{"id":477980,"date":"2026-04-29T14:31:00","date_gmt":"2026-04-29T14:31:00","guid":{"rendered":"https:\/\/savepearlharbor.com\/?p=477980"},"modified":"-0001-11-30T00:00:00","modified_gmt":"-0001-11-29T21:00:00","slug":"","status":"publish","type":"post","link":"https:\/\/savepearlharbor.com\/?p=477980","title":{"rendered":"\u041e \u0431\u0430\u043b\u043b\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043a\u0440\u0438\u0432\u043e\u0439"},"content":{"rendered":"<div xmlns=\"http:\/\/www.w3.org\/1999\/xhtml\">\n<p>\u0411\u0430\u043b\u043b\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043a\u0440\u0438\u0432\u0430\u044f \u2014 \u044d\u0442\u043e \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044f \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438, \u0434\u0432\u0438\u0436\u0443\u0449\u0435\u0439\u0441\u044f \u0432 \u0441\u043e\u043f\u0440\u043e\u0442\u0438\u0432\u043b\u044f\u044e\u0449\u0435\u0439\u0441\u044f \u0441\u0440\u0435\u0434\u0435 \u043f\u043e\u0434 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0435\u043c \u0441\u0438\u043b\u044b \u0442\u044f\u0436\u0435\u0441\u0442\u0438.<\/p>\n<p>\u041e\u0441\u043d\u043e\u0432\u043d\u043e\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u0431\u0430\u043b\u043b\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043a\u0440\u0438\u0432\u043e\u0439 \u2014 \u044d\u0442\u043e \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044f \u0434\u0440\u043e\u0431\u0438\u043d\u044b \u0432 \u0430\u0442\u043c\u043e\u0441\u0444\u0435\u0440\u0435.<\/p>\n<p>\u0421\u0438\u043b\u0430 \u0441\u043e\u043f\u0440\u043e\u0442\u0438\u0432\u043b\u0435\u043d\u0438\u044f \u0432\u043e\u0437\u0434\u0443\u0445\u0430 \u0441\u0447\u0438\u0442\u0430\u0435\u0442\u0441\u044f \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u043d\u043e\u0439 \u043f\u0440\u043e\u0442\u0438\u0432 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\mathbf{F} = -f(\\mathbf{v}) \\mathbf{v}.\" alt=\"\\mathbf{F} = -f(\\mathbf{v}) \\mathbf{v}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ef\/4efe2ffb0bede92b581060b9e85d3eb5.svg\" width=\"96\" height=\"16\" data-width=\"12.795\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ef\/4efe2ffb0bede92b581060b9e85d3eb5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ef\/4efe2ffb0bede92b581060b9e85d3eb5.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0427\u0430\u0449\u0435 \u0432\u0441\u0435\u0433\u043e \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u0433\u0438\u043f\u043e\u0442\u0435\u0437\u044b \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\u0433\u043e \u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0433\u043e \u0441\u043e\u043f\u0440\u043e\u0442\u0438\u0432\u043b\u0435\u043d\u0438\u044f. \u0412 \u044d\u0442\u0438\u0445 \u0441\u043b\u0443\u0447\u0430\u044f\u0445 <img decoding=\"async\" class=\"formula inline\" source=\"f = c_1|\\mathbf{v}|\" alt=\"f = c_1|\\mathbf{v}|\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/67\/673\/673c1622e74229d9c96b041cf6f2e5b7.svg\" width=\"64\" height=\"16\" data-width=\"8.86\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/67\/673\/673c1622e74229d9c96b041cf6f2e5b7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/67\/673\/673c1622e74229d9c96b041cf6f2e5b7.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"f = c_2\" alt=\"f = c_2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7c\/7c5\/7c516cda035873f0e07f7bc191ab1422.svg\" width=\"48\" height=\"16\" data-width=\"6.229\" data-height=\"2.059\" data-vertical-align=\"-0.464\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7c\/7c5\/7c516cda035873f0e07f7bc191ab1422.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7c\/7c5\/7c516cda035873f0e07f7bc191ab1422.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e. \u0417\u0434\u0435\u0441\u044c <img decoding=\"async\" class=\"formula inline\" source=\"c_1, c_2\" alt=\"c_1, c_2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6d\/6d6\/6d6df5df11fe5ab56cea337f31147fd1.svg\" width=\"32\" height=\"12\" data-width=\"4.941\" data-height=\"1.439\" data-vertical-align=\"-0.439\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6d\/6d6\/6d6df5df11fe5ab56cea337f31147fd1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6d\/6d6\/6d6df5df11fe5ab56cea337f31147fd1.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u044b\u0435. \u0412 \u043e\u0431\u043e\u0438\u0445 \u0441\u043b\u0443\u0447\u0430\u044f\u0445 \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0443\u0435\u0442\u0441\u044f \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0443\u0440\u0430\u0445. \u0421\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u0441\u043b\u0443\u0447\u0430\u0438 \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0443\u0435\u043c\u043e\u0441\u0442\u0438 (\u0441\u043c. \u0410\u043f\u043f\u0435\u043b\u044c \u041f. \u0422\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043c\u0435\u0445\u0430\u043d\u0438\u043a\u0430. \u0422. 1. \u041c.: \u0424\u0438\u0437\u043c\u0430\u0442\u043b\u0438\u0442, 1960).<\/p>\n<p>\u0425\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u043d\u043e\u0439 \u0447\u0435\u0440\u0442\u043e\u0439 \u0434\u0430\u043d\u043d\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0430\u043b\u0438\u0447\u0438\u0435 \u0443 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043e\u0432\u0430\u043d\u0438\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044c\u043d\u043e\u0439 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438, \u043a \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0447\u0430\u0441\u0442\u0438\u0446\u044b.<\/p>\n<p>\u041e\u0431\u0430 \u044d\u0442\u0438\u0445 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0432\u044b\u0432\u043e\u0434\u044f\u0442\u0441\u044f \u0432 \u0443\u0447\u0435\u0431\u043d\u0438\u043a\u0430\u0445 \u043f\u0443\u0442\u0451\u043c \u044f\u0432\u043d\u043e\u0433\u043e \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f.