Задача №12.33

Условие

Точка M движется по линии пересечения сферы x2+y2+z2=R2 и цилиндра (x-R/2)2+y2=R2/4. Уравнения движения точки в сферических координатах имеют вид (см. задачу 10.21)
r = R, φ = kt/2, θ = kt/2. Найти проекции и модуль ускорения точки в сферических координатах.

Решение




Предыдущая задача №32
Точка M движется по винтовой линии. Уравнения движения ее в цилиндрической системе координат имеют вид
r = a, φ = kt, z = νt. Найти проекции ускорения точки на оси цилиндрической системы координат, касательную и нормальную составляющие ускорения и радиус кривизны винтовой линии.
Следующая задача №34
Корабль движется под постоянным курсовым углом α к географическому меридиану, описывая при этом локсодромию (см. задачу 11.13). Считая, что модуль скорости v корабля не изменяется, определить проекции ускорения корабля на оси сферических координат r, λ и φ (λ — долгота, φ — широта места плавания), модуль ускорения и радиус кривизны локсодромии.
Источник: Решебник Мещерского 12 класс
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1.1
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2.1
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24.1
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28.1
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33.1
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38.1
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46.1
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47.1
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48.1
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49.1
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56.7
56.9
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