 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| N. I. Amel’kin, "Stability analysis of steady rotations of a rigid body bearing two-degree-of-freedom control moment gyros with dissipation in gimbal suspension axes," Mech. Solids. 42 (4), 517-529 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
4 |
Pages |
517-529 |
| Title |
Stability analysis of steady rotations of a rigid body bearing two-degree-of-freedom control moment gyros with dissipation in gimbal suspension axes |
| Author(s) |
N. I. Amel’kin (Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudny, Moscow oblast, 141700, Russia) |
| Abstract |
To study the stability of steady rotations of a control moment gyro system with internal dissipation, we use the Barbashin-Krasovskii theorem and the relation, established in [1], between the Lyapunov function and steady motions. Taking into account the special properties of the original problem, we reduce it to a lower-dimensional problem.
We give a detailed presentation of an algorithm for analyzing the stability of steady motions of a gyrostat and use this algorithm to perform a complete study for two systems consisting, respectively, of one and two gyros whose gimbal axes are parallel to the principal axis of inertia of the system. Each steady motion is identified as either asymptotically stable or unstable. We find periodic motions that exist only in the presence of dynamic symmetry and which are regular precessions. For the system with two gyros, we prove the asymptotic stability of quiescent states and prove that in the angular momentum range where these states are defined the system does not have any other stable motions. |
| References |
| 1. | N. I. Amel'kin,
"On the Motions of a Rigid Body Containing Two-Degree-of-Freedom Control Moment
Gyros with Dissipation in Gimbal Axes,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 19-30 (2006)
[Mech. Solids (Engl. Transl.)]. |
| 2. | E. A. Barbashin,
Introduction to the Theory of Stability
(Nauka, Moscow, 1967)
[in Russian]. |
| 3. | N. Rouché, P. Habets, and M. Laloy,
Stability Theory by Liapunov's Direct Method
(Springer, New York, Heidelberg, Berlin, 1977; Mir, Moscow, 1980). |
| 4. | V. V. Rumyantsev and A. S. Oziraner, Stability and
Stabilization of Motion with Respect to Part of the Variables
(Nauka, Moscow, 1987) [in Russian]. |
| 5. | A. V. Karapetyan,
Stability of Steady Motions
(Editorial URRS, Moscow, 1998)
[in Russian]. |
|
| Received |
15 February 2005 |
| Link to Fulltext |
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