Minimizing the linear combination of time and energy costs in the optimal control problem for a dynamically symmetric rigid body rotations

The paper investigates the problem of damping the angular velocity equatorial component of a dynamically symmetric solid body with given constraints on the control external moment vector. It is assumed that the angular velocity axial component is a known function of time. As an optimality criterion, the quality functional is used, which reflects the time expenditure and energy costs in a given proportion. The minimum value of the functional, optimal controls in the synthesis form, and angular velocities are analytically found using the maximum principle of L.S. Pontryagin.