Optimal deceleration of rotation of a symmetric gyrostat with a moving mass in a resistive medium

The problem of time-optimal deceleration of rotation of a free solid body is studied. It is assumed that the body contains a spherical cavity filled with highly viscous liquid. Solid body carries a moving point mass connected to the body by an elastic coupling with viscous friction. Low decelerating moment of linear friction forces acts on the solid body. It is assumed that the body is dynamically symmetric. The optimal control law for deceleration of rotation of the carrier solid body in the form of synthesis, the operation time, and the phase trajectories are determined.