u060c \u064a\u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u062a\u0627\u0628\u0639 \u062c\u062f\u064a\u062f \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0645\u0639\u0644\u0645\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span>:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">J(x,y(\\alpha, x)) = \\displaystyle \\int_{x_1}^{x_2} f\\left(x,y(\\alpha,x), \\dfrac{d}{dx}y(\\alpha,x)\\right)dx<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0644\u0643\u064a \u062a\u0643\u0648\u0646 \u0647\u0646\u0627\u0643 \u062d\u062f\u0648\u062f \u0645\u062d\u0644\u064a\u0629\u060c \u064a\u062c\u0628 \u062a\u062d\u0642\u064a\u0642 \u0627\u0644\u0634\u0631\u0637 \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.\\dfrac{\\partial J(x,y(\\alpha,x))}{\\partial \\alpha}\\right|_{\\alpha=0} = 0<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0644\u0623\u064a \u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\eta(x)<\/span><\/span><\/p>\n<p>.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c<\/h2>\n<p style=\"text-align:justify;\">\u0639\u0646\u062f \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\partial J(x,y(\\alpha,x))\/\\partial \\alpha<\/span><\/span>\u060c \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\">\\begin{array}{rll}\n\n{}\\dfrac{\\partial J(x,y(\\alpha,x))}{\\partial \\alpha}\n\n&amp;=&amp;\\dfrac{\\partial}{\\partial \\alpha} \\displaystyle \\int_{x_1}^{x_2} f\\left(x,y(\\alpha,x),\\dfrac{dy(\\alpha, x)}{dx}\\right)dx \\\\ \\\\\n\n&amp;=&amp;\\displaystyle \\int_{x_1}^{x_2} \\left(\\dfrac{\\partial f}{\\partial x}\\dfrac{\\partial x}{\\partial  \\alpha} + \\dfrac{\\partial f}{\\partial y(\\alpha, x)}\\dfrac{\\partial y(\\alpha, x)}{\\partial  \\alpha}  + \\dfrac{\\partial f }{ \\partial \\frac{dy(\\alpha,x)}{dx}} \\dfrac{\\partial \\frac{dy(\\alpha,x)}{dx}}{\\partial \\alpha}\\right)dx \\\\\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629\u060c \u0645\u0646 \u0627\u0644\u0645\u0647\u0645 \u0645\u0644\u0627\u062d\u0638\u0629 \u0623\u0646:<\/p>\n<p style=\"text-align:center;\"><span dir=ltr><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n\\dfrac{\\partial x}{\\partial \\alpha} &amp;=&amp; 0 \\\\ \\\\\n\n\\dfrac{\\partial y(\\alpha,x)}{\\partial \\alpha} &amp;=&amp; \\dfrac{\\partial}{\\partial \\alpha} \\left(y(x) + \\alpha \\eta(x) \\right) = \\eta(x) \\\\ \\\\\n\n\\dfrac{\\partial}{\\partial \\alpha}\\left( \\dfrac{dy(\\alpha, x)}{dx} \\right)&amp;=&amp; \\dfrac{\\partial}{\\partial \\alpha} \\left(\\dfrac{dy(x)}{dx} + \\alpha\\dfrac{d\\eta(x)}{dx} \\right) = \\dfrac{d\\eta}{dx}\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u064a\u0645\u0643\u0646 \u062a\u0628\u0633\u064a\u0637 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0643\u0645\u0627 \u064a\u0638\u0647\u0631 \u0623\u062f\u0646\u0627\u0647:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\n\n{} \\dfrac{\\partial J(x,y(\\alpha,x))}{\\partial \\alpha} &amp;=&amp; \\displaystyle \\int_{x_1}^{x_2} \\left(\\dfrac{\\partial f}{\\partial y(\\alpha,x)}\\eta(x) + \\dfrac{\\partial f}{\\partial  \\frac{dy(\\alpha,x)}{dx}} \\dfrac{d\\eta(x)}{dx} \\right)dx \\\\ \\\\\n\n&amp;=&amp;\\displaystyle \\int_{x_1}^{x_2} \\dfrac{\\partial f}{\\partial y(\\alpha,x)}\\eta(x) dx +  \\int_{x_1}^{x_2} \\dfrac{\\partial f}{\\partial  \\frac{dy(\\alpha,x)}{dx}} \\dfrac{d\\eta(x)}{dx} dx\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u062b\u0645 \u0625\u0630\u0627 \u0644\u0627\u062d\u0638\u0646\u0627 \u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0627\u0644\u062b\u0627\u0646\u064a\u060c \u0633\u0646\u0631\u0649 \u0623\u0646\u0647 \u064a\u0645\u0643\u0646 \u062a\u0628\u0633\u064a\u0637\u0647 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0628\u0627\u0644\u0623\u062c\u0632\u0627\u0621:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n\\displaystyle \\int_{x_1}^{x_2} \\dfrac{\\partial f}{\\partial  \\frac{dy(\\alpha,x)}{dx}} \\dfrac{d\\eta}{dx} dx\n\n&amp;=&amp; \\left. \\dfrac{\\partial f}{\\partial \\frac{dy(\\alpha,x)}{dx}} \\eta(x)\\right|_{x_1}^{x_2} - \\displaystyle \\int_{x_1}^{x_2}\\eta(x) \\dfrac{d}{dx}\\left( \\dfrac{\\partial f}{\\partial \\frac{dy(\\alpha, x)}{dx}} \\right) dx\\\\ \\\\\n\n&amp;=&amp; - \\displaystyle \\int_{x_1}^{x_2}\\eta(x) \\dfrac{d}{dx}\\left( \\dfrac{\\partial f}{\\partial \\frac{dy(\\alpha, x)}{dx}} \\right)dx\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n{} \\dfrac{\\partial J(x,y(\\alpha,x))}{\\partial \\alpha}\n\n&amp;=&amp; \\displaystyle \\int_{x_1}^{x_2} \\left[ \\eta(x) \\dfrac{\\partial f}{\\partial y(\\alpha, x)}  - \\eta(x) \\dfrac{d}{dx}\\left( \\dfrac{\\partial f}{\\partial \\frac{dy(\\alpha,x)}{dx}} \\right) \\right]dx \\\\ \\\\\n\n&amp;=&amp; \\displaystyle \\int_{x_1}^{x_2} \\left[ \\dfrac{\\partial f}{\\partial y(\\alpha, x)}  -  \\dfrac{d}{dx}\\left( \\dfrac{\\partial f}{\\partial \\frac{dy(\\alpha,x)}{dx}} \\right) \\right] \\eta(x) dx\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0648\u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u0634\u0631\u0637 \u0647\u0648 \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left.\\dfrac{\\partial J (x,y(\\alpha, x))}{\\partial \\alpha}\\right|_{\\alpha=0} = 0,<\/span><\/span> \u0648\u0628\u0645\u0627 \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\eta(x)<\/span><\/span> \u0647\u064a \u062f\u0627\u0644\u0629 \u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u062a\u062e\u0636\u0639 \u0644\u0644\u0634\u0631\u0637 \u0627\u0644\u0648\u062d\u064a\u062f \u0627\u0644\u0645\u062a\u0645\u062b\u0644 \u0641\u064a \u0625\u0644\u063a\u0627\u0621 \u0646\u0641\u0633\u0647\u0627 \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1<\/span><\/span> \u0648<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_2,<\/span><\/span> \u0644\u062f\u064a\u0646\u0627:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\dfrac{\\partial f}{\\partial y(0, x)}  -  \\dfrac{d}{dx}\\left( \\dfrac{\\partial f}{\\partial \\frac{dy(0,x)}{dx}}\\right) = \\dfrac{\\partial f}{\\partial y(x)}  -  \\dfrac{d}{dx}\\left( \\dfrac{\\partial f}{\\partial \\frac{dy(x)}{dx}}\\right) = 0.