Optimal deceleration of rotation of asymmetric quasi-solid body in a resistant medium

The problem of time-optimal deceleration of rotation of a free solid body is studied. It is assumed that the body contains spherical cavity filled with highly viscous liquid. Low decelerating torque of viscous friction also acts on the solid body. The body is assumed to be dynamically asymmetric. The optimal control law for deceleration of rotation of the solid body in the form of synthesis, the optimal time, and the phase trajectories are determined.