Optimal braking of the rotations of a rigid body with internal degrees of freedom

Summary form only given. We consider motion of a rigid body with internal degrees of freedom: a moving mass coupling viscoelastically or with a square low friction to the body and cavity containing viscous fluid. It is assumed the natural oscillations of mass attenuate much more rapidly than the rigid body makes one revolution. The obtained equations of system have the form similar to rigid body equations and torques due to internal dissipation. It is assumed that rotation is braked by means of a control moment that is bounded in modulus, the magnitude of the constraint may vary in time. Our problem is to find the response-optimal braking of the rotations of the system. We need to find an optimal control law, optimal phase trajectory, and minimum value of the functional