<\/p>\n<p>\u041c\u044b \u043e\u043f\u0438\u0448\u0435\u043c \u0434\u043e\u0432\u043e\u043b\u044c\u043d\u043e \u0448\u0438\u0440\u043e\u043a\u0438\u0439 \u043a\u043b\u0430\u0441\u0441 \u0441\u0438\u043b \u0441\u043e\u043f\u0440\u043e\u0442\u0438\u0432\u043b\u0435\u043d\u0438\u044f, \u0434\u043b\u044f \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044f \u043e\u0431\u043b\u0430\u0434\u0430\u0435\u0442 \u0443\u043a\u0430\u0437\u0430\u043d\u043d\u044b\u043c\u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c\u0438. \u0412 \u044d\u0442\u043e\u043c \u043a\u043b\u0430\u0441\u0441\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u0443\u0436\u0435 \u043d\u0435 \u043e\u0431\u044f\u0437\u0430\u043d\u044b \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0443\u0440\u0430\u0445, \u0438 \u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0430 \u0438\u0441\u0441\u043b\u0435\u0434\u0443\u0435\u0442\u0441\u044f \u043c\u0435\u0442\u043e\u0434\u0430\u043c\u0438 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0438\u0437\u0430.<\/p>\n<p>\u0418\u0442\u0430\u043a, \u0432\u0442\u043e\u0440\u043e\u0439 \u0437\u0430\u043a\u043e\u043d \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0434\u043b\u044f \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u043c\u0430\u0441\u0441\u044b <img decoding=\"async\" class=\"formula inline\" source=\"m\" alt=\"m\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6f8\/6f8f57715090da2632453988d9a1501b.svg\" width=\"12\" height=\"12\" data-width=\"1.986\" data-height=\"1.025\" data-vertical-align=\"-0.025\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6f8\/6f8f57715090da2632453988d9a1501b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6f8\/6f8f57715090da2632453988d9a1501b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"m\\mathbf{\\dot v}=m\\mathbf g-\\mathbf vf(\\mathbf{v}).\" alt=\"m\\mathbf{\\dot v}=m\\mathbf g-\\mathbf vf(\\mathbf{v}).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/db\/db7\/db7a3308907acb4dadabb95d247f8dc6.svg\" width=\"144\" height=\"16\" data-width=\"18.81\" data-height=\"2.419\" data-vertical-align=\"-0.644\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/db\/db7\/db7a3308907acb4dadabb95d247f8dc6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/db\/db7\/db7a3308907acb4dadabb95d247f8dc6.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0412\u0432\u0435\u0434\u0451\u043c \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u0443 \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"Oxy\" alt=\"Oxy\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bdf\/bdf2393e6495b69e296e3d574f0204cb.svg\" width=\"32\" height=\"16\" data-width=\"4.129\" data-height=\"2.057\" data-vertical-align=\"-0.464\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bdf\/bdf2393e6495b69e296e3d574f0204cb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bdf\/bdf2393e6495b69e296e3d574f0204cb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u043e\u0441\u044c <img decoding=\"async\" class=\"formula inline\" source=\"Oy\" alt=\"Oy\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b6\/8b644cd5134d4a2c95f112c84649b4dd.svg\" width=\"16\" height=\"16\" data-width=\"2.835\" data-height=\"2.057\" data-vertical-align=\"-0.464\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b6\/8b644cd5134d4a2c95f112c84649b4dd.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b6\/8b644cd5134d4a2c95f112c84649b4dd.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0431\u044b\u043b\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0430 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e \u0432\u0432\u0435\u0440\u0445. \u0422\u043e\u0433\u0434\u0430 \u0432\u0442\u043e\u0440\u043e\u0439 \u0437\u0430\u043a\u043e\u043d \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0435\u0442 \u0432\u0438\u0434:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"m\\dot v_x = -v_x f(v_x, v_y), \\qquad(1)\" alt=\"m\\dot v_x = -v_x f(v_x, v_y), \\qquad(1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8de\/8de5fb5b563961ae09037aa11032af26.svg\" width=\"216\" height=\"16\" data-width=\"27.866\" data-height=\"2.405\" data-vertical-align=\"-0.637\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8de\/8de5fb5b563961ae09037aa11032af26.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8de\/8de5fb5b563961ae09037aa11032af26.svg 781w\" loading=\"lazy\" decode=\"async\"\/><img decoding=\"async\" class=\"formula\" source=\"m\\dot v_y = -mg - v_y f(v_x, v_y), \\quad \\mathbf v=(v_x,v_y). \\qquad(2)\" alt=\"m\\dot v_y = -mg - v_y f(v_x, v_y), \\quad \\mathbf v=(v_x,v_y). \\qquad(2)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ed\/edd\/edd13d7654ad970915ef2d790f7286d2.svg\" width=\"384\" height=\"16\" data-width=\"48.129\" data-height=\"2.405\" data-vertical-align=\"-0.637\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ed\/edd\/edd13d7654ad970915ef2d790f7286d2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ed\/edd\/edd13d7654ad970915ef2d790f7286d2.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0411\u0443\u0434\u0435\u043c \u0441\u0447\u0438\u0442\u0430\u0442\u044c, \u0447\u0442\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u044b \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u044f:<\/p>\n<p>1) <img decoding=\"async\" class=\"formula inline\" source=\"f \\in C(\\mathbb{R}^2) \\cap C^1(\\mathbb{R}^2 \\setminus \\{0\\})\" alt=\"f \\in C(\\mathbb{R}^2) \\cap C^1(\\mathbb{R}^2 \\setminus \\{0\\})\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/866\/86601eb102b3370e5384960426319a0e.svg\" width=\"200\" height=\"16\" data-width=\"25.363\" data-height=\"2.565\" data-vertical-align=\"-0.717\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/866\/86601eb102b3370e5384960426319a0e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/866\/86601eb102b3370e5384960426319a0e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>;<\/p>\n<p>2)  \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e <img decoding=\"async\" class=\"formula inline\" source=\"f(u, v) = 0\" alt=\"f(u, v) = 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c92\/c9274a9676d07c4309cf2ff4d0d18d52.svg\" width=\"80\" height=\"16\" data-width=\"10.55\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c92\/c9274a9676d07c4309cf2ff4d0d18d52.