\n\n<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0628\u0625\u0633\u0642\u0627\u0637 \u0627\u0644\u062a\u0631\u0645\u064a\u0632 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u0623\u062e\u064a\u0631\u060c \u0646\u0635\u0644 \u0625\u0644\u0649 \u0645\u0627 \u064a\u0639\u0631\u0641 \u0628\u0627\u0633\u0645 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\dfrac{\\partial f}{\\partial y}= \\dfrac{d}{dx}\\left( \\dfrac{\\partial f}{\\partial y^\\prime} \\right)},<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0648\u0647\u0630\u0627 \u064a\u0645\u062b\u0644 \u0628\u0634\u0643\u0644 \u0623\u0643\u062b\u0631 \u0628\u0633\u0627\u0637\u0629 \u0627\u0644\u0634\u0631\u0637 \u0627\u0644\u0644\u0627\u0632\u0645 \u0644\u0643\u064a \u064a\u0635\u0644 \u0627\u0644\u062a\u0627\u0628\u0639 <span class=\"katex-eq\" data-katex-display=\"false\">J<\/span> \u0625\u0644\u0649 \u0642\u064a\u0645\u0629 \u0642\u0635\u0648\u0649.<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u0646<\/h2>\n<h3>\u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u0645\u0634\u0643\u0644\u0629<\/h3>\n<p style=\"text-align:justify;\">\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u0646 \u0647\u064a \u0645\u0634\u0643\u0644\u0629 \u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629 \u0641\u064a \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u064a\u0629 \u062a\u064f\u062d\u0644 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a. \u0627\u0644\u0648\u0636\u0639 \u0627\u0644\u0645\u0637\u0631\u0648\u062d \u0647\u0648 \u0643\u0627\u0644\u062a\u0627\u0644\u064a: \u0644\u0646\u0641\u062a\u0631\u0636 \u0623\u0646 \u0644\u062f\u064a\u0646\u0627 \u062c\u0633\u0645\u064b\u0627 \u0645\u0627\u062f\u064a\u064b\u0627 \u064a\u062a\u062d\u0631\u0643 \u062a\u062d\u062a \u062a\u0623\u062b\u064a\u0631 \u0645\u062c\u0627\u0644 \u0642\u0648\u0649 \u062b\u0627\u0628\u062a \u0648\u064a\u062a\u062d\u0631\u0643 \u0645\u0646 \u0646\u0642\u0637\u0629 \u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_1,y_1)<\/span><\/span> \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0646\u0647\u0627\u0626\u064a\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)<\/span><\/span>\u060c \u062d\u064a\u062b \u062a\u0642\u0639 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 \u0639\u0644\u0649 \u0627\u0631\u062a\u0641\u0627\u0639 \u0623\u0639\u0644\u0649 \u0645\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0646\u0647\u0627\u0626\u064a\u0629. \u0627\u0644\u0633\u0624\u0627\u0644 \u0627\u0644\u0630\u064a \u064a\u064f\u0637\u0631\u062d \u0647\u0648: \u0645\u0627 \u0647\u064a \u0627\u0644\u0645\u0633\u0627\u0631 \u0627\u0644\u0630\u064a \u064a\u062c\u0628 \u0623\u0646 \u064a\u0633\u0644\u0643\u0647 \u0627\u0644\u062c\u0633\u0645 \u0644\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u0649 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0646\u0647\u0627\u0626\u064a\u0629 \u0641\u064a \u0623\u0642\u0635\u0631 \u0648\u0642\u062a \u0645\u0645\u0643\u0646\u061f<\/p>\n<h3>\u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u062d\u0644<\/h3>\n<p style=\"text-align:justify;\">\u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u0646\u060c \u0645\u0646 \u0627\u0644\u0645\u0641\u064a\u062f \u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u0648\u0636\u0639 \u0628\u0634\u0643\u0644 \u0628\u0633\u064a\u0637. \u0644\u0630\u0644\u0643\u060c \u064a\u0645\u0643\u0646 \u062a\u062d\u062f\u064a\u062f \u0646\u0642\u0637\u0629 \u0627\u0644\u0628\u062f\u0627\u064a\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_1, y_1)<\/span><\/span> \u0641\u064a \u0623\u0635\u0644 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a\u060c \u0628\u064a\u0646\u0645\u0627 \u062a\u0642\u0639 \u0646\u0642\u0637\u0629 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)<\/span><\/span> \u0639\u0644\u0649 \u064a\u0645\u064a\u0646 \u0627\u0644\u0623\u0635\u0644 \u0648\u0623\u0633\u0641\u0644 \u0627\u0644\u0645\u062d\u0648\u0631 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span><\/span>.<\/p>\n<div style=\"text-align:center;\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/probbraquistocrona.png\" alt=\"\u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u064a - \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u0646\" width=\"711\" height=\"505\" class=\"aligncenter size-full wp-image-28729 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/probbraquistocrona.png\" alt=\"\u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u064a - \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u0646\" width=\"711\" height=\"505\" class=\"aligncenter size-full wp-image-28729 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/probbraquistocrona.png 711w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/probbraquistocrona-300x213.png 300w\" sizes=\"(max-width: 711px) 100vw, 711px\" \/><\/noscript><\/div>\n<p style=\"text-align:justify;\">\u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0648\u0636\u0639\u060c \u064a\u0645\u0643\u0646 \u0627\u0639\u062a\u0628\u0627\u0631 \u0648\u062c\u0648\u062f \u0645\u062c\u0627\u0644 \u0642\u0648\u0629 \u064a\u0639\u0645\u0644 \u0646\u062d\u0648 \u0627\u0644\u0623\u0633\u0641\u0644 (\u0641\u064a \u0627\u062a\u062c\u0627\u0647 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-\\hat{y}<\/span><\/span>) \u062a\u0645 \u062a\u0648\u0644\u064a\u062f\u0647 \u0628\u0648\u0627\u0633\u0637\u0629 \u0627\u0644\u062c\u0627\u0630\u0628\u064a\u0629\u060c \u0648\u0627\u0641\u062a\u0631\u0627\u0636 \u0623\u0646 \u0627\u0644\u062d\u0631\u0643\u0629 \u062a\u062a\u0645 \u0628\u062f\u0648\u0646 \u0627\u062d\u062a\u0643\u0627\u0643. \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0633\u064a\u0627\u0642\u060c \u064a\u062a\u0645 \u062a\u0642\u064a\u064a\u062f \u0627\u0644\u062c\u0633\u0645 \u0628\u0627\u062a\u0628\u0627\u0639 \u0645\u0633\u0627\u0631\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629 \u062a\u0631\u0628\u0637 \u0628\u064a\u0646 \u0646\u0642\u0627\u0637 \u0627\u0644\u0627\u0646\u0637\u0644\u0627\u0642 \u0648\u0627\u0644\u0648\u0635\u0648\u0644 \u0628\u0647\u062f\u0641 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0633\u0627\u0631 \u0627\u0644\u0630\u064a \u064a\u0642\u0644\u0644 \u0632\u0645\u0646 \u0627\u0644\u0633\u0641\u0631.