Attitude stabilization of a rigid body in conditions of decreasing dissipation

The article deals with the problem of triaxial stabilization of an angular position of a rigid body. The issue of the possibility of implementing a control system, in which dissipative torque tends to zero over time, and the only remaining control torque is a restoring one is raised. The case of vanishing damping considered in this paper is known as the most difficult one in the problem of analyzing the stability of mechanical systems with a nonstationary parameter at dissipative forces. A lemma about a lower estimate of the norm of the restoring torque in a neighborhood of the stabilized motion of a rigid body and two theorems on the asymptotic stability of the stabilized motion of a body are proved. It is shown that the sufficient conditions for asymptotic stability found in theorems are close to necessary ones. The results of numerical modeling illustrating the conclusions obtained in the work are presented. Refs 23. Figs 2.Работа выполнена при финансовой поддержке РФФИ (гранты №16-01-00587-а, №16-08-00997-а, №17-01-00672-а)