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c92\/c9274a9676d07c4309cf2ff4d0d18d52.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432\u043b\u0435\u0447\u0435\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"u=v = 0\" alt=\"u=v = 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e3\/3e30f5dee558e9c2822bbb350fc7f089.svg\" width=\"72\" height=\"12\" data-width=\"9.557\" data-height=\"1.692\" data-vertical-align=\"-0.186\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e3\/3e30f5dee558e9c2822bbb350fc7f089.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e3\/3e30f5dee558e9c2822bbb350fc7f089.svg 781w\" loading=\"lazy\" decode=\"async\"\/>;<\/p>\n<p>3)  <img decoding=\"async\" class=\"formula inline\" source=\"f \\ge 0\" alt=\"f \\ge 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0f\/0f5\/0f57acdd48e0530d2e2fda2d824788bc.svg\" width=\"40\" height=\"16\" data-width=\"5.393\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0f\/0f5\/0f57acdd48e0530d2e2fda2d824788bc.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0f\/0f5\/0f57acdd48e0530d2e2fda2d824788bc.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 <img decoding=\"async\" class=\"formula inline\" source=\"\\mathbb{R}^2\" alt=\"\\mathbb{R}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/44\/440\/4401afd1bb84dbcc0183f8b2f52dce48.svg\" width=\"16\" height=\"16\" data-width=\"2.621\" data-height=\"2.565\" data-vertical-align=\"-0.717\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/44\/440\/4401afd1bb84dbcc0183f8b2f52dce48.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/44\/440\/4401afd1bb84dbcc0183f8b2f52dce48.svg 781w\" loading=\"lazy\" decode=\"async\"\/>;<\/p>\n<p>4)  \u043d\u0430\u0439\u0434\u0443\u0442\u0441\u044f \u0442\u0430\u043a\u0438\u0435 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"r\" alt=\"r\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4b\/4b4\/4b43b0aee35624cd95b910189b3dc231.svg\" width=\"12\" height=\"12\" data-width=\"1.02\" data-height=\"1.025\" data-vertical-align=\"-0.025\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4b\/4b4\/4b43b0aee35624cd95b910189b3dc231.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4b\/4b4\/4b43b0aee35624cd95b910189b3dc231.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"k\" alt=\"k\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8c\/8ce\/8ce4b16b22b58894aa86c421e8759df3.svg\" width=\"12\" height=\"12\" data-width=\"1.179\" data-height=\"1.595\" data-vertical-align=\"-0.025\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8c\/8ce\/8ce4b16b22b58894aa86c421e8759df3.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8c\/8ce\/8ce4b16b22b58894aa86c421e8759df3.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0447\u0442\u043e \u0435\u0441\u043b\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"|\\mathbf{v}| &gt; r\" alt=\"|\\mathbf{v}| &gt; r\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e48\/e48a13946fc3d062a41b2473394e1bb7.svg\" width=\"48\" height=\"16\" data-width=\"6.669\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e48\/e48a13946fc3d062a41b2473394e1bb7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e48\/e48a13946fc3d062a41b2473394e1bb7.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"f(\\mathbf{v}) &gt; k\" alt=\"f(\\mathbf{v}) &gt; k\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e13\/e13353e777af17425a8de141583c04f5.svg\" width=\"64\" height=\"16\" data-width=\"8.574\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e13\/e13353e777af17425a8de141583c04f5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e13\/e13353e777af17425a8de141583c04f5.svg 781w\" loading=\"lazy\" decode=\"async\"\/>;<\/p>\n<p>5)  \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"mg + w f(0, w) = 0\" alt=\"mg + w f(0, w) = 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8a\/8a1\/8a15d41df33c889351a3088be4ad5e44.svg\" width=\"144\" height=\"16\" data-width=\"18.361\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8a\/8a1\/8a15d41df33c889351a3088be4ad5e44.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8a\/8a1\/8a15d41df33c889351a3088be4ad5e44.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043c\u0435\u0435\u0442 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"w = v_y^*\" alt=\"w = v_y^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/21\/218\/2187556bcecd43a99caee70bbc79e7c6.svg\" width=\"48\" height=\"16\" data-width=\"6.722\" data-height=\"2.565\" data-vertical-align=\"-0.887\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/21\/218\/2187556bcecd43a99caee70bbc79e7c6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/21\/218\/2187556bcecd43a99caee70bbc79e7c6.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043f\u0440\u0438\u0447\u0435\u043c<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d(w f(0, w))}{dw} \\bigg|_{w=v_y^*} \\ne 0.\" alt=\"\\frac{d(w f(0, w))}{dw} \\bigg|_{w=v_y^*} \\ne 0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/31\/315\/315295db71c43dbda97497126c992812.svg\" width=\"168\" height=\"40\" data-width=\"21.897\" data-height=\"5.76\" data-vertical-align=\"-2.314\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/31\/315\/315295db71c43dbda97497126c992812.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/31\/315\/315295db71c43dbda97497126c992812.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418\u0437 \u0434\u0430\u043d\u043d\u044b\u0445 \u0443\u0441\u043b\u043e\u0432\u0438\u0439 \u0432\u044b\u0442\u0435\u043a\u0430\u044e\u0442 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d(w f(0, w))}{dw} \\bigg|_{w=v_y^*} &gt; 0, \\qquad (3)\" alt=\"\\frac{d(w f(0, w))}{dw} \\bigg|_{w=v_y^*} &gt; 0, \\qquad (3)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/57\/576\/576855d67b2836eb261a1310fc92af68.svg\" width=\"232\" height=\"40\" data-width=\"29.69\" data-height=\"5.76\" data-vertical-align=\"-2.314\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/57\/576\/576855d67b2836eb261a1310fc92af68.