Influence of dissipative asymmetry on the of rotation stability in a resisting medium of a asymmetric rigid body under the action of a constant moment in inertial reference frame

Abstract

Assuming that the center of mass of an asymmetric rigid body is located on the third main axis of inertia of a rigid body, the influence of dissipative asymmetry on the stability of uniform rotation in a medium with resistance of a dynamically asymmetric rigid body is estimated. A rigid body rotates around a fixed point, is under the action of gravity, dissipative moment and constant moment in an inertial frame of reference. The stability conditions are represented by a system of three inequalities. The first and second inequalities have the first degree with respect to the dissipative asymmetry, and the third inequality has the third degree. The third inequality is the most difficult to study. Analytical studies of the influence of small and large dissipative asymmetries, restoring, overturning and constant moments on the stability of rotation of a rigid body are carried out. Conditions for asymptotic stability are obtained for sufficiently small values of the dissipative asymmetry and conditions for instability for sufficiently large values of the asymmetry. The stability conditions are written down to the second order of smallness with respect to the constant moment and the first - with respect to the restoring or overturning moments. Stability conditions for the rotation of a rigid body around the center of mass are studied.