THE MOTION OF A SOLID IN A FLOW OF PARTICLES

The problem of the motion of a solid in a flow of particles around a f ixed point is considered. This problem is well known to have an extrem ely non-conservative form. Nevertheless, it turns out that the dynamic s of the solid in this problem can be described, with certain assumpti ons, by a system of Hamiltonian equations. The conditions under which this quite unexpected fact can occur, are investigated. The presence o f a Hamiltonian structure considerably increases the interest in the p roblem of the existence of additional first integrals of the equations of motion. It turns out that there are certain cases when these integ rals exist. These include the case when the equations of motion allow the possibility of an integral similar to a Hess integral in the probl em of the motion of a heavy solid around a fixed point. The steady-sta te motions of the system considered are also determined, and their sta bility is investigated.