<\/p>\n<h3>\u0641\u062d\u0635 \u0627\u0644\u0637\u0627\u0642\u0629<\/h3>\n<p style=\"text-align:justify;\">\u0644\u062d\u0644 \u0647\u0630\u0647 \u0627\u0644\u0645\u0634\u0643\u0644\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u0627\u0633\u062a\u0641\u0627\u062f\u0629 \u0645\u0646 \u062d\u0641\u0638 \u0627\u0644\u0637\u0627\u0642\u0629 \u0641\u064a \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u062c\u0627\u0630\u0628\u064a. \u0633\u062a\u0638\u0644 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u0643\u0644\u064a\u0629 \u0644\u0644\u0646\u0638\u0627\u0645 \u062b\u0627\u0628\u062a\u0629\u060c \u0645\u0639 \u0627\u0644\u0623\u062e\u0630 \u0641\u064a \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631 \u0643\u0644 \u0645\u0646 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062d\u0631\u0643\u064a\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">E_{cin}=\\frac{1}{2}mv^2<\/span><\/span> \u0648\u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062c\u0627\u0630\u0628\u064a\u0629 \u0627\u0644\u0645\u062d\u062a\u0645\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">E_{pot,g}<\/span><\/span>\u060c \u062d\u064a\u062b <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0647\u064a \u0643\u062a\u0644\u0629 \u0627\u0644\u062c\u0633\u064a\u0645 \u0648<span class=\"katex-eq\" data-katex-display=\"false\">v<\/span> \u0647\u064a \u0633\u0631\u0639\u062a\u0647. \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062c\u0627\u0630\u0628\u064a\u0629 \u0627\u0644\u0645\u062d\u062a\u0645\u0644\u0629\u060c \u062a\u0645 \u0627\u0639\u062a\u0628\u0627\u0631 \u0627\u0644\u0623\u0635\u0644 \u0643\u0645\u0631\u062c\u0639\u060c \u0628\u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">E_{pot,g}(y=0)=0<\/span><\/span>\u060c \u0628\u064a\u0646\u0645\u0627 \u0641\u064a \u0623\u064a \u0627\u0631\u062a\u0641\u0627\u0639 \u0622\u062e\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u064a\u0643\u0648\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">E_{pot,g}(y)=mgy.<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u062c\u0633\u064a\u0645 \u064a\u0628\u062f\u0623 \u0645\u0646 \u0627\u0644\u0623\u0635\u0644 \u0628\u0633\u0631\u0639\u0629 \u0635\u0641\u0631\u060c \u0641\u0625\u0646 \u0637\u0627\u0642\u062a\u0647 \u0627\u0644\u0643\u0644\u064a\u0629 \u062a\u0633\u0627\u0648\u064a \u0635\u0641\u0631\u064b\u0627. \u0625\u0630\u0646\u060c \u0644\u062f\u064a\u0646\u0627:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">E_{cin} + E_{pot,g}=0<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u062c\u0633\u064a\u0645 \u064a\u0633\u0642\u0637 \u0623\u0633\u0641\u0644 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u0631\u062c\u0639\u064a\u0629\u060c \u0641\u0625\u0646 \u0637\u0627\u0642\u062a\u0647 \u0627\u0644\u062c\u0627\u0630\u0628\u064a\u0629 \u0627\u0644\u0645\u062d\u062a\u0645\u0644\u0629 \u0633\u062a\u0643\u0648\u0646 \u0633\u0644\u0628\u064a\u0629 \u0648\u0637\u0627\u0642\u062a\u0647 \u0627\u0644\u062d\u0631\u0643\u064a\u0629 \u0633\u062a\u0643\u0648\u0646 \u0625\u064a\u062c\u0627\u0628\u064a\u0629. \u0628\u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0641\u0635\u0644 \u0627\u0644\u0633\u0631\u0639\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">v<\/span> \u0645\u0646 \u0645\u0639\u0627\u062f\u0644\u0629 \u062d\u0641\u0638 \u0627\u0644\u0637\u0627\u0642\u0629 \u0648\u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649:<\/p>\n<p style=\"text-align:center\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n{} &amp;\\dfrac{1}{2}mv^2 + (-mgy) = 0 \\\\ \\\\\n\n\\vdash &amp;\\dfrac{1}{2}mv^2 = mgy \\\\ \\\\\n\n\\vdash &amp;v^2 = 2gy \\\\ \\\\\n\n\\vdash &amp;v = \\sqrt{2gy}\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0628\u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062d\u0633\u0627\u0628 \u0633\u0631\u0639\u0629 \u0627\u0644\u062c\u0633\u064a\u0645 \u0641\u064a \u0623\u064a \u0646\u0642\u0637\u0629 \u0645\u0646 \u0645\u0633\u0627\u0631\u0647 \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0627\u0644\u0627\u0631\u062a\u0641\u0627\u0639 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u0627\u0644\u0630\u064a \u064a\u0648\u062c\u062f \u0639\u0646\u062f\u0647. <\/p>\n<h3>\u0641\u062d\u0635 \u0632\u0645\u0646 \u0627\u0644\u0631\u062d\u0644\u0629<\/h2>\n<p style=\"text-align:justify;\">\u0628\u0645\u062c\u0631\u062f \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0633\u0631\u0639\u0629 \u0627\u0644\u062d\u0631\u0643\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0628\u0646\u0627\u0621 \u0639\u0646\u0635\u0631 \u0627\u0644\u0632\u0645\u0646 \u0644\u0644\u0631\u062d\u0644\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0639\u0646\u0635\u0631 \u0627\u0644\u0625\u0632\u0627\u062d\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">ds=\\sqrt{dx^2 + dy^2}<\/span><\/span> \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\">\\begin{array}{rl}\n\n{} dt &amp;= \\dfrac{ds}{v} = \\dfrac{\\sqrt{dx^2 + dy^2}}{\\sqrt{2gy}}\\\\ \\\\\n\n&amp;= \\sqrt{\\dfrac{dx^2 + dy^2}{2gy} }\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0628\u062d\u064a\u062b \u064a\u0645\u0643\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0632\u0645\u0646 \u0627\u0644\u0625\u0632\u0627\u062d\u0629 \u0628\u064a\u0646 \u0627\u0644\u0646\u0642\u0637\u062a\u064a\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_1,y_1)<\/span><\/span> \u0648<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)<\/span><\/span> \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062a\u0643\u0627\u0645\u0644<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n{} t &amp;= \\displaystyle \\int_{(x_1,y_1)}^{(x_2,y_2)} dt \\\\ \\\\\n\n&amp;= \\displaystyle \\int_{(x_1,y_1)}^{(x_2,y_2)} \\sqrt{\\dfrac{dx^2 + dy^2}{2gy}} \\\\ \\\\\n\n&amp;= \\displaystyle \\dfrac{1}{\\sqrt{2g}}\\int_{y_1}^{y_2} \\sqrt{\\dfrac{1+ \\left(\\dfrac{dx}{dy}\\right)^2 }{y}}dy \\\\ \\\\\n\n\\end{array}<\/span><\/span><\/p>\n<h3>\u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0629<\/h3>\n<p style=\"text-align:justify;\">\u0645\u0639 \u0647\u0630\u0627 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u0623\u062e\u064a\u0631\u060c \u062a\u0645\u0643\u0646\u0627 \u0645\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0627\u0644\u0632\u0645\u0646 \u0643\u062f\u0627\u0644\u0629 \u0628\u0627\u0644\u0634\u0643\u0644<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n{}t = J(y,x(y)) = \\displaystyle \\int_{y_1}^{y_2} f\\left(y,x(y),\\dfrac{dx(y)}{dy} \\right) dy\n\n<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u062d\u064a\u062b<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f\\left(y,x(y), \\dfrac{dx(y)}{dx}\\right) = \\sqrt{\\dfrac{1+ \\left(\\dfrac{dx(y)}{dy} \\right)^2}{y}} <\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0631\u062d\u0644\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u062c\u0627\u0648\u0632 \u0627\u0644\u0639\u0627\u0645\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{2g},<\/span><\/span> \u0644\u0623\u0646 \u062a\u062d\u0633\u064a\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">J<\/span> \u0647\u0648 \u0646\u0641\u0633\u0647 \u062a\u0645\u0627\u0645\u064b\u0627 \u0645\u062b\u0644 \u062a\u062d\u0633\u064a\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{2g}J<\/span><\/span>.