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/57\/576\/576855d67b2836eb261a1310fc92af68.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"v_y^* &lt; 0\" alt=\"v_y^* &lt; 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/685\/6858586824f0b30dc637cb55e8d58789.svg\" width=\"48\" height=\"16\" data-width=\"6.233\" data-height=\"2.565\" data-vertical-align=\"-0.887\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/685\/6858586824f0b30dc637cb55e8d58789.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/685\/6858586824f0b30dc637cb55e8d58789.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p><strong>\u0422\u0435\u043e\u0440\u0435\u043c\u0430.<\/strong> <em>\u0412\u0441\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b (1), (2) \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u044b \u043f\u0440\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t \\in [0, \\infty)\" alt=\"t \\in [0, \\infty)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f3\/f36\/f36446543130a35d8ec1666f25a54ee2.svg\" width=\"72\" height=\"16\" data-width=\"9.491\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f3\/f36\/f36446543130a35d8ec1666f25a54ee2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f3\/f36\/f36446543130a35d8ec1666f25a54ee2.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041a\u0430\u0436\u0434\u0430\u044f \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044f <img decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{r}(t) = (x(t), y(t))\" alt=\"\\mathbf{r}(t) = (x(t), y(t))\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/67\/679\/67994cd8b39ec5260248b0a50484f55f.svg\" width=\"128\" height=\"16\" data-width=\"16.989\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/67\/679\/67994cd8b39ec5260248b0a50484f55f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/67\/679\/67994cd8b39ec5260248b0a50484f55f.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043c\u0435\u0435\u0442 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0443\u044e \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0443:<\/em><\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x(t) \\to x^*, \\quad y(t) \\to -\\infty \\quad \\text{\u043f\u0440\u0438} \\quad t \\to \\infty.\" alt=\"x(t) \\to x^*, \\quad y(t) \\to -\\infty \\quad \\text{\u043f\u0440\u0438} \\quad t \\to \\infty.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6c\/6cd\/6cdbc19492094ac68cd5403c6cba5c80.svg\" width=\"312\" height=\"16\" data-width=\"39.993\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6c\/6cd\/6cdbc19492094ac68cd5403c6cba5c80.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6c\/6cd\/6cdbc19492094ac68cd5403c6cba5c80.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p><em>\u0411\u043e\u043b\u0435\u0435 \u0442\u043e\u0433\u043e,<\/em><\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"v_x(t) \\to 0, \\quad v_y(t) \\to v_y^*.\" alt=\"v_x(t) \\to 0, \\quad v_y(t) \\to v_y^*.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0f\/0f7\/0f725cdfad241952b52eb65abb85c884.svg\" width=\"184\" height=\"16\" data-width=\"23.575\" data-height=\"2.584\" data-vertical-align=\"-0.726\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0f\/0f7\/0f725cdfad241952b52eb65abb85c884.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0f\/0f7\/0f725cdfad241952b52eb65abb85c884.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p><strong>\u0414\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u043e.<\/strong><\/p>\n<p>\u0414\u0430\u043b\u044c\u043d\u0435\u0439\u0448\u0435\u0435 \u0438\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0431\u0443\u0435\u0442 \u043e\u0442 \u0447\u0438\u0442\u0430\u0442\u0435\u043b\u044f \u0432\u043b\u0430\u0434\u0435\u043d\u0438\u044f \u0430\u043f\u043f\u0430\u0440\u0430\u0442\u043e\u043c \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0432 \u043e\u0431\u044a\u0435\u043c\u0435 \u043a\u043d\u0438\u0433\u0438: \u041d\u0435\u043c\u044b\u0446\u043a\u0438\u0439 \u0412.\u0412., \u0421\u0442\u0435\u043f\u0430\u043d\u043e\u0432 \u0412.\u0412. \u041a\u0430\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0442\u0435\u043e\u0440\u0438\u044f \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439. \u041c.: \u0415\u0434\u0438\u0442\u043e\u0440\u0438\u0430\u043b \u0423\u0420\u0421\u0421, 2004.<\/p>\n<p>\u0412 \u0441\u0438\u043b\u0443 \u0443\u0441\u043b\u043e\u0432\u0438\u044f 4) \u0438 \u044d\u043d\u0435\u0440\u0433\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{m}{2}\\frac{d}{dt}|\\mathbf{v}|^2 = m(\\mathbf{g}, \\mathbf{v}) - |\\mathbf{v}|^2 f(\\mathbf{v}) \\le mg|\\mathbf{v}| - |\\mathbf{v}|^2 f(\\mathbf{v})\" alt=\"\\frac{m}{2}\\frac{d}{dt}|\\mathbf{v}|^2 = m(\\mathbf{g}, \\mathbf{v}) - |\\mathbf{v}|^2 f(\\mathbf{v}) \\le mg|\\mathbf{v}| - |\\mathbf{v}|^2 f(\\mathbf{v})\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/13a\/13afc600737534f9864a583fe5bd9893.svg\" width=\"400\" height=\"32\" data-width=\"50.272\" data-height=\"4.676\" data-vertical-align=\"-1.773\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/13a\/13afc600737534f9864a583fe5bd9893.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/13a\/13afc600737534f9864a583fe5bd9893.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0432\u0441\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b (1), (2) \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u044b \u0438, \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e \u043f\u0440\u043e\u0434\u043e\u043b\u0436\u0430\u0435\u043c\u044b \u0432\u043f\u0440\u0430\u0432\u043e.