{"id":28784,"date":"2024-09-19T17:27:47","date_gmt":"2024-09-19T17:27:47","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28784"},"modified":"2024-09-19T17:38:39","modified_gmt":"2024-09-19T17:38:39","slug":"%e0%a4%ac%e0%a5%8d%e0%a4%b0%e0%a5%88%e0%a4%95%e0%a4%bf%e0%a4%b8%e0%a5%8d%e0%a4%9f%e0%a5%8b%e0%a4%95%e0%a5%8d%e0%a4%b0%e0%a5%8b%e0%a4%a8-%e0%a4%94%e0%a4%b0-%e0%a4%af%e0%a5%82%e0%a4%87%e0%a4%b2%e0%a4%b0","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%ac%e0%a5%8d%e0%a4%b0%e0%a5%88%e0%a4%95%e0%a4%bf%e0%a4%b8%e0%a5%8d%e0%a4%9f%e0%a5%8b%e0%a4%95%e0%a5%8d%e0%a4%b0%e0%a5%8b%e0%a4%a8-%e0%a4%94%e0%a4%b0-%e0%a4%af%e0%a5%82%e0%a4%87%e0%a4%b2%e0%a4%b0\/","title":{"rendered":"\u092c\u094d\u0930\u0948\u0915\u093f\u0938\u094d\u091f\u094b\u0915\u094d\u0930\u094b\u0928 \u0914\u0930 \u092f\u0942\u0907\u0932\u0930-\u0932\u0948\u0917\u094d\u0930\u0947\u0902\u091c \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e 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\u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0938\u0928\u094d\u0928\u093f\u0915\u091f\u0928 \u0938\u092e\u093e\u0927\u093e\u0928 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u0910\u0938\u0940 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u091c\u0939\u093e\u0902 \u092c\u0932\u094b\u0902 \u0915\u094b \u092d\u093f\u0928\u094d\u0928\u093e\u0924\u094d\u092e\u0915 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0928\u093e \u0915\u0920\u093f\u0928 \u0939\u094b\u0924\u093e \u0939\u0948, \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0915\u094d\u0930\u093f\u092f\u093e \u0915\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u092e\u0948\u0915\u0947\u0928\u093f\u0915\u094d\u0938 \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0905\u0927\u093f\u0915 \u0915\u0941\u0936\u0932 \u0924\u0930\u0940\u0915\u093e \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0938\u0902\u0915\u094d\u0937\u0947\u092a \u092e\u0947\u0902, \u0935\u0947\u0930\u093f\u090f\u0936\u0928\u0932 \u0915\u0948\u0932\u0915\u0941\u0932\u0938 \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0909\u092a\u0915\u0930\u0923 \u0939\u0948 \u091c\u094b \u0928\u094d\u092f\u0942\u091f\u0928 \u0915\u0947 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u093e \u0935\u0948\u0915\u0932\u094d\u092a\u093f\u0915 \u0938\u0942\u0924\u094d\u0930\u0940\u0915\u0930\u0923, \u092d\u094c\u0924\u093f\u0915\u0940 \u0915\u0947 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u093e \u090f\u0915\u0940\u0915\u0930\u0923, \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u093e\u0927\u093e\u0928 \u092e\u0947\u0902 \u0905\u0927\u093f\u0915 \u0926\u0915\u094d\u0937\u0924\u093e \u0914\u0930 \u092a\u094d\u0930\u092f\u094b\u0917\u093e\u0924\u094d\u092e\u0915 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u0940 \u092d\u0935\u093f\u0937\u094d\u092f\u0935\u093e\u0923\u0940 \u092e\u0947\u0902 \u0905\u0927\u093f\u0915 \u0938\u091f\u0940\u0915\u0924\u093e \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0935\u0947\u0930\u093f\u090f\u0936\u0928\u0932 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0940 \u0938\u0902\u0930\u091a\u0928\u093e<\/h2>\n<p style=\"text-align:justify;\">\u0935\u0947\u0930\u093f\u090f\u0936\u0928\u0932 \u0915\u0948\u0932\u0915\u0941\u0932\u0938 \u0915\u093e \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f \u0909\u0938 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span> \u0915\u094b \u0916\u094b\u091c\u0928\u093e \u0939\u0948 \u091c\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092b\u093c\u0902\u0915\u094d\u0936\u0928\u0932 \u0915\u0947 \u092e\u093e\u0928 \u0915\u094b \u0905\u0927\u093f\u0915\u0924\u092e \u092f\u093e \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0915\u0930\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><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>\n<p style=\"text-align:justify;\">\u0907\u0938\u0915\u093e \u0905\u0927\u093f\u0915\u0924\u092e \u092f\u093e \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092e\u093e\u0928 \u0916\u094b\u091c\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f\u0964 \u0907\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902, \u092b\u093c\u0902\u0915\u094d\u0936\u0928\u0932 <span class=\"katex-eq\" data-katex-display=\"false\">J<\/span> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span> \u0914\u0930 \u0907\u0938\u0915\u0940 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">dy(x)\/dx,<\/span> \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u093e \u0939\u0948 \u091c\u092c\u0915\u093f \u090f\u0915\u0940\u0915\u0930\u0923 \u0915\u0940 \u0938\u0940\u092e\u093e\u090f\u0902 \u0938\u094d\u0925\u093f\u0930 \u0930\u0939\u0924\u0940 \u0939\u0948\u0902\u0964 \u0938\u0902\u092a\u0942\u0930\u094d\u0923\u0924\u093e \u0915\u094b \u0905\u0927\u093f\u0915\u0924\u092e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u092b\u093c\u0902\u0915\u094d\u0936\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span> \u092a\u0930 \u0935\u093f\u0935\u093f\u0927\u0924\u093e\u090f\u0902 \u0932\u093e\u0917\u0942 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0902, \u091c\u093f\u0938\u0938\u0947 \u0935\u0939 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u094b \u092b\u093c\u0902\u0915\u094d\u0936\u0928\u0932 \u0915\u0947 \u092e\u093e\u0928 \u0915\u094b \u090f\u0915 \u091a\u0930\u092e \u092a\u0930 \u0932\u093e\u0924\u093e \u0939\u0948\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u092f\u0926\u093f \u0938\u0902\u092a\u0942\u0930\u094d\u0923\u0924\u093e \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092e\u093e\u0928 \u0924\u0915 \u092a\u0939\u0941\u0901\u091a\u0924\u0940 \u0939\u0948, \u0924\u094b \u0915\u094b\u0908 \u092d\u0940 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 <em>\u0907\u0938\u0915\u0947 \u092a\u0921\u093c\u094b\u0938 \u092e\u0947\u0902<\/em>, \u091a\u093e\u0939\u0947 \u0935\u0939 <span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span> \u0915\u0947 \u0915\u093f\u0924\u0928\u0947 \u0939\u0940 \u0915\u0930\u0940\u092c \u0939\u094b, \u092b\u093c\u0902\u0915\u094d\u0936\u0928\u0932 \u0915\u0947 \u092e\u093e\u0928 \u0915\u094b \u092c\u0922\u093c\u093e\u090f\u0917\u093e\u0964<\/p>\n<p style=\"text-align:justify;\">\u00ab\u092a\u0921\u093c\u094b\u0938\u0940 \u092b\u093c\u0902\u0915\u094d\u0936\u0928\u00bb \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0938\u092d\u0940 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u092b\u093c\u0902\u0915\u094d\u0936\u0928\u094b\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u0915\u094b \u090f\u0915 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u094d\u0930\u093f\u0915 \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 <span class=\"katex-eq\" data-katex-display=\"false\">y=(\\alpha,x)<\/span> \u0938\u094c\u0902\u092a \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u0924\u093e\u0915\u093f \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha=0<\/span>, \u0924\u094b <span class=\"katex-eq\" data-katex-display=\"false\">y(0,x)=y(x)<\/span> \u0935\u0939 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0939\u0948 \u091c\u094b <span class=\"katex-eq\" data-katex-display=\"false\">J<\/span> \u0915\u094b \u091a\u0930\u092e \u092c\u0928\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">y(\\alpha, x) = y(x) + \\alpha \\eta(x),<\/span>\n<p style=\"text-align:justify;\">\u091c\u0939\u093e\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">\\eta(x)<\/span> \u090f\u0915 \u092a\u094d\u0930\u0915\u093e\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{C}^1<\/span> \u0915\u093e \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0939\u0948 \u091c\u094b <span class=\"katex-eq\" data-katex-display=\"false\">x_1<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">x_2<\/span> \u092a\u0930 \u0936\u0942\u0928\u094d\u092f \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948, \u0924\u093e\u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">y(\\alpha,x)<\/span> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u091c\u094b \u0907\u0938 \u0935\u093f\u0935\u093f\u0927\u0924\u093e \u0915\u094b \u0936\u093e\u092e\u093f\u0932 \u0915\u0930\u0924\u093e \u0939\u0948 \u0935\u0939 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0914\u0930 \u0905\u0902\u0924\u093f\u092e \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u092a\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span> \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u094b\u0964<\/p>\n<p style=\"text-align:justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">J<\/span> \u092b\u093c\u0902\u0915\u094d\u0936\u0928\u0932 \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0947 \u0938\u0902\u092a\u0942\u0930\u094d\u0923\u0924\u093e \u092e\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span> \u0915\u0947 \u092c\u091c\u093e\u092f <span class=\"katex-eq\" data-katex-display=\"false\">y(\\alpha,x)<\/span> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u094b \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0915\u0947 \u091c\u094b \u0935\u093f\u0935\u093f\u0927\u0924\u093e <span class=\"katex-eq\" data-katex-display=\"false\">\\eta(x)<\/span> \u0915\u094b \u0936\u093e\u092e\u093f\u0932 \u0915\u0930\u0924\u093e \u0939\u0948, \u090f\u0915 \u0928\u092f\u093e \u092b\u093c\u0902\u0915\u094d\u0936\u0928\u0932 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u094b \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span> \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><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>\n<p style=\"text-align:justify;\">\u0938\u094d\u0925\u093e\u0928\u0940\u092f \u091a\u0930\u092e \u0915\u094b \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0932\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u092f\u0939 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948 \u0915\u093f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0936\u0930\u094d\u0924 \u092a\u0942\u0930\u0940 \u0939\u094b:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left.\\dfrac{\\partial J(x,y(\\alpha,x))}{\\partial \\alpha}\\right|_{\\alpha=0} = 0<\/span>\n<p style=\"text-align:justify;\">\u0915\u093f\u0938\u0940 \u092d\u0940 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">\\eta(x)<\/span> \u0915\u0947 \u0932\u093f\u090f\u0964<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u092f\u0942\u0907\u0932\u0930-\u0932\u0948\u0917\u094d\u0930\u0947\u0902\u091c \u0938\u092e\u0940\u0915\u0930\u0923<\/h2>\n<p style=\"text-align:justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\partial J(x,y(\\alpha,x))\/\\partial \\alpha<\/span> \u0915\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0924\u0947 \u0938\u092e\u092f, \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><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>\n<p style=\"text-align:justify;\">\u0907\u0938 \u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u092f\u0939 \u0928\u094b\u091f \u0915\u0930\u0928\u093e \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948 \u0915\u093f:<\/p>\n<p style=\"text-align:center;\"><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>\n<p style=\"text-align:justify;\">\u0907\u0938\u0932\u093f\u090f, \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u093e\u0928\u0941\u0938\u093e\u0930 \u0938\u0930\u0932 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><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>\n<p style=\"text-align:justify;\">\u092b\u093f\u0930 \u0905\u0917\u0930 \u0939\u092e \u0926\u0942\u0938\u0930\u0940 \u0938\u0902\u092a\u0942\u0930\u094d\u0923\u0924\u093e \u0915\u093e \u0905\u0935\u0932\u094b\u0915\u0928 \u0915\u0930\u0947\u0902, \u0924\u094b \u0939\u092e \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f \u0907\u0938\u0947 \u0906\u0902\u0936\u093f\u0915 \u090f\u0915\u0940\u0915\u0930\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0938\u0930\u0932 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><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>\n<p style=\"text-align:justify;\">\u0914\u0930 \u0907\u0938\u0932\u093f\u090f<\/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;\">\u0907\u0938\u0932\u093f\u090f <span class=\"katex-eq\" data-katex-display=\"false\">\\left.