<\/p>\n<p style=\"text-align:justify;\">\u0645\u0639 \u0645\u0627 \u0633\u0628\u0642\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u0622\u0646 \u0628\u0646\u0627\u0621 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u062a\u0628\u0627\u0639 \u0646\u0641\u0633 \u0627\u0644\u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645 \u0633\u0627\u0628\u0642\u064b\u0627\u060c \u0644\u0646\u0635\u0644 \u0641\u064a \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0625\u0644\u0649:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{\\partial f}{\\partial x} = \\dfrac{d}{dy} \\dfrac{\\partial f}{\\partial x^\\prime}<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0647\u0646\u0627 \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0631\u0649 \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{\\partial f}{\\partial x} = 0,<\/span><\/span> \u0644\u0630\u0644\u0643 \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\">\\dfrac{d}{dy}\\dfrac{\\partial f}{\\partial x^\\prime} = 0,<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0623\u0648 \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{\\partial f}{\\partial x^\\prime} = \\dfrac{1}{\\sqrt{2a}},<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u062d\u064a\u062b <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0647\u064a \u062b\u0627\u0628\u062a\u0629 \u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u0645\u0643\u062a\u0648\u0628\u0629 \u0628\u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0644\u0623\u0646\u0647\u0627 \u00ab\u0645\u0644\u0627\u0626\u0645\u0629\u00bb \u0644\u0644\u062a\u0637\u0648\u064a\u0631\u0627\u062a \u0627\u0644\u0644\u0627\u062d\u0642\u0629.<\/p>\n<h3>\u062d\u0644 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0629<\/h3>\n<p style=\"text-align:justify;\">\u0639\u0646\u062f \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u0623\u062e\u064a\u0631 \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\">\\begin{array}{rl}\n\n{} &amp;\\dfrac{\\partial }{\\partial x^\\prime} \\sqrt{\\dfrac{1+ x^{\\prime 2}}{y}}  = \\dfrac{1}{\\sqrt{2a}} \\\\ \\\\\n\n\\vdash &amp; \\dfrac{1}{2}\\left( \\dfrac{1 + x^{\\prime 2} }{y} \\right)^{-1\/2} \\left(\\dfrac{2x^\\prime}{y} \\right) = \\dfrac{1}{\\sqrt{2a}} \\\\ \\\\\n\n\\vdash &amp; \\dfrac{1}{2}\\sqrt{\\dfrac{y}{1 + x^{\\prime 2}}} \\left(\\dfrac{2x^\\prime}{y} \\right) = \\dfrac{1}{\\sqrt{2a}} \\\\ \\\\\n\n\\vdash &amp; \\sqrt{\\dfrac{4x^{\\prime 2} y}{4y^2 (1 + x^{\\prime 2})} }  = \\sqrt{\\dfrac{1}{2a}} \\\\ \\\\\n\n\\vdash &amp;  \\dfrac{y x^{\\prime 2} }{y^2 (1 + x^{\\prime 2})}   = \\dfrac{1}{ 2a} \\\\ \\\\\n\n\\vdash &amp; 2ayx^{\\prime 2} = y^2 + y^2 x^{\\prime 2} \\\\ \\\\\n\n\\vdash &amp;  x^{\\prime 2} (2ay - y^2) = y^2 \\\\ \\\\\n\n\\vdash &amp; \\left(\\dfrac{dx}{dy}\\right)^2 = \\dfrac{y^2}{2ay - y^2} \\\\ \\\\\n\n\\vdash &amp; \\dfrac{dx}{dy} = \\pm \\sqrt{\\dfrac{y^2}{2ay - y^2}} \\\\ \\\\\n\n\\vdash &amp; dx = \\pm \\dfrac{ydy}{\\sqrt{2ay - y^2}} \\\\ \\\\\n\n\\vdash &amp; x = \\displaystyle  \\pm \\int \\dfrac{y}{\\sqrt{2ay - y^2}}dy\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0644\u062d\u0644 \u0647\u0630\u0627 \u0627\u0644\u062a\u0643\u0627\u0645\u0644\u060c \u062e\u064a\u0627\u0631 \u064a\u062c\u0628 \u0645\u0631\u0627\u0639\u0627\u062a\u0647 \u0647\u0648 \u0627\u0644\u0642\u064a\u0627\u0645 \u0628\u0627\u0644\u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0627\u0644\u062a\u0627\u0644\u064a<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\n\n{} y &amp;=&amp; a[1-\\cos(\\theta)] \\\\\n\n dy &amp;=&amp; a\\sin(\\theta) d\\theta\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0648\u0628\u0630\u0644\u0643 \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\">\\begin{array}{rl}\n\n{} x= &amp; \\pm \\displaystyle \\int \\dfrac{y}{\\sqrt{2ay - y^2}}dy = \\displaystyle \\int \\dfrac{a[1-\\cos(\\theta)]a\\sin(\\theta)}{\\sqrt{2a^2[1-\\cos(\\theta)] - a^2[1-\\cos(\\theta)]^2 }}d\\theta \\\\ \\\\\n\n&amp; {} = \\pm \\displaystyle \\int \\dfrac{a^2[1-\\cos(\\theta)]\\sin(\\theta)}{\\sqrt{a^2[1-\\cos(\\theta)]\\left\\{ 2 - [1-\\cos(\\theta)] \\right\\} }}d\\theta \\\\ \\\\\n\n&amp; {} = \\pm \\displaystyle \\int \\dfrac{a[1-\\cos(\\theta)]\\sin(\\theta)}{\\sqrt{[1-\\cos(\\theta)]  [1 + \\cos(\\theta)]  }}d\\theta \\\\ \\\\\n\n&amp; {} = \\pm \\displaystyle \\int \\dfrac{a[1-\\cos(\\theta)]\\sin(\\theta)}{\\sqrt{ 1-\\cos^2(\\theta)}}d\\theta \\\\ \\\\\n\n&amp; {} = \\pm \\displaystyle \\int \\dfrac{a[1-\\cos(\\theta)]\\sin(\\theta)}{\\sin(\\theta)}d\\theta \\\\ \\\\\n\n&amp; {} = \\pm \\displaystyle \\int a[1-\\cos(\\theta)] d\\theta \\\\ \\\\\n\n&amp; {} = \\pm a(\\theta - \\sin(\\theta)) + C\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u064a\u0645\u0643\u0646\u0646\u0627 \u0645\u0644\u0627\u062d\u0638\u0629 \u0623\u0646 \u0645\u0646\u062d\u0646\u0649 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u0646 \u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646\u0647 \u0643\u0645\u0646\u062d\u0646\u0649 \u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a \u0641\u064a \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0642\u0637\u0628\u064a\u0629\u060c \u0627\u0644\u0630\u064a \u064a\u062a\u0648\u0627\u0641\u0642 \u0645\u0639 \u062d\u0644\u0642\u0629 \u062f\u0627\u0626\u0631\u064a\u0629 \u062a\u0628\u062f\u0623 \u0645\u0646 \u0627\u0644\u0623\u0635\u0644.<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\n\n{} &amp; x(\\theta) &amp;=&amp; \\pm a(\\theta - \\sin(\\theta)) \\\\\n\n   &amp; y(\\theta) &amp;=&amp; a(1-\\cos(\\theta))\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u062a\u0645 \u0625\u0644\u063a\u0627\u0621 \u062b\u0627\u0628\u062a \u0627\u0644\u062a\u0643\u0627\u0645\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> \u0644\u062a\u0644\u0628\u064a\u0629 \u0627\u0644\u0634\u0631\u0637 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a \u0628\u0623\u0646 \u0627\u0644\u0645\u0633\u0627\u0631 \u064a\u0628\u062f\u0623 \u0645\u0646 \u0627\u0644\u0623\u0635\u0644. