The evolution of the motions of a rigid body close to the Lagrange case under the action of an unsteady torque

Perturbed rotational motions of a rigid body, close to the Lagrange case, under the action of a torque that is slowly varying in time are investigated. Conditions for the possibility of averaging the equations of motion with respect to the nutation phase angle are presented and an averaged system of equations is obtained. An example, corresponding to the motion of a body in a medium with linear dissipation, is considered.