\\dfrac{\\partial J (x,y(\\alpha, x))}{\\partial \\alpha}\\right|_{\\alpha=0} = 0,<\/span> \u0914\u0930 \u0915\u094d\u092f\u094b\u0902\u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">\\eta(x)<\/span> \u090f\u0915 \u0910\u0938\u093e \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0939\u0948 \u091c\u094b <span class=\"katex-eq\" data-katex-display=\"false\">x_1<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">x_2<\/span> \u092a\u0930 \u0936\u0942\u0928\u094d\u092f \u0939\u094b\u0928\u0947 \u0915\u0940 \u0936\u0930\u094d\u0924 \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0924\u093e \u0939\u0948, \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/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;\">\u0905\u0902\u0924 \u092e\u0947\u0902, \u00ab\u0938\u0902\u0915\u0947\u0924 \u0915\u094b \u0939\u091f\u093e\u0928\u0947\u00bb \u0915\u0947 \u092c\u093e\u0926 \u0939\u092e\u0947\u0902 \u091c\u094b \u092e\u093f\u0932\u0924\u093e \u0939\u0948 \u0935\u0939 \u092f\u0942\u0907\u0932\u0930-\u0932\u0948\u0917\u094d\u0930\u0947\u0902\u091c \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u091c\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><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>\n<p style=\"text-align:justify;\">\u0914\u0930 \u092f\u0939 <span class=\"katex-eq\" data-katex-display=\"false\">J<\/span> \u092b\u093c\u0902\u0915\u094d\u0936\u0928\u0932 \u0915\u0947 \u090f\u0915 \u091a\u0930\u092e \u092e\u093e\u0928 \u0924\u0915 \u092a\u0939\u0941\u0901\u091a\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0906\u0935\u0936\u094d\u092f\u0915 \u0936\u0930\u094d\u0924 \u0915\u093e \u090f\u0915 \u0938\u0930\u0932 \u0930\u0942\u092a \u0938\u0947 \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u092c\u094d\u0930\u0948\u0915\u093f\u0938\u094d\u091f\u094b\u0915\u094d\u0930\u094b\u0928 \u0938\u092e\u0938\u094d\u092f\u093e<\/h2>\n<h3>\u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0940 \u0938\u0902\u0930\u091a\u0928\u093e<\/h3>\n<p style=\"text-align:justify;\">\u092c\u094d\u0930\u0948\u0915\u093f\u0938\u094d\u091f\u094b\u0915\u094d\u0930\u094b\u0928 \u0938\u092e\u0938\u094d\u092f\u093e \u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915 \u092d\u094c\u0924\u093f\u0915\u0940 \u0915\u093e \u090f\u0915 \u0915\u094d\u0932\u093e\u0938\u093f\u0915 \u0909\u0926\u093e\u0939\u0930\u0923 \u0939\u0948 \u091c\u093f\u0938\u0947 \u0935\u0948\u0930\u093f\u090f\u0936\u0928\u0932 \u0915\u0948\u0932\u0915\u0941\u0932\u0938 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0939\u0932 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0938\u094d\u0925\u093f\u0924\u093f \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948: \u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u090f\u0915 \u092d\u094c\u0924\u093f\u0915 \u0935\u0938\u094d\u0924\u0941 \u0939\u0948 \u091c\u094b \u090f\u0915 \u0938\u094d\u0925\u093f\u0930 \u092c\u0932 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u0915\u0947 \u092a\u094d\u0930\u092d\u093e\u0935 \u092e\u0947\u0902 \u091a\u0932\u0924\u0940 \u0939\u0948 \u0914\u0930 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u092c\u093f\u0902\u0926\u0941 <span class=\"katex-eq\" data-katex-display=\"false\">(x_1,y_1)<\/span> \u0938\u0947 \u0905\u0902\u0924\u093f\u092e \u092c\u093f\u0902\u0926\u0941 <span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)<\/span> \u0924\u0915 \u091c\u093e\u0924\u0940 \u0939\u0948, \u091c\u0939\u093e\u0901 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u092c\u093f\u0902\u0926\u0941 \u0905\u0902\u0924\u093f\u092e \u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0905\u0927\u093f\u0915 \u090a\u0902\u091a\u093e\u0908 \u092a\u0930 \u0939\u0948\u0964 \u0938\u0935\u093e\u0932 \u092f\u0939 \u0939\u0948: \u0915\u094c\u0928 \u0938\u0940 \u092e\u093e\u0930\u094d\u0917 \u0915\u093e \u0905\u0928\u0941\u0938\u0930\u0923 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0915\u0923 \u0915\u094b \u0938\u092c\u0938\u0947 \u0915\u092e \u0938\u092e\u092f \u092e\u0947\u0902 \u0905\u0902\u0924\u093f\u092e \u092c\u093f\u0902\u0926\u0941 \u0924\u0915 \u092a\u0939\u0941\u0902\u091a\u0928\u093e \u091a\u093e\u0939\u093f\u090f?<\/p>\n<h3>\u0938\u092e\u093e\u0927\u093e\u0928 \u0915\u0940 \u0938\u0902\u0930\u091a\u0928\u093e<\/h3>\n<p style=\"text-align:justify;\">\u092c\u094d\u0930\u0948\u0915\u093f\u0938\u094d\u091f\u094b\u0915\u094d\u0930\u094b\u0928 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u094b \u0938\u0930\u0932 \u0930\u0942\u092a \u092e\u0947\u0902 \u0926\u0947\u0916\u0928\u093e \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f, \u0939\u092e \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u092c\u093f\u0902\u0926\u0941 <span class=\"katex-eq\" data-katex-display=\"false\">(x_1, y_1)<\/span> \u0915\u094b \u0938\u092e\u0928\u094d\u0935\u092f \u0915\u0947 \u092e\u0942\u0932 \u092e\u0947\u0902 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u091c\u092c\u0915\u093f \u0905\u0902\u0924\u093f\u092e \u092c\u093f\u0902\u0926\u0941 <span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)<\/span> \u092e\u0942\u0932 \u0915\u0947 \u0926\u093e\u0908\u0902 \u0913\u0930 \u0914\u0930 \u0905\u0915\u094d\u0937 <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> \u0915\u0947 \u0928\u0940\u091a\u0947 \u0938\u094d\u0925\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/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=\"\u0935\u0948\u0930\u093f\u090f\u0936\u0928\u0932 \u0915\u0948\u0932\u0915\u0941\u0932\u0938 - \u092c\u094d\u0930\u0948\u0915\u093f\u0938\u094d\u091f\u094b\u0915\u094d\u0930\u094b\u0928 \u0938\u092e\u0938\u094d\u092f\u093e\" 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=\"\u0935\u0948\u0930\u093f\u090f\u0936\u0928\u0932 \u0915\u0948\u0932\u0915\u0941\u0932\u0938 - \u092c\u094d\u0930\u0948\u0915\u093f\u0938\u094d\u091f\u094b\u0915\u094d\u0930\u094b\u0928 \u0938\u092e\u0938\u094d\u092f\u093e\" 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;\">\u0907\u0938 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902, \u090f\u0915 \u092c\u0932 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u091c\u094b \u0928\u0940\u091a\u0947 \u0915\u0940 \u0913\u0930 (\u0926\u093f\u0936\u093e <span class=\"katex-eq\" data-katex-display=\"false\">-\\hat{y}<\/span>) \u0917\u0941\u0930\u0941\u0924\u094d\u0935\u093e\u0915\u0930\u094d\u0937\u0923 \u0926\u094d\u0935\u093e\u0930\u093e \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0939\u094b\u0924\u093e \u0939\u0948, \u0914\u0930 \u092e\u093e\u0928 \u0932\u0947\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0917\u0924\u093f \u092c\u093f\u0928\u093e \u0918\u0930\u094d\u0937\u0923 \u0915\u0947 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902, \u0915\u0923 \u0915\u094b \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u092e\u093e\u0930\u094d\u0917\u094b\u0902 \u0915\u093e \u0905\u0928\u0941\u0938\u0930\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u0924\u093f\u092c\u0902\u0927\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u094b \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0914\u0930 \u0905\u0902\u0924\u093f\u092e \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902 \u0924\u093e\u0915\u093f \u092f\u0939 \u092a\u0924\u093e \u0932\u0917\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0947 \u0915\u093f \u0915\u094c\u0928 \u0938\u093e \u092e\u093e\u0930\u094d\u0917 \u092f\u093e\u0924\u094d\u0930\u093e \u0915\u0947 \u0938\u092e\u092f \u0915\u094b \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n<h3>\u090a\u0930\u094d\u091c\u093e \u0915\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/h3>\n<p style=\"text-align:justify;\">\u0907\u0938 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0917\u0941\u0930\u0941\u0924\u094d\u0935\u093e\u0915\u0930\u094d\u0937\u0923 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0940 \u090a\u0930\u094d\u091c\u093e \u0938\u0902\u0930\u0915\u094d\u0937\u0923 \u0915\u093e \u0932\u093e\u092d \u0909\u0920\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0940 \u0915\u0941\u0932 \u090a\u0930\u094d\u091c\u093e \u0938\u094d\u0925\u093f\u0930 \u092c\u0928\u0940 \u0930\u0939\u0947\u0917\u0940, \u091c\u093f\u0938\u092e\u0947\u0902 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e <span class=\"katex-eq\" data-katex-display=\"false\">E_{cin}=\\frac{1}{2}mv^2<\/span> \u0914\u0930 \u0917\u0941\u0930\u0941\u0924\u094d\u0935\u093e\u0915\u0930\u094d\u0937\u0923 \u0938\u094d\u0925\u093f\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e <span class=\"katex-eq\" data-katex-display=\"false\">E_{pot,g}<\/span> \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0924\u0940 \u0939\u0948, \u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0915\u0923 \u0915\u093e \u0926\u094d\u0930\u0935\u094d\u092f\u092e\u093e\u0928 \u0939\u0948 \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">v<\/span> \u0909\u0938\u0915\u0940 \u0935\u0947\u0917\u0964 \u0938\u094d\u0925\u093f\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0915\u0947 \u0932\u093f\u090f \u092e\u0942\u0932 \u0915\u094b \u0938\u0902\u0926\u0930\u094d\u092d \u0932\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">E_{pot,g}(y=0)=0<\/span>, \u091c\u092c\u0915\u093f \u0915\u093f\u0938\u0940 \u0905\u0928\u094d\u092f \u090a\u0902\u091a\u093e\u0908 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u092a\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">E_{pot,g}(y)=mgy.<\/span>\n<p style=\"text-align:justify;\">\u091a\u0942\u0902\u0915\u093f \u0915\u0923 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0936\u0942\u0928\u094d\u092f \u0935\u0947\u0917 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0939\u094b\u0924\u093e \u0939\u0948, \u0909\u0938\u0915\u0940 \u0915\u0941\u0932 \u090a\u0930\u094d\u091c\u093e \u0936\u0942\u0928\u094d\u092f \u0939\u0948\u0964 \u0924\u094b, \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">E_{cin} + E_{pot,g}=0<\/span>\n<p style=\"text-align:justify;\">\u091a\u0942\u0902\u0915\u093f \u0915\u0923 \u0938\u0902\u0926\u0930\u094d\u092d \u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0928\u0940\u091a\u0947 \u0917\u093f\u0930\u0924\u093e \u0939\u0948, \u0909\u0938\u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0928\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u094b\u0917\u0940 \u0914\u0930 \u0909\u0938\u0915\u0940 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0938\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u094b\u0917\u0940\u0964 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u0939\u092e \u090a\u0930\u094d\u091c\u093e \u0938\u0902\u0930\u0915\u094d\u0937\u0923 \u0938\u092e\u0940\u0915\u0930\u0923 \u0938\u0947 \u0935\u0947\u0917 <span class=\"katex-eq\" data-katex-display=\"false\">v<\/span> \u0928\u093f\u0915\u093e\u0932 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center\"><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>\n<p style=\"text-align:justify;\">\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u0939\u092e \u0915\u0923 \u0915\u0940 \u0935\u0947\u0917 \u0915\u094b \u0909\u0938\u0915\u0940 \u092a\u0925 \u0915\u0947 \u0915\u093f\u0938\u0940 \u092d\u0940 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930 \u090a\u0902\u091a\u093e\u0908 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0928\u093f\u0915\u093e\u0932 