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0645\u0644\u0627\u062d\u0638\u0629 \u0623\u0646 \u0647\u0646\u0627\u0643 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0642\u062f\u0645 \u062d\u0644\u0648\u0644\u064b\u0627 \u0645\u0645\u0643\u0646\u0629 \u0644\u0644\u0645\u0634\u0643\u0644\u0629\u060c \u062d\u064a\u062b \u064a\u0645\u0643\u0646 \u0636\u0628\u0637 \u0627\u0644\u062b\u0627\u0628\u062a <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0644\u062c\u0639\u0644 \u0627\u0644\u0645\u0646\u062d\u0646\u0649 \u064a\u0645\u0631 \u0628\u0627\u0644\u0646\u0642\u0637\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)<\/span><\/span> \u0641\u064a \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0645\u0633\u0627\u0631. \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u064a:<\/p>\n<p style=\"text-align:center;\"><strong>\u0627\u0644\u062e\u064a\u0627\u0631 1:<\/strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\begin{array}\n\n{} &amp; x(\\theta) &amp;=&amp; a(\\theta - \\sin(\\theta)) \\\\\n\n   &amp; y(\\theta) &amp;=&amp; a(1-\\cos(\\theta))\n\n\\end{array}}<\/span><\/span><\/p>\n<p style=\"text-align:center;\"><strong>\u0627\u0644\u062e\u064a\u0627\u0631 2:<\/strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\begin{array}\n\n{} &amp; x(\\theta) &amp;=&amp; - a(\\theta - \\sin(\\theta)) \\\\\n\n   &amp; y(\\theta) &amp;=&amp; a(1-\\cos(\\theta))\n\n\\end{array}}<\/span> <\/span><\/p>\n<p style=\"text-align:justify;\">\u0627\u0644\u062d\u0644 \u0627\u0644\u0635\u0627\u0644\u062d \u0644\u0647\u0630\u0647 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u064a\u0623\u062a\u064a \u0645\u0646 \u0627\u0644\u062e\u064a\u0627\u0631 \u0627\u0644\u062b\u0627\u0646\u064a\u060c \u0648\u0628\u0636\u0628\u0637 \u0627\u0644\u062b\u0627\u0628\u062a <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0643\u0642\u064a\u0645\u0629 \u0633\u0627\u0644\u0628\u0629\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0645\u0646\u062d\u0646\u0649 \u064a\u0644\u0628\u064a \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0644\u0627\u0632\u0645\u0629 \u0644\u064a\u0643\u0648\u0646 \u062d\u0644\u0627\u064b.<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/solbraquis.png\" alt=\"\u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u062d\u0644 \u0645\u0645\u0643\u0646\u060c \u0642\u0648\u0633 \u0645\u0646 \u062d\u0644\u0642\u0629 \u062f\u0627\u0626\u0631\u064a\u0629\" width=\"497\" height=\"329\" class=\"aligncenter size-full wp-image-28731 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/solbraquis.png\" alt=\"\u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u062d\u0644 \u0645\u0645\u0643\u0646\u060c \u0642\u0648\u0633 \u0645\u0646 \u062d\u0644\u0642\u0629 \u062f\u0627\u0626\u0631\u064a\u0629\" width=\"497\" height=\"329\" class=\"aligncenter size-full wp-image-28731 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/solbraquis.png 497w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/solbraquis-300x199.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/noscript><\/center><\/p>\n<h3>\u0627\u0644\u062a\u0639\u062f\u064a\u0644 \u0627\u0644\u0646\u0647\u0627\u0626\u064a \u0644\u0644\u062d\u0644<\/h3>\n<p style=\"text-align:justify;\">\u0628\u0639\u062f \u0627\u0644\u062a\u0639\u062f\u064a\u0644\u0627\u062a \u0627\u0644\u0623\u062e\u064a\u0631\u0629\u060c \u064a\u062d\u062a\u0648\u064a \u0645\u0646\u062d\u0646\u0649 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u0646 \u0639\u0644\u0649 \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\n\n{} x(\\theta) &amp;= b(\\theta - \\sin(\\theta)) \\\\\n\n   y(\\theta) &amp;= -b(1-\\cos(\\theta))\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u062a\u0645 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a=-b,<\/span><\/span> \u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\lt b.<\/span><\/span> \u064a\u062d\u062a\u0648\u064a \u0627\u0644\u0645\u0646\u062d\u0646\u0649 \u0639\u0644\u0649 \u0641\u062a\u0631\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2b\\pi<\/span><\/span> \u0648\u064a\u062c\u0628 \u0623\u0646 \u064a\u062d\u0642\u0642 \u0627\u0644\u0634\u0631\u0637 <span class=\"katex-eq\" data-katex-display=\"false\">x_2 \\in ]0,2b\\pi[<\/span> \u0648<span class=\"katex-eq\" data-katex-display=\"false\">y_2 \\in ]-2b,0[.<\/span> \u0647\u0630\u0627 \u0627\u0644\u0623\u0645\u0631 \u0645\u0647\u0645 \u0644\u0644\u063a\u0627\u064a\u0629\u060c \u0644\u0623\u0646\u0647 \u064a\u062a\u0637\u0644\u0628 \u0623\u0646 \u064a\u062a\u0645 \u062a\u0645\u062b\u064a\u0644 \u0645\u0646\u062d\u0646\u0649 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u0646 \u0643\u0642\u0648\u0633 \u0648\u0627\u062d\u062f \u0641\u0642\u0637 \u0645\u0646 \u062d\u0644\u0642\u0629 \u062f\u0627\u0626\u0631\u064a\u0629\u060c \u062d\u064a\u062b \u064a\u0635\u0628\u062d \u0627\u0644\u062d\u0644 \u063a\u064a\u0631 \u0635\u0627\u0644\u062d \u0625\u0630\u0627 \u0639\u0627\u062f \u0627\u0644\u062c\u0633\u0645 \u0625\u0644\u0649 \u0627\u0644\u0633\u0643\u0648\u0646 \u0639\u0646\u062f \u0627\u0644\u0639\u0648\u062f\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0627\u0631\u062a\u0641\u0627\u0639 \u0635\u0641\u0631.<\/p>\n<p style=\"text-align:justify;\">\u0644\u0636\u0628\u0637 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0639 \u0627\u0644\u0645\u0634\u0643\u0644\u0629\u060c \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0625\u064a\u062c\u0627\u062f \u0642\u064a\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span> \u0648<span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0627\u0644\u062a\u064a \u062a\u062d\u0642\u0642 \u0627\u0644\u0646\u0638\u0627\u0645:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\n\n{} x_2 &amp;= b(\\theta - \\sin(\\theta))\\\\\n\ny_2 &amp;= - b(1-\\cos(\\theta))\n\n\\end{array}<\/span>\n<p style=\"text-align:justify;\">\u064a\u0628\u062f\u0648 \u0623\u0646 \u0647\u0630\u0627 \u0627\u0644\u0646\u0638\u0627\u0645 \u063a\u064a\u0631 \u0627\u0644\u062e\u0637\u064a \u0644\u0627 \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u062d\u0644\u0648\u0644 \u062a\u062d\u0644\u064a\u0644\u064a\u0629\u060c \u0644\u0630\u0644\u0643 \u0633\u0646\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0641\u064a \u0648\u0644\u0641\u0631\u0627\u0645 \u0645\u0627\u062b\u064a\u0645\u0627\u062a\u064a\u0643\u0627. \u0641\u064a\u0645\u0627 \u064a\u0644\u064a \u0633\u0644\u0633\u0644\u0629 \u0645\u0646 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0644\u062d\u0644 \u0627\u0644\u0645\u0634\u0643\u0644\u0629:<\/p>\n<p><\/br><\/p>\n<h4>\u0627\u0644\u062e\u0637\u0648\u0629 1: \u0625\u0646\u0634\u0627\u0621 \u0627\u0644\u0646\u0638\u0627\u0645<\/h4>\n<p style=\"text-align:justify;\">\u0625\u0646\u0634\u0627\u0621 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0645\u0631\u0627\u062f \u062d\u0644\u0647<\/p>\n<p><span dir=\"ltr\"><code>eq1 = x2 == b*(theta - Sin[theta])<br \/>\n eq2 = y2 == -b*(1 - Cos[theta])<\/code><\/span><br \/>\n<\/br><\/p>\n<h4>\u0627\u0644\u062e\u0637\u0648\u0629 2: \u062a\u062d\u062f\u064a\u062f \u0646\u0642\u0637\u0629 \u0627\u0644\u0648\u0635\u0648\u0644<\/h4>\n<p style=\"text-align:justify;\">\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u064a \u0633\u064a\u0635\u0644 \u0625\u0644\u064a\u0647\u0627 \u0627\u0644\u062c\u0633\u0645 \u0641\u064a \u0646\u0647\u0627\u064a\u0629 \u0645\u0633\u0627\u0631\u0647. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u0633\u0646\u062d\u062f\u062f\u0647\u0627 \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)=(1,-2).<\/span><\/span> \u064a\u0645\u0643\u0646\u0643 \u062a\u0639\u062f\u064a\u0644 \u0647\u0630\u0647 \u0627\u0644\u0642\u064a\u0645 \u0644\u0627\u062e\u062a\u0628\u0627\u0631 \u062a\u0643\u0648\u064a\u0646\u0627\u062a \u0623\u062e\u0631\u0649 \u0645\u0645\u0627\u062b\u0644\u0629.<\/p>\n<p><span dir=\"ltr\"><code>x2val = 1; y2val = -2;<\/code><\/span><br \/>\n<\/br><\/p>\n<h4>\u0627\u0644\u062e\u0637\u0648\u0629 3: \u062d\u0633\u0627\u0628 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0645\u0637\u0644\u0648\u0628\u0629 \u0639\u062f\u062f\u064a\u0627\u064b<\/h4>\n<p style=\"text-align:justify;\">\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062f\u0627\u0644\u0629 \u00abFindRoot\u00bb \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u062d\u0644 \u0627\u0644\u0639\u062f\u062f\u064a \u0644\u0644\u0645\u0634\u0643\u0644\u0629<\/p>\n<p><span dir=\"ltr\"><code>sol = FindRoot[{eq1, eq2} \/. {x2 -> x2val, y2 -> y2val}, {{b,1}, {theta, 1}}]<\/code><\/span><\/p>\n<p style=\"text-align:justify;\">\u0647\u0646\u0627 \u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0642\u064a\u0645 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=1<\/span><\/span> \u0648<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta=1<\/span><\/span> \u0643\u0646\u0642\u0637\u0629 \u0628\u062f\u0627\u064a\u0629 \u0644\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0639\u062f\u062f\u064a \u0644\u0644\u062d\u0644. \u0628\u0647\u0630\u0627\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0627\u0644\u062d\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\approx 2.4056<\/span><\/span> \u0648<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta \\approx 1.40138<\/span><\/span><\/p>\n<p><\/br><\/p>\n<h4>\u0627\u0644\u062e\u0637\u0648\u0629 4: \u062a\u0623\u0643\u064a\u062f \u0627\u0644\u0646\u062a\u0627\u0626\u062c<\/h4>\n<p style=\"text-align:justify;\">\u0646\u062a\u0630\u0643\u0631 \u0623\u0646\u0647 \u0644\u0643\u064a \u062a\u0643\u0648\u0646 \u0647\u0630\u0647 \u0627\u0644\u0625\u062c\u0627\u0628\u0627\u062a \u0630\u0627\u062a \u0645\u0639\u0646\u0649 \u0641\u064a\u0632\u064a\u0627\u0626\u064a\u060c \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_2 \\in ]0,2b\\pi[<\/span><\/span> \u0648<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y_2 \\in ]-2b, 0[.<\/span><\/span> \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u062d\u062f\u0648\u062b \u0630\u0644\u0643 \u0628\u0633\u0631\u0639\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u062a\u0627\u0644\u064a<\/p>\n<p style=\"text-align:justify;\">\u0623\u0648\u0644\u0627\u064b \u0646\u0633\u062a\u062e\u0631\u062c \u0642\u064a\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0648<span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span> \u0627\u0644\u062a\u064a \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0643\u062d\u0644<\/p>\n<p><span dir=\"ltr\"><code>bval = sol[[1, 2]]; thetaval = sol[[2, 2]];<\/code><\/span><\/p>\n<p style=\"text-align:justify;\">\u062b\u0645 \u0646\u0637\u0644\u0628 \u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u062a\u0623\u0643\u064a\u062f<\/p>\n<p><span dir=\"ltr\"><code>If[0 < x2val < 2*Pi*bval &#038;&#038; -2*bval < y2val < 0 \"Valores v\u00e1lidos\", \"Valores inv\u00e1lidos\"]\n<\/code><\/span><\/p>\n<p style=\"text-align:justify;\">\u0625\u0630\u0627 \u062a\u0645 \u0643\u0644 \u0634\u064a\u0621 \u0628\u0634\u0643\u0644 \u0635\u062d\u064a\u062d\u060c \u064a\u062c\u0628 \u0623\u0646 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \"\u0642\u064a\u0645 \u0635\u0627\u0644\u062d\u0629\" \u0641\u064a \u0627\u0644\u0646\u062a\u064a\u062c\u0629. \u0647\u0630\u0627 \u0627\u0644\u062c\u0632\u0621 \u0645\u0646 \u0627\u0644\u0643\u0648\u062f \u0633\u064a\u0633\u0627\u0639\u062f\u0643 \u0641\u064a \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0648\u0636\u0639 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a \u0642\u062f \u062a\u0645 \u0646\u0645\u0630\u062c\u062a\u0647 \u0628\u0634\u0643\u0644 \u0635\u062d\u064a\u062d.<\/p>\n<p style=\"text-align:justify;\">\u0645\u0639 \u0647\u0630\u0647 \u0627\u0644\u0625\u062c\u0631\u0627\u0621\u0627\u062a\u060c \u0644\u062f\u064a\u0646\u0627 \u0641\u064a \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0645\u0646\u062d\u0646\u0649 \u0627\u0644\u062d\u0644 \u0645\u0636\u0628\u0648\u0637 \u062a\u0645\u0627\u0645\u064b\u0627\u060c \u0648\u0627\u0644\u0630\u064a \u064a\u0631\u0628\u0637 \u0628\u064a\u0646 \u0627\u0644\u0646\u0642\u0637\u062a\u064a\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_1,y_1)=(0,0)<\/span><\/span> \u0648<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)=(1,-2).