<\/p>\n<p>\u041f\u043e\u043a\u0430\u0436\u0435\u043c, \u0447\u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"v_x(t) \\to 0\" alt=\"v_x(t) \\to 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/878\/87879d844570b7c93b7b267c5262d874.svg\" width=\"72\" height=\"16\" data-width=\"9.428\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/878\/87879d844570b7c93b7b267c5262d874.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/878\/87879d844570b7c93b7b267c5262d874.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0414\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0435\u0440\u0435\u043f\u0438\u0448\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (1) \u0432 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u043e\u0440\u043c\u0435:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"v_x(t) = v_x(0) \\exp \\left( -\\frac{1}{m} \\int_0^t f(\\mathbf{v}(\\tau)) \\, d\\tau \\right).\" alt=\"v_x(t) = v_x(0) \\exp \\left( -\\frac{1}{m} \\int_0^t f(\\mathbf{v}(\\tau)) \\, d\\tau \\right).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/55\/558\/558a933a0f54a867dc969eb8ed0ba877.svg\" width=\"312\" height=\"40\" data-width=\"39.642\" data-height=\"5.611\" data-vertical-align=\"-2.24\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/55\/558\/558a933a0f54a867dc969eb8ed0ba877.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/55\/558\/558a933a0f54a867dc969eb8ed0ba877.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0412 \u0441\u0438\u043b\u0443 \u0443\u0441\u043b\u043e\u0432\u0438\u044f 3) \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0442\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435\u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043f\u0440\u0435\u0434\u0435\u043b <img decoding=\"async\" class=\"formula inline\" source=\"v_x(t) \\to v_x^*\" alt=\"v_x(t) \\to v_x^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/62\/629\/6297d566a4c8b7d13146aa7b2dbb9da6.svg\" width=\"80\" height=\"16\" data-width=\"10.497\" data-height=\"2.273\" data-vertical-align=\"-0.571\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/62\/629\/6297d566a4c8b7d13146aa7b2dbb9da6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/62\/629\/6297d566a4c8b7d13146aa7b2dbb9da6.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, <img decoding=\"async\" class=\"formula inline\" source=\"\\omega\" alt=\"\\omega\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/260\/260b57b4fdee8c5a001c09b555ccd28d.svg\" width=\"12\" height=\"16\" data-width=\"1.407\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/260\/260b57b4fdee8c5a001c09b555ccd28d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/260\/260b57b4fdee8c5a001c09b555ccd28d.svg 781w\" loading=\"lazy\" decode=\"async\"\/>-\u043f\u0440\u0435\u0434\u0435\u043b\u044c\u043d\u043e\u0435 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0434\u0430\u043d\u043d\u043e\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043b\u0435\u0436\u0438\u0442 \u043d\u0430 \u043f\u0440\u044f\u043c\u043e\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"\\{v_x = v_x^*\\}\" alt=\"\\{v_x = v_x^*\\}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a0\/a08\/a0816fc8d4d77e29aa43245d4af85141.svg\" width=\"72\" height=\"16\" data-width=\"9.68\" data-height=\"2.273\" data-vertical-align=\"-0.571\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a0\/a08\/a0816fc8d4d77e29aa43245d4af85141.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a0\/a08\/a0816fc8d4d77e29aa43245d4af85141.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0412\u0441\u044f\u043a\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0441\u0438\u0441\u0442\u0435\u043c\u044b (1), (2), \u043b\u0435\u0436\u0430\u0449\u0435\u0435 \u0432 <img decoding=\"async\" class=\"formula inline\" source=\"\\omega\" alt=\"\\omega\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/260\/260b57b4fdee8c5a001c09b555ccd28d.svg\" width=\"12\" height=\"16\" data-width=\"1.407\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/260\/260b57b4fdee8c5a001c09b555ccd28d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/260\/260b57b4fdee8c5a001c09b555ccd28d.svg 781w\" loading=\"lazy\" decode=\"async\"\/>-\u043f\u0440\u0435\u0434\u0435\u043b\u044c\u043d\u043e\u043c \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435, \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"v_x(t) = v_x^*, \\quad v_y = v_y(t).\" alt=\"v_x(t) = v_x^*, \\quad v_y = v_y(t).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1f\/1f1\/1f10208fc9b8afa91548cce3a03de72e.svg\" width=\"184\" height=\"16\" data-width=\"23.624\" data-height=\"2.364\" data-vertical-align=\"-0.616\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1f\/1f1\/1f10208fc9b8afa91548cce3a03de72e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1f\/1f1\/1f10208fc9b8afa91548cce3a03de72e.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u044d\u0442\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (1):<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"0 = v_x^* f(v_x^*, v_y(t)).\" alt=\"0 = v_x^* f(v_x^*, v_y(t)).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/136\/13696b16795e849ff9215d552ca3489b.svg\" width=\"136\" height=\"16\" data-width=\"17.834\" data-height=\"2.364\" data-vertical-align=\"-0.667\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/136\/13696b16795e849ff9215d552ca3489b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/136\/13696b16795e849ff9215d552ca3489b.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043c, \u0447\u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"v_x^* \\neq 0\" alt=\"v_x^* \\neq 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/60\/609\/609eaa2b06bcd88b9cae944fcb49e9a3.svg\" width=\"48\" height=\"16\" data-width=\"6.348\" data-height=\"2.273\" data-vertical-align=\"-0.571\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/60\/609\/609eaa2b06bcd88b9cae944fcb49e9a3.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/60\/609\/609eaa2b06bcd88b9cae944fcb49e9a3.