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 <\/p>\n<h3>\u092a\u0925 \u0915\u093e \u0938\u092e\u092f \u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/h3>\n<p style=\"text-align:justify;\">\u090f\u0915 \u092c\u093e\u0930 \u091c\u092c \u0939\u092e\u0947\u0902 \u0917\u0924\u093f \u0915\u0940 \u0924\u0947\u091c\u0940 \u092e\u093f\u0932 \u0917\u0908 \u0939\u0948, \u0939\u092e \u092a\u0925 \u0915\u0947 \u0924\u0924\u094d\u0935 \u0915\u093e \u0938\u092e\u092f \u0928\u093f\u0915\u093e\u0932 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0907\u0938\u0947 \u0935\u093f\u0938\u094d\u0925\u093e\u092a\u0928 \u0924\u0924\u094d\u0935 <span class=\"katex-eq\" data-katex-display=\"false\">ds=\\sqrt{dx^2 + dy^2}<\/span> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/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;\">\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u092c\u093f\u0902\u0926\u0941\u0913\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">(x_1,y_1)<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)<\/span> \u0915\u0947 \u092c\u0940\u091a \u0935\u093f\u0938\u094d\u0925\u093e\u092a\u0928 \u0915\u093e \u0938\u092e\u092f \u0928\u093f\u0915\u093e\u0932\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e \u0907\u0938\u0947 \u0907\u0902\u091f\u0940\u0917\u094d\u0930\u0947\u091f \u0915\u0930\u0915\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/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>\u0935\u0948\u0930\u093f\u090f\u0936\u0928\u0932 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0940 \u0938\u0902\u0930\u091a\u0928\u093e<\/h3>\n<p style=\"text-align:justify;\">\u0907\u0938 \u0905\u0902\u0924\u093f\u092e \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0915\u0947 \u0938\u093e\u0925, \u0939\u092e \u0938\u092e\u092f \u0915\u094b \u090f\u0915 \u092b\u093c\u0902\u0915\u094d\u0936\u0928\u0932 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0938\u092b\u0932 \u0930\u0939\u0947 \u0939\u0948\u0902:<\/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;\">\u091c\u0939\u093e\u0901<\/p>\n<p style=\"text-align:center;\"><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>\n<p style=\"text-align:justify;\">\u0907\u0938 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930 \u0939\u092e \u0915\u093e\u0930\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{2g},<\/span> \u0915\u094b \u091b\u094b\u0921\u093c \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u094d\u092f\u094b\u0902\u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">J<\/span> \u0915\u094b \u0911\u092a\u094d\u091f\u093f\u092e\u093e\u0907\u091c \u0915\u0930\u0928\u093e <span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{2g}J<\/span> \u0915\u094b \u0911\u092a\u094d\u091f\u093f\u092e\u093e\u0907\u091c \u0915\u0930\u0928\u0947 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0940 \u0939\u0948\u0964<\/p>\n<p style=\"text-align:justify;\">\u0909\u092a\u0930\u094b\u0915\u094d\u0924 \u0915\u0947 \u0938\u093e\u0925, \u0905\u092c \u0939\u092e \u092a\u0939\u0932\u0947 \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u090f \u0917\u090f \u0938\u092e\u093e\u0928 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u093e \u0905\u0928\u0941\u0938\u0930\u0923 \u0915\u0930\u0915\u0947 \u092f\u0942\u0907\u0932\u0930-\u0932\u0948\u0917\u094d\u0930\u0947\u0902\u091c \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0905\u0902\u0924 \u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{\\partial f}{\\partial x} = \\dfrac{d}{dy} \\dfrac{\\partial f}{\\partial x^\\prime}<\/span>\n<p style=\"text-align:justify;\">\u0939\u093e\u0932\u093e\u0902\u0915\u093f, \u092f\u0939\u093e\u0901 \u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{\\partial f}{\\partial x} = 0,<\/span> \u0907\u0938\u0932\u093f\u090f \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0917\u093e<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dy}\\dfrac{\\partial f}{\\partial x^\\prime} = 0,<\/span>\n<p style=\"text-align:justify;\">\u092f\u093e \u0905\u0928\u094d\u092f \u0936\u092c\u094d\u0926\u094b\u0902 \u092e\u0947\u0902<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{\\partial f}{\\partial x^\\prime} = \\dfrac{1}{\\sqrt{2a}},<\/span>\n<p style=\"text-align:justify;\">\u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u090f\u0915 \u092e\u0928\u092e\u093e\u0928\u093e \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 \u0939\u0948 \u091c\u093f\u0938\u0947 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0932\u093f\u0916\u093e \u0917\u092f\u093e \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092f\u0939 \u092d\u0935\u093f\u0937\u094d\u092f \u0915\u0947 \u0935\u093f\u0915\u093e\u0938 \u0915\u0947 \u0932\u093f\u090f \u00ab\u0938\u0941\u0935\u093f\u0927\u093e\u091c\u0928\u0915\u00bb \u0939\u0948\u0964<\/p>\n<h3>\u0935\u0948\u0930\u093f\u090f\u0936\u0928\u0932 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u093e \u0938\u092e\u093e\u0927\u093e\u0928<\/h3>\n<p style=\"text-align:justify;\">\u0905\u0902\u0924\u093f\u092e \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u092e\u0947\u0902 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0915\u094b \u092c\u0926\u0932\u0928\u0947 \u092a\u0930 \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0924\u093e \u0939\u0948:<\/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;\">\u0907\u0938 \u0907\u0902\u091f\u0940\u0917\u094d\u0930\u0932 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u090f\u0915 \u0935\u093f\u0915\u0932\u094d\u092a \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u0928 \u0915\u0930\u0928\u093e \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948:<\/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;\">\u0907\u0938\u0915\u0947 \u0938\u093e\u0925 \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0924\u093e \u0939\u0948:<\/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;\">\u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092c\u094d\u0930\u0948\u0915\u093f\u0938\u094d\u091f\u094b\u0915\u094d\u0930\u094b\u0928 \u0935\u0915\u094d\u0930 \u0915\u094b \u0927\u094d\u0930\u0941\u0935\u0940\u092f \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u092e\u0947\u0902 \u090f\u0915 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u094d\u0930\u093f\u0915 \u0935\u0915\u094d\u0930 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u091c\u094b \u090f\u0915 \u0938\u093e\u0907\u0915\u094d\u0932\u0949\u0907\u0921 \u0915\u0947 \u0938\u093e\u0925 \u092e\u0947\u0932 \u0916\u093e\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u092c\u093f\u0902\u0926\u0941 \u092e\u0942\u0932 \u092e\u0947\u0902 \u0939\u0948\u0964<\/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;\">\u090f\u0915\u0940\u0915\u0930\u0923 \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> \u0915\u094b \u0936\u0942\u0928\u094d\u092f \u0915\u0930 \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0924\u093e\u0915\u093f \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930 \u092a\u0925 \u0936\u0941\u0930\u0942 \u0939\u094b \u0938\u0915\u0947\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0947 \u0938\u092e\u093e\u0927\u093e\u0928 \u0915\u0947 \u0932\u093f\u090f \u0926\u094b \u0938\u092e\u0940\u0915\u0930\u0923 \u0939\u0948\u0902, \u091c\u0939\u093e\u0901 \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0915\u094b \u0907\u0938 \u0924\u0930\u0939 \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0924\u093e\u0915\u093f \u0935\u0915\u094d\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)<\/span> \u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0939\u094b\u0915\u0930 \u0917\u0941\u091c\u0930\u0947\u0964 \u092f\u0947 \u0938\u092e\u0940\u0915\u0930\u0923 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><strong>\u0935\u093f\u0915\u0932\u094d\u092a 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>\u0935\u093f\u0915\u0932\u094d\u092a 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;\">\u0907\u0938 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u0938\u092e\u093e\u0927\u093e\u0928 \u0926\u0942\u0938\u0930\u0940 \u0935\u093f\u0915\u0932\u094d\u092a \u0926\u094d\u0935\u093e\u0930\u093e \u0926\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948, \u0914\u0930 \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0915\u094b \u090f\u0915 \u0928\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u092e\u093e\u0928 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u0930\u0915\u0947, \u0939\u092e \u090f\u0915 \u0935\u0915\u094d\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b \u0938\u092e\u093e\u0927\u093e\u0928 \u0915\u0947 \u0932\u093f\u090f \u0906\u0935\u0936\u094d\u092f\u0915 \u0936\u0930\u094d\u0924\u094b\u0902 \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0924\u0940 \u0939\u0948\u0964<\/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=\"\u0938\u0902\u092d\u0935 \u0938\u092e\u093e\u0927\u093e\u0928 \u0915\u093e \u0909\u0926\u093e\u0939\u0930\u0923, \u090f\u0915 \u0938\u093e\u0907\u0915\u094d\u0932\u0949\u0907\u0921 \u0915\u093e \u090f\u0915 \u091a\u093e\u092a\" 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=\"\u0938\u0902\u092d\u0935 \u0938\u092e\u093e\u0927\u093e\u0928 \u0915\u093e \u0909\u0926\u093e\u0939\u0930\u0923, \u090f\u0915 \u0938\u093e\u0907\u0915\u094d\u0932\u0949\u0907\u0921 \u0915\u093e \u090f\u0915 \u091a\u093e\u092a\" 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>\u0938\u092e\u093e\u0927\u093e\u0928 \u0915\u093e \u0905\u0902\u0924\u093f\u092e \u0938\u092e\u093e\u092f\u094b\u091c\u0928<\/h3>\n<p style=\"text-align:justify;\">\u0905\u0902\u0924\u093f\u092e \u0938\u092e\u093e\u092f\u094b\u091c\u0928\u094b\u0902 \u0915\u0947 \u092c\u093e\u0926, \u092c\u094d\u0930\u0948\u0915\u093f\u0938\u094d\u091f\u094b\u0915\u094d\u0930\u094b\u0928 \u0935\u0915\u094d\u0930 \u0915\u0940 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u094d\u0930\u093f\u0915 \u0930\u0942\u092a\u0930\u0947\u0916\u093e \u0939\u094b\u0924\u0940 \u0939\u0948:<\/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;\">\u092f\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">a=-b,<\/span> \u0915\u094b \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">0\\lt b.<\/span> \u0935\u0915\u094d\u0930 \u0915\u0940 \u0905\u0935\u0927\u093f <span class=\"katex-eq\" data-katex-display=\"false\">2b\\pi<\/span> \u0939\u094b\u0924\u0940 \u0939\u0948 \u0914\u0930 \u0907\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">x_2 \\in ]0,2b\\pi[<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">y_2 \\in ]-2b,0[.<\/span> \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964 \u092f\u0939 \u0905\u0902\u0924\u093f\u092e \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092f\u0939 \u092c\u094d\u0930\u0948\u0915\u093f\u0938\u094d\u091f\u094b\u0915\u094d\u0930\u094b\u0928 \u0935\u0915\u094d\u0930 \u0915\u094b \u090f\u0915 \u0939\u0940 \u091a\u093e\u092a \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u092e\u093e\u0902\u0917 \u0915\u0930\u0924\u0940 \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0938\u092e\u093e\u0927\u093e\u0928 \u092e\u093e\u0928\u094d\u092f \u0928\u0939\u0940\u0902 \u0930\u0939\u0947\u0917\u093e \u092f\u0926\u093f \u0915\u0923 \u0936\u0942\u0928\u094d\u092f \u090a\u0902\u091a\u093e\u0908 \u092a\u0930 \u0932\u094c\u091f\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align:justify;\">\u0907\u0928 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u094b \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0947 \u0932\u093f\u090f \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0915\u0947 \u0935\u0947 \u092e\u093e\u0928 \u0916\u094b\u091c\u0928\u0947 \u0939\u094b\u0902\u0917\u0947 \u091c\u094b \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u094b \u0938\u0902\u0924\u0941\u0937\u094d\u091f \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:<\/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;\">\u092f\u0939 \u0917\u0948\u0930-\u0930\u0947\u0916\u0940\u092f \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u092e\u093e\u0927\u093e\u0928 \u0928\u0939\u0940\u0902 \u0930\u0916\u0924\u0940, \u0907\u0938\u0932\u093f\u090f \u0939\u092e Wolfram Mathematica \u092e\u0947\u0902 \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0935\u093f\u0927\u093f\u092f\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u092f\u0939\u093e\u0902 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u091a\u0930\u0923 \u0926\u093f\u090f \u0917\u090f \u0939\u0948\u0902:<\/p>\n<p><\/br><\/p>\n<h4>\u091a\u0930\u0923 1: \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0947\u0902<\/h4>\n<p style=\"text-align:justify;\">\u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u094b \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0947\u0902<\/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>\u091a\u0930\u0923 2: \u0905\u0902\u0924\u093f\u092e \u092c\u093f\u0902\u0926\u0941 \u0928\u093f\u0930\u094d\u0926\u093f\u0937\u094d\u091f \u0915\u0930\u0947\u0902<\/h4>\n<p style=\"text-align:justify;\">\u0909\u0938 \u092c\u093f\u0902\u0926\u0941 \u0915\u094b \u0928\u093f\u0930\u094d\u0926\u093f\u0937\u094d\u091f \u0915\u0930\u0947\u0902 \u091c\u0939\u093e\u0901 \u0915\u0923 \u0905\u092a\u0928\u0940 \u092f\u093e\u0924\u094d\u0930\u093e \u0915\u0947 \u0905\u0902\u0924 \u092e\u0947\u0902 \u092a\u0939\u0941\u0902\u091a\u0947\u0917\u093e\u0964 \u0907\u0938 \u092e\u093e\u092e\u0932\u0947 \u092e\u0947\u0902 \u0939\u092e \u0907\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)=(1,-2).<\/span> \u092a\u0930 \u0928\u093f\u0930\u094d\u0926\u093f\u0937\u094d\u091f \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0906\u092a \u0907\u0928 \u092e\u093e\u0928\u094b\u0902 \u0915\u094b \u0905\u0928\u094d\u092f \u0938\u092e\u093e\u0928 \u0938\u0902\u0930\u091a\u0928\u093e\u0913\u0902 \u0915\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092c\u0926\u0932 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p><code>x2val = 1; y2val = -2;<\/code><br \/>\n<\/br><\/p>\n<h4>\u091a\u0930\u0923 3: \u0906\u0935\u0936\u094d\u092f\u0915 \u092e\u093e\u0928\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902<\/h4>\n<p style=\"text-align:justify;\">\u00abFindRoot\u00bb \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u093e \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0938\u092e\u093e\u0927\u093e\u0928 \u0915\u0930\u0947\u0902<\/p>\n<p><code>sol = FindRoot[{eq1, eq2} \/. {x2 -> x2val, y2 -> y2val}, {{b,1}, {theta, 1}}]<\/code><\/p>\n<p style=\"text-align:justify;\">\u092f\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">b=1<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta=1<\/span> \u092e\u093e\u0928\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0924\u093e\u0915\u093f \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0938\u092e\u093e\u0927\u093e\u0928 \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u092c\u093f\u0902\u0926\u0941 \u0926\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0947\u0964 \u0907\u0938\u0915\u0947 \u0938\u093e\u0925, \u0939\u092e\u0947\u0902 \u0938\u092e\u093e\u0927\u093e\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">b\\approx 2.4056<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta \\approx 1.40138<\/span> \u092e\u093f\u0932\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><\/br><\/p>\n<h4>\u091a\u0930\u0923 4: \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u0940 \u092a\u0941\u0937\u094d\u091f\u093f<\/h4>\n<p style=\"text-align:justify;\">\u092f\u093e\u0926 \u0930\u0916\u0947\u0902 \u0915\u093f \u092d\u094c\u0924\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u0907\u0928 \u0909\u0924\u094d\u0924\u0930\u094b\u0902 \u0915\u093e \u0905\u0930\u094d\u0925\u092a\u0942\u0930\u094d\u0923 \u0939\u094b\u0928\u093e \u091c\u0930\u0942\u0930\u0940 \u0939\u0948, \u091c\u093f\u0938\u0915\u0947 \u0932\u093f\u090f \u092f\u0939 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948 \u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">x_2 \\in ]0,2b\\pi[<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">y_2 \\in ]-2b, 0[.<\/span> \u0939\u092e \u0907\u0938\u0947 \u0924\u0947\u091c\u0940 \u0938\u0947 \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0928\u093f\u092e\u094d\u0928 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947:<\/p>\n<p style=\"text-align:justify;\">\u092a\u0939\u0932\u0947 \u0938\u092e\u093e\u0927\u093e\u0928 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span> \u0915\u0947 \u092e\u093e\u0928\u094b\u0902 \u0915\u094b \u0928\u093f\u0915\u093e\u0932\u0947\u0902<\/p>\n<p><code>bval = sol[[1, 2]]; thetaval = sol[[2, 2]];<\/code><\/p>\n<p style=\"text-align:justify;\">\u092b\u093f\u0930 \u092a\u0941\u0937\u094d\u091f\u093f \u0915\u0930\u0947\u0902<\/p>\n<p><code>If[0 < x2val < 2*Pi*bval &#038;&#038; -2*bval < y2val < 0 \"\u092e\u093e\u0928\u094d\u092f \u092e\u093e\u0928\", \"\u0905\u092e\u093e\u0928\u094d\u092f \u092e\u093e\u0928\"]\n<\/code><\/p>\n<p style=\"text-align:justify;\">\u0905\u0917\u0930 \u0938\u092c \u0915\u0941\u091b \u0920\u0940\u0915 \u0939\u094b \u0917\u092f\u093e \u0939\u0948, \u0924\u094b \u0939\u092e\u0947\u0902 \"\u092e\u093e\u0928\u094d\u092f \u092e\u093e\u0928\" \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0906\u0909\u091f\u092a\u0941\u091f \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964 \u092f\u0939 \u0915\u094b\u0921 \u0915\u093e \u091f\u0941\u0915\u0921\u093c\u093e \u0906\u092a\u0915\u0940 \u092e\u0926\u0926 \u0915\u0930\u0947\u0917\u093e \u092f\u0939 \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0915\u093f \u092d\u094c\u0924\u093f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u0939\u0940 \u0922\u0902\u0917 \u0938\u0947 \u092e\u0949\u0921\u0932 \u0915\u0940 \u0917\u0908 \u0939\u0948\u0964<\/p>\n<p style=\"text-align:justify;\">\u0907\u0928 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0915\u0947 \u0938\u093e\u0925, \u0939\u092e \u0906\u0916\u093f\u0930\u0915\u093e\u0930 \u0905\u092a\u0928\u0940 \u0938\u092e\u093e\u0927\u093e\u0928 \u0935\u0915\u094d\u0930 \u0915\u094b \u092a\u0942\u0930\u0940 \u0924\u0930\u0939 \u0938\u0947 \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u0930 \u091a\u0941\u0915\u0947 \u0939\u0948\u0902, \u091c\u094b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">(x_1,y_1)=(0,0)<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)=(1,-2).