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

Research outputpeer-review

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.

Original languageEnglish
Pages (from-to)187-193
JournalVestnik St. Petersburg University: Mathematics
Volume52
Issue number2
DOIs
Publication statusPublished - 1 Apr 2019

Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

Cite this

@article{7cfa0a41d91d49958433ef09515320e7,
title = "Uniaxial Attitude Stabilization of a Rigid Body under Conditions of Nonstationary Perturbations with Zero Mean Values",
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 = "asymptotic stability, attitude motion, nonlinear perturbations, uniaxial stabilization",
author = "Aleksandrov, {A. Yu.} and Tikhonov, {A. A.}",
note = "Aleksandrov, A.Y. & Tikhonov, A.A. Vestnik St.Petersb. Univ.Math. (2019) 52: 187. https://doi.org/10.1134/S106345411902002X",
year = "2019",
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TY - JOUR

T1 - Uniaxial Attitude Stabilization of a Rigid Body under Conditions of Nonstationary Perturbations with Zero Mean Values

AU - Aleksandrov, A. Yu.

AU - Tikhonov, A. A.

N1 - Aleksandrov, A.Y. & Tikhonov, A.A. Vestnik St.Petersb. Univ.Math. (2019) 52: 187. https://doi.org/10.1134/S106345411902002X

PY - 2019/4/1

Y1 - 2019/4/1

N2 - 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.

AB - 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.

KW - asymptotic stability

KW - attitude motion

KW - nonlinear perturbations

KW - uniaxial stabilization

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U2 - 10.1134/S106345411902002X

DO - 10.1134/S106345411902002X

M3 - Article

VL - 52

SP - 187

EP - 193

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

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