The motion of a solid in a flow of particlesстатья
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Дата последнего поиска статьи во внешних источниках: 30 октября 2013 г.
Аннотация:The problem of the motion of a solid in a flow of particles around a fixed point is considered. This problem is well known to have an extremely non-conservative form. Nevertheless, it turns out that the dynamics of the solid in this problem can be described, with certain assumptions, by a system of Hamiltonian equations. The conditions under which this quite unexpected fact can occur, are investigated. The presence of a Hamiltonian structure considerably increases the interest in the problem of the existence of additional first integrals of the equations of motion. It turns out that there are certain cases when these integrals exist. These include the case when the equations of motion allow the possibility of an integral similar to a Hess integral in the problem of the motion of a heavy solid around a fixed point. The steady-state motions of the system considered are also determined, and their stability is investigated.