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0422\u043e\u0433\u0434\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"f(v_x^*, v_y(t)) = 0\" alt=\"f(v_x^*, v_y(t)) = 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1e6\/1e69a16362540af52e80a3405f3117ac.svg\" width=\"120\" height=\"16\" data-width=\"15.005\" data-height=\"2.364\" data-vertical-align=\"-0.667\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1e6\/1e69a16362540af52e80a3405f3117ac.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1e6\/1e69a16362540af52e80a3405f3117ac.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0412 \u0441\u0438\u043b\u0443 \u0443\u0441\u043b\u043e\u0432\u0438\u044f 2) \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"v_x^* = 0\" alt=\"v_x^* = 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ec\/ec3\/ec37db9745cb205ef28295ed4012f0b2.svg\" width=\"48\" height=\"16\" data-width=\"6.348\" data-height=\"2.255\" data-vertical-align=\"-0.576\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ec\/ec3\/ec37db9745cb205ef28295ed4012f0b2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ec\/ec3\/ec37db9745cb205ef28295ed4012f0b2.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u0440\u0435\u0447\u0438\u0435 \u0434\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442, \u0447\u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"v_x^* = 0\" alt=\"v_x^* = 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ec\/ec3\/ec37db9745cb205ef28295ed4012f0b2.svg\" width=\"48\" height=\"16\" data-width=\"6.348\" data-height=\"2.255\" data-vertical-align=\"-0.576\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ec\/ec3\/ec37db9745cb205ef28295ed4012f0b2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ec\/ec3\/ec37db9745cb205ef28295ed4012f0b2.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u041d\u0430 \u043f\u0440\u044f\u043c\u043e\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"\\{v_x = 0\\}\" alt=\"\\{v_x = 0\\}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/29\/292\/292bcf79aae1169d44a063028dc4b7de.svg\" width=\"64\" height=\"16\" data-width=\"8.611\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/29\/292\/292bcf79aae1169d44a063028dc4b7de.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/29\/292\/292bcf79aae1169d44a063028dc4b7de.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (1) \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u0430 \u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0430 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c (2), \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0435\u0442 \u0432\u0438\u0434:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"m\\dot{v}_y = -mg - v_y f(0, v_y). \\qquad (4)\" alt=\"m\\dot{v}_y = -mg - v_y f(0, v_y). \\qquad (4)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/02\/02c\/02c88786219cc69c42ae3d16458c4983.svg\" width=\"256\" height=\"16\" data-width=\"32.366\" data-height=\"2.405\" data-vertical-align=\"-0.637\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/02\/02c\/02c88786219cc69c42ae3d16458c4983.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/02\/02c\/02c88786219cc69c42ae3d16458c4983.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041b\u0435\u0433\u043a\u043e \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u044c, \u0447\u0442\u043e \u0432\u0441\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0441\u0442\u0440\u0435\u043c\u044f\u0442\u0441\u044f \u043a \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u043c\u0443 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044e \u0440\u0430\u0432\u043d\u043e\u0432\u0435\u0441\u0438\u044f <img decoding=\"async\" class=\"formula inline\" source=\"v_y^*\" alt=\"v_y^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1c\/1c5\/1c55781e699b0bf699977870da96e144.svg\" width=\"16\" height=\"16\" data-width=\"2.085\" data-height=\"2.565\" data-vertical-align=\"-0.887\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1c\/1c5\/1c55781e699b0bf699977870da96e144.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1c\/1c5\/1c55781e699b0bf699977870da96e144.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0418\u0437 \u044d\u0442\u043e\u0433\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u044f \u0441\u043b\u0435\u0434\u0443\u0435\u0442, \u0447\u0442\u043e \u0432\u0441\u044f\u043a\u043e\u0435 \u0437\u0430\u043c\u043a\u043d\u0443\u0442\u043e\u0435 \u0438\u043d\u0432\u0430\u0440\u0438\u0430\u043d\u0442\u043d\u043e\u0435 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f (4) \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u0442\u043e\u0447\u043a\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"v_y^*\" alt=\"v_y^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1c\/1c5\/1c55781e699b0bf699977870da96e144.svg\" width=\"16\" height=\"16\" data-width=\"2.085\" data-height=\"2.565\" data-vertical-align=\"-0.887\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1c\/1c5\/1c55781e699b0bf699977870da96e144.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1c\/1c5\/1c55781e699b0bf699977870da96e144.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0430 \u0437\u043d\u0430\u0447\u0438\u0442, <img decoding=\"async\" class=\"formula inline\" source=\"\\omega\" alt=\"\\omega\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/260\/260b57b4fdee8c5a001c09b555ccd28d.svg\" width=\"12\" height=\"16\" data-width=\"1.407\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/260\/260b57b4fdee8c5a001c09b555ccd28d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/260\/260b57b4fdee8c5a001c09b555ccd28d.svg 781w\" loading=\"lazy\" decode=\"async\"\/>-\u043f\u0440\u0435\u0434\u0435\u043b\u044c\u043d\u043e\u0435 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u043b\u044e\u0431\u043e\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b (1), (2) \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u0442\u043e\u0447\u043a\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"(0, v_y^*)\" alt=\"(0, v_y^*)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/34\/343\/34380470586ff2d94fe4317e147ca3f1.svg\" width=\"40\" height=\"16\" data-width=\"5.982\" data-height=\"2.584\" data-vertical-align=\"-0.887\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/34\/343\/34380470586ff2d94fe4317e147ca3f1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/34\/343\/34380470586ff2d94fe4317e147ca3f1.