<\/span> \u0915\u094b \u091c\u094b\u0921\u093c\u0924\u0940 \u0939\u0948\u0964 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0935\u0915\u094d\u0930 \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><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>\n<p style=\"text-align:justify;\">\u0917\u094d\u0930\u093e\u092b\u093f\u0915\u0932 \u0930\u0942\u092a \u092e\u0947\u0902 \u092f\u0939 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0926\u093f\u0916\u0924\u0940 \u0939\u0948:<\/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>\u0935\u094b\u0932\u094d\u092b\u094d\u0930\u093e\u092e \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u0915\u0947 \u0938\u093e\u0925 \u0917\u093f\u091f\u0939\u092c \u0930\u093f\u092a\u0949\u091c\u093f\u091f\u0930\u0940<\/h2>\n<p style=\"text-align:justify;\">\u092c\u094d\u0930\u0948\u0915\u093f\u0938\u094d\u091f\u094b\u0915\u094d\u0930\u094b\u0928 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0947 \u0938\u092e\u093e\u0927\u093e\u0928 \u0915\u093e \u092a\u0942\u0930\u093e \u0915\u094b\u0921, \u091c\u093f\u0938\u092e\u0947\u0902 \u0935\u094b\u0932\u094d\u092b\u094d\u0930\u093e\u092e \u092e\u0948\u0925\u0947\u092e\u0948\u091f\u093f\u0915\u093e \u092e\u0947\u0902 \u0935\u093f\u0915\u0938\u093f\u0924 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u0936\u093e\u092e\u093f\u0932 \u0939\u0948, \u092e\u0947\u0930\u0947 \u0917\u093f\u091f\u0939\u092c \u0930\u093f\u092a\u0949\u091c\u093f\u091f\u0930\u0940 \u092e\u0947\u0902 \u0921\u093e\u0909\u0928\u0932\u094b\u0921 \u0914\u0930 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u0948\u0964 \u0907\u0938 \u0930\u093f\u092a\u0949\u091c\u093f\u091f\u0930\u0940 \u092e\u0947\u0902 \u0907\u0902\u091f\u0930\u0948\u0915\u094d\u091f\u093f\u0935 \u0928\u094b\u091f\u092c\u0941\u0915 \u092b\u0949\u0930\u094d\u092e\u0947\u091f \u092e\u0947\u0902 \u0915\u094b\u0921 \u0915\u0947 \u0938\u093e\u0925 `.nb` \u092b\u093c\u093e\u0907\u0932 \u0914\u0930 \u0938\u0940\u0927\u0947 \u0915\u094b\u0921 \u0926\u0947\u0916\u0928\u0947 \u0915\u0947 \u0907\u091a\u094d\u091b\u0941\u0915 \u0932\u094b\u0917\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0938\u093e\u0926\u093e \u092a\u093e\u0920 \u0938\u0902\u0938\u094d\u0915\u0930\u0923 `.m` \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0964<\/p>\n<p style=\"text-align:justify;\"><strong>\u0906\u092a \u0917\u093f\u091f\u0939\u092c \u0938\u0947 \u0930\u093f\u092a\u0949\u091c\u093f\u091f\u0930\u0940 \u0921\u093e\u0909\u0928\u0932\u094b\u0921 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 <a href=\"https:\/\/github.com\/girebz\/Braquist-crona\" target=\"_blank\" rel=\"noopener\">\u092f\u0939\u093e\u0902<\/a>.<\/strong><\/p>\n<p style=\"text-align:justify;\">\u0915\u094b\u0921 \u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u0930\u093f\u092a\u0949\u091c\u093f\u091f\u0930\u0940 \u092e\u0947\u0902 \"README\" \u092b\u093c\u093e\u0907\u0932 \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0914\u0930 \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0928\u093f\u0930\u094d\u0926\u0947\u0936 \u0939\u0948\u0902, \u0938\u093e\u0925 \u0939\u0940 \u092c\u094d\u0930\u0948\u0915\u093f\u0938\u094d\u091f\u094b\u0915\u094d\u0930\u094b\u0928 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0947 \u0938\u092e\u093e\u0927\u093e\u0928 \u0915\u0940 \u091a\u0930\u0923-\u0926\u0930-\u091a\u0930\u0923 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u092d\u0940 \u0939\u0948\u0964 \u092e\u0941\u091d\u0947 \u0909\u092e\u094d\u092e\u0940\u0926 \u0939\u0948 \u0915\u093f \u092f\u0939 \u0906\u092a\u0915\u094b \u0909\u092a\u092f\u094b\u0917\u0940 \u0932\u0917\u0947\u0917\u093e!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u092e\u0948\u0915\u0947\u0928\u093f\u0915\u094d\u0938 \u092e\u0947\u0902 \u0935\u0947\u0930\u093f\u090f\u0936\u0928\u0932 \u0915\u0948\u0932\u0915\u0941\u0932\u0938 \u0914\u0930 \u0911\u0907\u0932\u0930-\u0932\u093e\u0917\u094d\u0930\u093e\u0902\u091c \u0938\u092e\u0940\u0915\u0930\u0923 \u0938\u093e\u0930\u093e\u0902\u0936:\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u0935\u0947\u0930\u093f\u090f\u0936\u0928\u0932 \u0915\u0948\u0932\u0915\u0941\u0932\u0938 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923\u093e\u0924\u094d\u092e\u0915 \u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915\u0940 \u0938\u0947 \u0911\u0907\u0932\u0930-\u0932\u093e\u0917\u094d\u0930\u093e\u0902\u091c \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947, \u0914\u0930 \u0907\u0938\u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0907\u0938\u0915\u093e \u092c\u094d\u0930\u0948\u0915\u093f\u0938\u094d\u091f\u094b\u0915\u094d\u0930\u0949\u0928 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0947 \u0938\u092e\u093e\u0927\u093e\u0928 \u092e\u0947\u0902 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917 \u0926\u093f\u0916\u093e\u092f\u093e \u091c\u093e\u090f\u0917\u093e\u0964 \u0905\u0927\u093f\u0917\u092e \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f\u094b\u0902: \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u092c\u093e\u0926, \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0902\u0917\u0947: \u0938\u092e\u091d\u0928\u093e 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