Stabilizing the programmed motion of a rigid body with a cavity filled with viscous fluid

This paper is devoted to synthesizing the asymptotically stable arbitrary programmed motion for a rigid body with a cavity entirely filled with viscous fluid. To solve this problem, we synthesize an active program control applied to the system and a stabilizing feedback control. The control is synthesized as an exact analytical solution in the class of continuous functions. The problem is solved based on Lyapunov’s second method for stability analysis by using Lyapunov functions with sign-constant derivatives.