 | | 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, "On Steady Motions of a Rigid Body Bearing Three-Degree-of-Freedom Control Momentum Gyroscopes and Their Stability," Mech. Solids. 46 (3), 335-347 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
3 |
Pages |
335-347 |
| DOI |
10.3103/S0025654411030010 |
| Title |
On Steady Motions of a Rigid Body Bearing Three-Degree-of-Freedom Control Momentum Gyroscopes and Their Stability |
| Author(s) |
N.I. Amel'kin (Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141700 Russia, namelkin@mail.ru) |
| Abstract |
Equations of motion are obtained for a rigid body bearing N three-degree-of-freedom control momentum gyroscopes in gimbals and the entire set of steady motions in a homogeneous external field is determined. The steady motion dependence on the magnitude of the system angular momentum is studied and a detailed analysis of the secular stability is performed.
In the case of dissipative forces acting in the gyroscope gimbal axes, the Barbashin-Krasovskii theorem is used to study stability in the sense of Lyapunov. It is shown that, depending on the angular momentum magnitude, either static states of the system or two motions corresponding to rotations of the bearing body about the axis of the greatest moment of inertia are asymptotically stable, while all the other stationary motions are unstable in the sense of Lyapunov. |
| Keywords |
rigid-body, control momentum gyroscope, steady motions, secular stability, stability in the sense of Lyapunov |
| 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.)
41 (4), 12-20 (2006)]. |
| 2. | 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,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 26-40 (2007)
[Mech. Solids (Engl. Transl.)
42 (4), 517-529 (2007)]. |
| 3. | N. I. Amel'kin,
"On Limit Motions of a System of Control Moment Gyros
with Intrinsic Dissipation in a Homogeneous Gravitational Field,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 23-32 (2008)
[Mech. Solids (Engl. Transl.)
43 (3), 333-341 (2008)]. |
| 4. | V. V. Rumyantsev and A. S. Oziraner,
Stability and Stabilization of Motion in Part of Variables
(Nauka, Moscow, 1987)
[in Russian]. |
| 5. | A. V. Karapetyan,
Stability of Stationary Motions
(Editorial URRS, Moscow, 1998)
[in Russian]. |
| 6. | N. Rouché, P. Habets, and M. Lalou,
Stability Theory by Liapunov's Direct Method
(Springer, Berlin, 1977; Mir, Moscow, 1980). |
|
| Received |
03 March 2010 |
| Link to Fulltext |
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