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f <img decoding=\"async\" class=\"formula inline\" source=\"(v_x, v_y)(t)\" alt=\"(v_x, v_y)(t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/19\/196\/196801b4cae68d07b513d6adf055642c.svg\" width=\"72\" height=\"16\" data-width=\"9.612\" data-height=\"2.364\" data-vertical-align=\"-0.667\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/19\/196\/196801b4cae68d07b513d6adf055642c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/19\/196\/196801b4cae68d07b513d6adf055642c.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441\u0438\u0441\u0442\u0435\u043c\u044b (1), (2) \u043d\u0430\u0439\u0434\u0451\u0442\u0441\u044f \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"t_k \\to \\infty\" alt=\"t_k \\to \\infty\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/ff\/ff0\/ff04cf475bb75e6383f5de49dfbbdd96.svg\" width=\"56\" height=\"16\" data-width=\"7.62\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/ff\/ff0\/ff04cf475bb75e6383f5de49dfbbdd96.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/ff\/ff0\/ff04cf475bb75e6383f5de49dfbbdd96.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0442\u0430\u043a\u0430\u044f, \u0447\u0442\u043e<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"(v_x, v_y)(t_k) \\to (0, v_y^*). \\qquad (5)\" alt=\"(v_x, v_y)(t_k) \\to (0, v_y^*). \\qquad (5)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bd7\/bd711c093067ec43f380e3ff3a05ace6.svg\" width=\"224\" height=\"16\" data-width=\"28.558\" data-height=\"2.584\" data-vertical-align=\"-0.726\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bd7\/bd711c093067ec43f380e3ff3a05ace6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bd7\/bd711c093067ec43f380e3ff3a05ace6.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041b\u0438\u043d\u0435\u0430\u0440\u0438\u0437\u0443\u0435\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u0443 (1), (2) \u0432 \u043e\u043a\u0440\u0435\u0441\u0442\u043d\u043e\u0441\u0442\u0438 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0440\u0430\u0432\u043d\u043e\u0432\u0435\u0441\u0438\u044f <img decoding=\"async\" class=\"formula inline\" source=\"(0, v_y^*)\" alt=\"(0, v_y^*)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/34\/343\/34380470586ff2d94fe4317e147ca3f1.svg\" width=\"40\" height=\"16\" data-width=\"5.982\" data-height=\"2.584\" data-vertical-align=\"-0.887\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/34\/343\/34380470586ff2d94fe4317e147ca3f1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/34\/343\/34380470586ff2d94fe4317e147ca3f1.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0421\u0438\u0441\u0442\u0435\u043c\u0430 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0433\u043e \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"m \\begin{pmatrix} \\dot{\\xi} \\\\ \\dot{\\eta} \\end{pmatrix} =\\begin{pmatrix}-f^* &amp; 0 \\\\-v_y^* f_1 &amp; -(f^* + f_2 v_y^*)\\end{pmatrix}\\begin{pmatrix} \\xi \\\\ \\eta \\end{pmatrix},\" alt=\"m \\begin{pmatrix} \\dot{\\xi} \\\\ \\dot{\\eta} \\end{pmatrix} =\\begin{pmatrix}-f^* &amp; 0 \\\\-v_y^* f_1 &amp; -(f^* + f_2 v_y^*)\\end{pmatrix}\\begin{pmatrix} \\xi \\\\ \\eta \\end{pmatrix},\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5e\/5e7\/5e7b8fe3c2bbb5a21634ea0f886bf180.svg\" width=\"312\" height=\"48\" data-width=\"39.903\" data-height=\"6.785\" data-vertical-align=\"-2.827\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5e\/5e7\/5e7b8fe3c2bbb5a21634ea0f886bf180.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5e\/5e7\/5e7b8fe3c2bbb5a21634ea0f886bf180.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0433\u0434\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"f^* = f(0, v_y^*)\" alt=\"f^* = f(0, v_y^*)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/73\/73b\/73b1df509316528cf37b8421e9120665.svg\" width=\"96\" height=\"16\" data-width=\"12.596\" data-height=\"2.584\" data-vertical-align=\"-0.887\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/73\/73b\/73b1df509316528cf37b8421e9120665.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/73\/73b\/73b1df509316528cf37b8421e9120665.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, <img decoding=\"async\" class=\"formula inline\" source=\"f_1 = \\frac{\\partial f}{\\partial v_x}(0, v_y^*)\" alt=\"f_1 = \\frac{\\partial f}{\\partial v_x}(0, v_y^*)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a3\/a32\/a323e4f1425f11e573dfa3f68739473c.svg\" width=\"120\" height=\"40\" data-width=\"15.572\" data-height=\"5.056\" data-vertical-align=\"-1.962\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a3\/a32\/a323e4f1425f11e573dfa3f68739473c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a3\/a32\/a323e4f1425f11e573dfa3f68739473c.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, <img decoding=\"async\" class=\"formula inline\" source=\"f_2 = \\frac{\\partial f}{\\partial v_y}(0, v_y^*)\" alt=\"f_2 = \\frac{\\partial f}{\\partial v_y}(0, v_y^*)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5e\/5e0\/5e08d9807cb571dbc17a68b5afd16d0e.svg\" width=\"120\" height=\"40\" data-width=\"15.441\" data-height=\"5.366\" data-vertical-align=\"-2.118\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5e\/5e0\/5e08d9807cb571dbc17a68b5afd16d0e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5e\/5e0\/5e08d9807cb571dbc17a68b5afd16d0e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0421\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430 \u044d\u0442\u043e\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"-\\frac{f^*}{m} &lt; 0, \\quad -\\frac{f^* + f_2 v_y^*}{m} &lt; 0.