To the problem of controlled rotations of a dynamically symmetric rigid body

The paper studies the problem of damping the Equatorial component of the angular velocity of a dynamically symmetric solid. It is assumed that the axial component of the angular velocity is a given function of time. The optimality criterion is the minimization of energy costs. Using Pontryagin’s maximum principle and the method of averaging in the analytical form, an approximate solution is constructed. The optimal controls in the form of synthesis, angular velocities, minimum energy costs are determined. The condition when the solution for the considered problem does not exist is specified.