A control for a rotor with a cavity containing an ideal liquid. I

The Cauchy problem in the linear statement is considered for the motion of a body with a cavity containing an ideal liquid. The motion is perturbed relative to uniform rotation. Note that there are no constraints imposed on the cavity shape and the nature of the perturbed motion. The problem of the joint solution of hydrodynamical and mechanical equations is reduced to solving a certain eigenvalue problem depending only on the cavity geometry and to the subsequent integration of a system of differential equations. Based on the equations obtained, the stability of steady-state rotation of a body with liquid is investigated. For the system considered, the problem of optimal control with a terminal functional is posed. Analytical solutions are presented for the case when there are no constraints on the control.