\" alt=\"-\\frac{f^*}{m} &lt; 0, \\quad -\\frac{f^* + f_2 v_y^*}{m} &lt; 0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e1\/3e1c2f7f41fd7a0c65a89ac37aee60db.svg\" width=\"232\" height=\"40\" data-width=\"29.356\" data-height=\"5.099\" data-vertical-align=\"-1.984\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e1\/3e1c2f7f41fd7a0c65a89ac37aee60db.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e1\/3e1c2f7f41fd7a0c65a89ac37aee60db.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u0435\u0440\u0432\u043e\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0432\u044b\u0442\u0435\u043a\u0430\u0435\u0442 \u0438\u0437 \u0443\u0441\u043b\u043e\u0432\u0438\u0439 3),5);  \u0432\u0442\u043e\u0440\u043e\u0435 \u2014 \u0438\u0437 \u0444\u043e\u0440\u043c\u0443\u043b\u044b (3).<\/p>\n<p>\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0440\u0430\u0432\u043d\u043e\u0432\u0435\u0441\u0438\u044f <img decoding=\"async\" class=\"formula inline\" source=\"(0, v_y^*)\" alt=\"(0, v_y^*)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/34\/343\/34380470586ff2d94fe4317e147ca3f1.svg\" width=\"40\" height=\"16\" data-width=\"5.982\" data-height=\"2.584\" data-vertical-align=\"-0.887\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/34\/343\/34380470586ff2d94fe4317e147ca3f1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/34\/343\/34380470586ff2d94fe4317e147ca3f1.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e \u0443\u0441\u0442\u043e\u0439\u0447\u0438\u0432\u043e. \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043d\u043e (5), \u0442.\u0435. \u043a\u0430\u0436\u0434\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u043f\u043e\u0441\u0435\u0449\u0430\u0435\u0442 \u0441\u043a\u043e\u043b\u044c \u0443\u0433\u043e\u0434\u043d\u043e \u043c\u0430\u043b\u0443\u044e \u043e\u043a\u0440\u0435\u0441\u0442\u043d\u043e\u0441\u0442\u044c \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0440\u0430\u0432\u043d\u043e\u0432\u0435\u0441\u0438\u044f, \u0438\u043c\u0435\u0435\u043c<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"(v_x, v_y)(t) \\to (0, v_y^*), \\quad t \\to \\infty.\" alt=\"(v_x, v_y)(t) \\to (0, v_y^*), \\quad t \\to \\infty.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/17\/17a\/17a3fb04631c708fbe0fbb687356f081.svg\" width=\"232\" height=\"16\" data-width=\"29.61\" data-height=\"2.584\" data-vertical-align=\"-0.726\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/17\/17a\/17a3fb04631c708fbe0fbb687356f081.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/17\/17a\/17a3fb04631c708fbe0fbb687356f081.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0411\u043e\u043b\u0435\u0435 \u0442\u043e\u0433\u043e,<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"v_x(t) = O(e^{-\\alpha t}), \\quad v_y(t) = v_y^* + O(e^{-\\alpha t}), 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width=\"12\" height=\"16\" data-width=\"1.448\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7b\/7b7\/7b7f9dbfea05c83784f8b85149852f08.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7b\/7b7\/7b7f9dbfea05c83784f8b85149852f08.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c\u0438 \u0447\u0438\u0441\u043b\u0430\u043c\u0438.<\/p>\n<p>\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0438\u043a\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x(t) \\to x^*\" alt=\"x(t) \\to x^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9c\/9ce\/9ce50b7c3b67d450fd72d9a89cdc18c9.svg\" width=\"72\" height=\"16\" data-width=\"9.672\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9c\/9ce\/9ce50b7c3b67d450fd72d9a89cdc18c9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9c\/9ce\/9ce50b7c3b67d450fd72d9a89cdc18c9.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"y(t) \\to -\\infty\" alt=\"y(t) \\to -\\infty\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/58\/587\/5871f9b92e88773b28b653653d6f73e3.svg\" width=\"88\" height=\"16\" data-width=\"11.228\" data-height=\"2.262\" data-vertical-align=\"-0.566\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/58\/587\/5871f9b92e88773b28b653653d6f73e3.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/58\/587\/5871f9b92e88773b28b653653d6f73e3.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441\u043b\u0435\u0434\u0443\u044e\u0442 \u043d\u0435\u043f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u0438\u0437 \u0444\u043e\u0440\u043c\u0443\u043b (6) \u0438 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x(t) = x(0) + \\int_0^t v_x(\\tau) d\\tau, \\quad y(t) = y(0) + \\int_0^t v_y(\\tau) d\\tau.\" alt=\"x(t) = x(0) + \\int_0^t v_x(\\tau) d\\tau, \\quad y(t) = y(0) + \\int_0^t v_y(\\tau) d\\tau.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1d\/1df\/1dfc9216a4d49222d92abee9bb3b22f2.svg\" width=\"416\" height=\"40\" data-width=\"52.897\" data-height=\"5.526\" data-vertical-align=\"-2.198\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1d\/1df\/1dfc9216a4d49222d92abee9bb3b22f2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1d\/1df\/1dfc9216a4d49222d92abee9bb3b22f2.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0435\u043e\u0440\u0435\u043c\u0430 \u0434\u043e\u043a\u0430\u0437\u0430\u043d\u0430.<\/p>\n<\/div>\n<p>\u0441\u0441\u044b\u043b\u043a\u0430 \u043d\u0430 \u043e\u0440\u0438\u0433\u0438\u043d\u0430\u043b \u0441\u0442\u0430\u0442\u044c\u0438 <a href=\"https:\/\/habr.com\/ru\/articles\/1029708\/\">https:\/\/habr.com\/ru\/articles\/1029708\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0411\u0430\u043b\u043b\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043a\u0440\u0438\u0432\u0430\u044f \u2014 \u044d\u0442\u043e \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044f \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438, \u0434\u0432\u0438\u0436\u0443\u0449\u0435\u0439\u0441\u044f \u0432 \u0441\u043e\u043f\u0440\u043e\u0442\u0438\u0432\u043b\u044f\u044e\u0449\u0435\u0439\u0441\u044f \u0441\u0440\u0435\u0434\u0435 \u043f\u043e\u0434 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