Vestnik St. Petersburg University, Mathematics

, Volume 52, Issue 2, pp 187–193

# Uniaxial Attitude Stabilization of a Rigid Body under Conditions of Nonstationary Perturbations with Zero Mean Values

• A. Yu. Aleksandrov
• A. A. Tikhonov
Mechanics

## Abstract

This paper deals with the problem of uniaxial stabilization of the angular position of a rigid body exposed to a nonstationary perturbing torque. The perturbing torque is represented as a linear combination of homogeneous functions with variable coefficients. It is assumed that the order of homogeneity of perturbations does not exceed the order of homogeneity of the restoring torque, and the variable coefficients in the components of the disturbing torque have zero mean values. A theorem on sufficient conditions for the asymptotic stability of a programmed motion of the body is proven using the Lyapunov direct method. The determined conditions guaranteeing the solution to the problem of body uniaxial stabilization do not impose any restrictions on the amplitudes of oscillations of the disturbance torque coefficients. Results of numerical modeling are presented that confirm the conclusions obtained analytically.

## Keywords

uniaxial stabilization attitude motion nonlinear perturbations asymptotic stability

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