Fuel minimization in the problem of optimal controlled rotations a dynamically symmetric rigid body

The paper studies the fuel-optimal control problem of damping the Equatorial component of the angular velocity of a dynamically symmetric solid. Pontryagin's maximum principle and the averaging method are applied to construct the optimal solution. The angular velocities, optimal control in the form of synthesis, and minimum value of fuel consumption are found in analytical form. Illustrative examples are provided.