<\/span><\/span> \u0627\u0644\u0645\u0646\u062d\u0646\u0649 \u0627\u0644\u0646\u0627\u062a\u062c \u0647\u0648:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\n\n{} x(\\theta) &amp;\\approx 2.4056(\\theta - \\sin(\\theta)) \\\\\n\ny(\\theta) &amp;\\approx -2.4056(1-\\cos(\\theta))\n\n\\end{array}\\;\\;;\\theta\\in [0, 1.40138]<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">\u0648\u0627\u0644\u0630\u064a \u064a\u0628\u062f\u0648 \u0647\u0643\u0630\u0627 \u0628\u064a\u0627\u0646\u064a\u064b\u0627:<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/sol2braquis.png\" alt=\"\" width=\"296\" height=\"345\" class=\"aligncenter size-full wp-image-28733 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/sol2braquis.png\" alt=\"\" width=\"296\" height=\"345\" class=\"aligncenter size-full wp-image-28733 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/sol2braquis.png 296w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/sol2braquis-257x300.png 257w\" sizes=\"(max-width: 296px) 100vw, 296px\" \/><\/noscript><\/center><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u0645\u0633\u062a\u0648\u062f\u0639 Github \u0645\u0639 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 Wolfram<\/h2>\n<p style=\"text-align:justify;\">\u0627\u0644\u0643\u0648\u062f \u0627\u0644\u0643\u0627\u0645\u0644 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u0646\u060c \u0628\u0645\u0627 \u0641\u064a \u0630\u0644\u0643 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0645\u0637\u0648\u0631\u0629 \u0641\u064a Wolfram Mathematica\u060c \u0645\u062a\u0627\u062d \u0644\u0644\u062a\u062d\u0645\u064a\u0644 \u0648\u0627\u0644\u0645\u0631\u0627\u062c\u0639\u0629 \u0641\u064a \u0645\u0633\u062a\u0648\u062f\u0639\u064a \u0639\u0644\u0649 GitHub. \u064a\u062a\u0636\u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u062f\u0639 \u0645\u0644\u0641 `.nb` \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0627\u0644\u0643\u0648\u062f \u0641\u064a \u0634\u0643\u0644 \u062f\u0641\u062a\u0631 \u062a\u0641\u0627\u0639\u0644\u064a\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0646\u0633\u062e\u0629 \u0646\u0635\u064a\u0629 \u0628\u0633\u064a\u0637\u0629 `.m` \u0644\u0623\u0648\u0644\u0626\u0643 \u0627\u0644\u0630\u064a\u0646 \u064a\u0641\u0636\u0644\u0648\u0646 \u0631\u0624\u064a\u0629 \u0627\u0644\u0643\u0648\u062f \u0645\u0628\u0627\u0634\u0631\u0629.<\/p>\n<p style=\"text-align:justify;\"><strong>\u064a\u0645\u0643\u0646\u0643 \u062a\u0646\u0632\u064a\u0644 \u0627\u0644\u0645\u0633\u062a\u0648\u062f\u0639 \u0645\u0646 GitHub <a href=\"https:\/\/github.com\/girebz\/Braquist-crona\" target=\"_blank\" rel=\"noopener\">\u0647\u0646\u0627<\/a>.<\/strong><\/p>\n<p style=\"text-align:justify;\">\u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0627\u0644\u0643\u0648\u062f\u060c \u064a\u062d\u062a\u0648\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u062f\u0639 \u0639\u0644\u0649 \u0645\u0644\u0641 \"README\" \u0645\u0639 \u062a\u0639\u0644\u064a\u0645\u0627\u062a \u0645\u0641\u0635\u0644\u0629 \u062d\u0648\u0644 \u0643\u064a\u0641\u064a\u0629 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0648\u0641\u0647\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0634\u0631\u062d \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u0646. \u0622\u0645\u0644 \u0623\u0646 \u062a\u062c\u062f\u0647 \u0645\u0641\u064a\u062f\u0627\u064b!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0641\u064a \u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0645\u0644\u062e\u0635:\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u0646\u0631\u0627\u062c\u0639 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0645\u0646 \u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0642\u0646\u064a\u0627\u062a \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a\u060c \u0648\u0645\u0646 \u062e\u0644\u0627\u0644 \u0630\u0644\u0643 \u0633\u0646\u0648\u0636\u062d \u0628\u062a\u0641\u0635\u064a\u0644 \u0643\u064a\u0641\u064a\u0629 \u062a\u0637\u0628\u064a\u0642\u0647\u0627 \u0641\u064a \u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646. \u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645: \u0639\u0646\u062f \u0627\u0644\u0627\u0646\u062a\u0647\u0627\u0621 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0627\u0644\u0628 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649: \u0641\u0647\u0645 \u0645\u0628\u062f\u0623 \u0647\u0627\u0645\u064a\u0644\u062a\u0648\u0646 \u0644\u0644\u0641\u0639\u0644 \u0627\u0644\u0623\u062f\u0646\u0649 \u0625\u062b\u0628\u0627\u062a \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28745,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":12,"footnotes":""},"categories":[641,942],"tags":[],"class_list":["post-28773","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-641","category-942"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u062a\u0639\u0644\u0645 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0648\u0645\u0628\u062f\u0623 \u0627\u0644\u0641\u0639\u0644 \u0627\u0644\u0623\u0642\u0644 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/toposuranos.com\/material\/ar\/\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646-\u0648\u0645\u0639\u0627\u062f\u0644\u0629-\u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a\" \/>\n<meta property=\"og:description\" content=\"\u062a\u0639\u0644\u0645 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0648\u0645\u0628\u062f\u0623 \u0627\u0644\u0641\u0639\u0644 \u0627\u0644\u0623\u0642\u0644 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/ar\/\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646-\u0648\u0645\u0639\u0627\u062f\u0644\u0629-\u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c\/\" \/>\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=\"2024-09-19T17:27:48+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-09-19T17:32:56+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/eulerlagrange-1024x547.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a\" \/>\n<meta name=\"twitter:description\" content=\"\u062a\u0639\u0644\u0645 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0648\u0645\u0628\u062f\u0623 \u0627\u0644\u0641\u0639\u0644 \u0627\u0644\u0623\u0642\u0644 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646.\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/eulerlagrange.