# Attitude Stabilization of a Rigid Body in Conditions of Decreasing Dissipation

Результат исследований: Научные публикации в периодических изданияхстатья

3 Цитирования (Scopus)

### Выдержка

The paper presents the problem of triaxial stabilization of the angular position of a rigid body. The possibility of implementing a control system in which dissipative torque tends to zero over time and the restoring torque is the only remaining control torque is considered. The case of vanishing damping considered in this study is known as the most complicated one in the problem of stability analysis of mechanical systems with a nonstationary parameter at the vector of dissipative forces. The lemma of the estimate from below for the norm of the restoring torque in the neighborhood of the stabilized motion of a rigid body and two theorems on asymptotic stability of the stabilized motion of a body are proven. It is shown that the sufficient conditions of asymptotic stability found in the theorems are close to the necessary ones. The results of numerical simulation illustrating the conclusions obtained in this study are presented.

Язык оригинала Английский 384-391 8 Vestnik St. Petersburg University: Mathematics 50 4 https://doi.org/10.3103/S1063454117040021 Опубликовано - окт 2017

### Цитировать

@article{c697d2bc898b41b58e36435235a3ce3e,
title = "Attitude Stabilization of a Rigid Body in Conditions of Decreasing Dissipation",
abstract = "The paper presents the problem of triaxial stabilization of the angular position of a rigid body. The possibility of implementing a control system in which dissipative torque tends to zero over time and the restoring torque is the only remaining control torque is considered. The case of vanishing damping considered in this study is known as the most complicated one in the problem of stability analysis of mechanical systems with a nonstationary parameter at the vector of dissipative forces. The lemma of the estimate from below for the norm of the restoring torque in the neighborhood of the stabilized motion of a rigid body and two theorems on asymptotic stability of the stabilized motion of a body are proven. It is shown that the sufficient conditions of asymptotic stability found in the theorems are close to the necessary ones. The results of numerical simulation illustrating the conclusions obtained in this study are presented.",
keywords = "triaxial stabilization, attitude motion, dissipation, evolution, asymptotic stability, ASYMPTOTIC STABILITY, ELECTRODYNAMIC STABILIZATION, EQUILIBRIUM POSITIONS, MECHANICAL SYSTEMS, GEOMAGNETIC-FIELD, SATELLITES, PARAMETERS",
author = "Александров, {Александр Юрьевич} and Tikhonov, {A. A.}",
year = "2017",
month = "10",
doi = "10.3103/S1063454117040021",
language = "Английский",
volume = "50",
pages = "384--391",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
number = "4",

}

В: Vestnik St. Petersburg University: Mathematics, Том 50, № 4, 10.2017, стр. 384-391.

Результат исследований: Научные публикации в периодических изданияхстатья

TY - JOUR

T1 - Attitude Stabilization of a Rigid Body in Conditions of Decreasing Dissipation

AU - Александров, Александр Юрьевич

AU - Tikhonov, A. A.

PY - 2017/10

Y1 - 2017/10

N2 - The paper presents the problem of triaxial stabilization of the angular position of a rigid body. The possibility of implementing a control system in which dissipative torque tends to zero over time and the restoring torque is the only remaining control torque is considered. The case of vanishing damping considered in this study is known as the most complicated one in the problem of stability analysis of mechanical systems with a nonstationary parameter at the vector of dissipative forces. The lemma of the estimate from below for the norm of the restoring torque in the neighborhood of the stabilized motion of a rigid body and two theorems on asymptotic stability of the stabilized motion of a body are proven. It is shown that the sufficient conditions of asymptotic stability found in the theorems are close to the necessary ones. The results of numerical simulation illustrating the conclusions obtained in this study are presented.

AB - The paper presents the problem of triaxial stabilization of the angular position of a rigid body. The possibility of implementing a control system in which dissipative torque tends to zero over time and the restoring torque is the only remaining control torque is considered. The case of vanishing damping considered in this study is known as the most complicated one in the problem of stability analysis of mechanical systems with a nonstationary parameter at the vector of dissipative forces. The lemma of the estimate from below for the norm of the restoring torque in the neighborhood of the stabilized motion of a rigid body and two theorems on asymptotic stability of the stabilized motion of a body are proven. It is shown that the sufficient conditions of asymptotic stability found in the theorems are close to the necessary ones. The results of numerical simulation illustrating the conclusions obtained in this study are presented.

KW - triaxial stabilization

KW - attitude motion

KW - dissipation

KW - evolution

KW - asymptotic stability

KW - ASYMPTOTIC STABILITY

KW - ELECTRODYNAMIC STABILIZATION

KW - EQUILIBRIUM POSITIONS

KW - MECHANICAL SYSTEMS

KW - GEOMAGNETIC-FIELD

KW - SATELLITES

KW - PARAMETERS

U2 - 10.3103/S1063454117040021

DO - 10.3103/S1063454117040021

M3 - статья

VL - 50

SP - 384

EP - 391

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -