perturbed motions of a rigid body similar to pseudoregular precession in the lagrange case

The paper investigated the perturbed rotational motions of a rigid body, close to pseudoregular precession in the lagrange case. it is assumed that the direction of the rigid body angular velocity is close to the axis of dynamic symmetry of the body; the angular velocity of the body is sufficiently large. an averaging method is used for solving the problem. conditions for the possibility of averaging the equations of motion with respect to phase of nutation angle are presented. the averaged system of motion equations is obtained in the first approximation. the variable θ for unperturbed motion expressed in terms of elementary function of sine. this is an element of novelty in this investigation. we consider another possible variant of the application of averaging method for the perturbed motion close to lagrange's top, this variant being different from the known ones. as an example of the developed procedure, we investigate the perturbed motion of the body similar to pseudoregular precession of lagrange's top under the action: 1) of the medium with linear dissipation, 2) of the constant body-fixed torques, 3) of linear dissipative torques of forces, slowly changing in time. a new class of rotational motions similar to lagrange's top is studied. the advantage of this paper is in obtaining the original asymptotic and numerical calculations, as well as solutions that describe the perturbed motions of a rigid body, close to pseudoregular precession in the lagrange case.