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=\"10 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a\",\"datePublished\":\"2024-09-19T17:27:48+00:00\",\"dateModified\":\"2024-09-19T17:32:56+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\\\/\"},\"wordCount\":1430,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/09\\\/eulerlagrange.jpg\",\"articleSection\":[\"\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621\",\"\u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\\\/\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\\\/\",\"name\":\"\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a - toposuranos.com\\\/material\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/09\\\/eulerlagrange.jpg\",\"datePublished\":\"2024-09-19T17:27:48+00:00\",\"dateModified\":\"2024-09-19T17:32:56+00:00\",\"description\":\"\u062a\u0639\u0644\u0645 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0648\u0645\u0628\u062f\u0623 \u0627\u0644\u0641\u0639\u0644 \u0627\u0644\u0623\u0642\u0644 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\\\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\\\/#primaryimage\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/09\\\/eulerlagrange.jpg\",\"contentUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/09\\\/eulerlagrange.jpg\",\"width\":1792,\"height\":958},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/es\\\/cursos-de-matematica-y-fisica\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#website\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/\",\"name\":\"toposuranos.com\\\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\",\"name\":\"toposuranos.com\\\/material\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\\\/\\\/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\":\"https:\\\/\\\/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\":\"https:\\\/\\\/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\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/author\\\/giorgio-reveco\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a - toposuranos.com\/material","description":"\u062a\u0639\u0644\u0645 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0648\u0645\u0628\u062f\u0623 \u0627\u0644\u0641\u0639\u0644 \u0627\u0644\u0623\u0642\u0644 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646.","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":"https:\/\/toposuranos.com\/material\/ar\/\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646-\u0648\u0645\u0639\u0627\u062f\u0644\u0629-\u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c\/","og_locale":"es_ES","og_type":"article","og_title":"\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a","og_description":"\u062a\u0639\u0644\u0645 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0648\u0645\u0628\u062f\u0623 \u0627\u0644\u0641\u0639\u0644 \u0627\u0644\u0623\u0642\u0644 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646.","og_url":"https:\/\/toposuranos.com\/material\/ar\/\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646-\u0648\u0645\u0639\u0627\u062f\u0644\u0629-\u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2024-09-19T17:27:48+00:00","article_modified_time":"2024-09-19T17:32:56+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/eulerlagrange-1024x547.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a","twitter_description":"\u062a\u0639\u0644\u0645 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0648\u0645\u0628\u062f\u0623 \u0627\u0644\u0641\u0639\u0644 \u0627\u0644\u0623\u0642\u0644 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646.","twitter_image":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/eulerlagrange.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"10 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\/#article","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\/"},"author":{"name":"giorgio.reveco","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a","datePublished":"2024-09-19T17:27:48+00:00","dateModified":"2024-09-19T17:32:56+00:00","mainEntityOfPage":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\/"},"wordCount":1430,"commentCount":0,"publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/eulerlagrange.jpg","articleSection":["\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621","\u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/toposuranos.com\/material\/ar\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\/","url":"https:\/\/toposuranos.com\/material\/ar\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\/","name":"\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a - toposuranos.com\/material","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\/#primaryimage"},"image":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/eulerlagrange.jpg","datePublished":"2024-09-19T17:27:48+00:00","dateModified":"2024-09-19T17:32:56+00:00","description":"\u062a\u0639\u0644\u0645 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0648\u0645\u0628\u062f\u0623 \u0627\u0644\u0641\u0639\u0644 \u0627\u0644\u0623\u0642\u0644 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646.","breadcrumb":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["https:\/\/toposuranos.com\/material\/ar\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\/#primaryimage","url":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/eulerlagrange.jpg","contentUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/eulerlagrange.jpg","width":1792,"height":958},{"@type":"BreadcrumbList","@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a8%d8%b1%d8%a7%d9%83%d9%8a%d8%b3%d8%aa%d9%88%d9%83%d8%b1%d9%88%d9%8a%d9%86-%d9%88%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-%d9%84%d8%a7%d8%ba%d8%b1%d8%a7%d9%86%d8%ac\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"http:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u0628\u0631\u0627\u0643\u064a\u0633\u062a\u0648\u0643\u0631\u0648\u064a\u0646 \u0648\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0648\u064a\u0644\u0631-\u0644\u0627\u063a\u0631\u0627\u0646\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a"}]},{"@type":"WebSite","@id":"https:\/\/toposuranos.com\/material\/#website","url":"https:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"https:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"https:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/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":"https:\/\/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":"https:\/\/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":"https:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/28773","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=28773"}],"version-history":[{"count":0,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/28773\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/28745"}],"wp:attachment":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=28773"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=28773"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=28773"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}