Abstract
In the proposed cycle of work, we study the equations of the motion of dynamically symmetric fixed n-dimensional rigid bodiespendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of the motion of a free n-dimensional rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint. In this work, we study the case of independence of force fields on the tensor of angular velocity.
Highlights
Вводные замечанияВыберем функцию rN в следующем виде (диск Dn−1 задается уравнением x1N ≡ 0): rN =.
X2N = R(α) cos β1, x3N = R(α) sin β1 cos β2, .
Sin βn−3 cos βn−2, xnN = R(α) sin β1 .
Summary
Выберем функцию rN в следующем виде (диск Dn−1 задается уравнением x1N ≡ 0): rN =. X2N = R(α) cos β1, x3N = R(α) sin β1 cos β2, . Sin βn−3 cos βn−2, xnN = R(α) sin β1 . Убеждающие нас о том, что в рассматриваемой системе отсутствует зависимость момента сил от тензора угловой скорости Для построения силового поля используется пара функций R(α), s(α), информация о которых носит качественный характер. Подобно выбору аналитических функций типа Чаплыгина [1, 2], динамические функции s и R примем в следующем виде: R(α) = A sin α, s(α) = B cos α, A, B > 0.
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