On the Stability of a Class of Permanent Rotations of a Heavy Asymmetric Gyrostat

被引：10

作者：

Iarrea, Manuel ^{[1
]}

Lanchares, Victor ^{[1
]}

Pascual, Ana I. ^{[1
]}

Elipe, Antonio ^{[2
]}

机构：

[1] Univ La Rioja, Fac Ciencias & Tecnol, Madre de Dios 53, Logrono 26006, Spain

[2] Ctr Univ Def Zaragoza, Carretera Huesca S-N, Zaragoza 50090, Spain

来源：

REGULAR & CHAOTIC DYNAMICS | 2017年 / 22卷 / 07期

关键词：

gyrostat rotation; stability; Energy - Casimir method; DUAL-SPIN SPACECRAFT; TIME-DEPENDENT MOMENTS; RIGID-BODY DYNAMICS; ORBITAL STABILITY; FIXED-POINT; TRIAXIAL GYROSTAT; ALGEBRAIC METHODS; PERIODIC MOTIONS; CHAOTIC DYNAMICS; ROTOR;

D O I：

10.1134/S156035471707005X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the motion of an asymmetric gyrostat under the attraction of a uniform Newtonian field. It is supposed that the center of mass lies along one of the principal axes of inertia, while a rotor spins around a different axis of inertia. For this problem, we obtain the possible permanent rotations, that is, the equilibria of the system. The Lyapunov stability of these permanent rotations is analyzed by means of the Energy-Casimir method and necessary and sufficient conditions are derived, proving that there exist permanent stable rotations when the gyrostat is oriented in any direction of the space. The geometry of the gyrostat and the value of the gyrostatic momentum are relevant in order to get stable permanent rotations. Moreover, it seems that the necessary conditions are also sufficient, but this fact can only be proved partially.

引用

页码：824 / 839

页数：16

共 50 条

[41] THE LIPAUNOV STABILITY OF THE ROTATION OF A GYROSTAT
GE, ZM
CHEN, HK
TRANSACTIONS OF THE CANADIAN SOCIETY FOR MECHANICAL ENGINEERING, 1994, 18 (02) : 131 - 146
[42] Stability of Permanent Rotations of Interconnected Rigid Bodies System with Small Asymmetry
I. Bolgrabskaya
Multibody System Dynamics, 2001, 6 : 59 - 72
[43] Liapunov stability of the rotation of a gyrostat
Ge, Zheng-Ming
Chen, Hsien-Keng
Transactions of the Canadian Society for Mechanical Engineering, 1994, 18 (02): : 131 - 146
[44] PERIODIC MOTIONS OF A HEAVY GYROSTAT.
Demin, V.G.
Tsopa, M.P.
Mechanics of Solids (English translation of Izvestiya Akademii Nauk SSSR, Mekhanika Tverdogo Tela), 1976, 11 (05): : 9 - 11
[45] Dynamics and Chaos Control of Asymmetric Gyrostat Satellites
Aslanov, V. S.
Yudintsev, V. V.
COSMIC RESEARCH, 2014, 52 (03) : 216 - 228
[46] ON BIFURCATION AND STABILITY OF PERMANENT ROTATIONS OF A HEAVY SOLID BODY WHOSE CENTER OF MASS IS CLOSE TO THE PRINCIPAL PLANE OF ITS ELLIPSOID OF INERTIA.
Rubanovskii, V.N.
Journal of Applied Mathematics and Mechanics, 1983, 46 (05): : 609 - 615
[47] Chaotic motion of an asymmetric gyrostat in the gravitational field
Int J Non Linear Mech, 3 (191):
[48] A Family of Oscillations Connecting Stable and Unstable Permanent Rotations of a Heavy Solid with a Fixed Point
V. N. Tkhai
Mechanics of Solids, 2023, 58 : 2067 - 2079
[49] ON THE STABILITY OF PERMANENT ROTATIONS OF A CHAIN OF TWO LAGRANGE GYROSTATS IN A CENTRAL GRAVITATIONAL FIELD
Chebanov, Dmitriy
Salas, Jose A.
PROCEEDINGS OF THE ASME INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES AND COMPUTERS AND INFORMATION IN ENGINEERING CONFERENCE, 2016, VOL 6, 2016,
[50] Dynamics and chaos control of asymmetric gyrostat satellites
V. S. Aslanov
V. V. Yudintsev
Cosmic Research, 2014, 52 : 216 - 228

← 1 2 3 4 5 →