Perturbed rotational motions of a rigid body similar to regular precession (Q1180852)

Perturbed rotational motions of a rigid body, similar to regular precession in the Lagrange case, when the restoring torque depends on the angle of nutation, are investigated. It is assumed that the angular velocity of the body is fairly large, its direction are close to the dynamic axis of symmetry of the body and the perturbing torques are small compared with the restoring torques. A small parameter is introduced in a special way and the method of averaging is used. The averaged equations of motion are derived in the first and second approximations. Specific mechanical models of the perturbations are considered.