Optimal rotation deceleration of a dynamically symmetric body with movable mass in a resistant medium

A minimum-time problem on deceleration of rotation of a free rigid body is studied. The body is assumed to contain a viscous-elastic element, which is modeled as a movable point mass attached to the body via a damper. In addition, the body is subjected to a retarding torque generated by linear medium resistance forces. In an undeformed state, the body is assumed to be dynamically symmetric, with the mass being located on the symmetry axis. An optimal control law for deceleration of rotation of the body is synthesized, and the corresponding time and phase trajectories are determined.