 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| V.V. Lyubimov, "External Stability of Resonances in the Motion of an Asymmetric Rigid Body with a Strong Magnet in the Geomagnetic Field," Mech. Solids. 45 (1), 10-21 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
1 |
Pages |
10-21 |
| DOI |
10.3103/S0025654410010036 |
| Title |
External Stability of Resonances in the Motion of an Asymmetric Rigid Body with a Strong Magnet in the Geomagnetic Field |
| Author(s) |
V.V. Lyubimov (Korolyov Samara State Aerospace University, Moskovskoe sh. 34, Samara, 443086 Russia, vlubimov@mail.ru) |
| Abstract |
We consider a precession motion, close to the classical Lagrange case, of an asymmetric rigid body with a strong magnet in an orbit in the geomagnetic field. For the principal moment we take the restoring torque due to the interaction between the planet magnetic fields and the rigid body. The perturbing actions are due to small moments of the rigid body mass-inertial asymmetry and small constant moments. We show that these perturbations result in the realization of secondary resonance effects in the rotational motion of the rigid body caused by the influence of resonance denominators in higher-order approximations of the averaging method. These effects were discovered in the study of rotational motion of a satellite with a magnetic damper in the nearly Euler case. In the present paper, we analyze both the secondary resonance effects themselves and the external stability of resonances. We obtain conditions ensuring a decrease in the angular velocity of the rigid body rotation about its center of mass. We also discover several new laws of influence of resonances on the nonresonance evolution of slow variables, which is related to the appearance of stable resonances. |
| Keywords |
stability, resonance, rotation, asymmetry, moment, velocity, averaging |
| References |
| 1. | V. V. Beletskii and A. A. Khentov,
Rotational Motion of a Magnetized Satellite
(Nauka, Moscow, 1985)
[in Russian]. |
| 2. | A. A. Khentov,
"Passive Stabilization of Artificial Satellites with Respect to the Earth's Magnetic Field,"
Kosmich. Issled.
5 (4), 540-553 (1967)
[Cosmic Res. (Engl. Transl.)
5 (4), 466-478 (1967)]. |
| 3. | V. V. Sazonov and V. A. Sarychev,
"Effect of Dissipative Magnetic Moment on Rotation of a Satellite Relative to the Center of Mass,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 2, 3-12 (1983)
[Mech. Solids (Engl. Transl.)
18 (2), 1-9 (1983)]. |
| 4. | V. A. Sarychev and M. Yu. Ovchinnikov,
"Motion of a Satellite with a Permanent Magnet Relative to Its Center of Mass,"
Kosmich. Issled.
24 (4), 527-543 (1986)
[Cosmic Res. (Engl. Transl.)
24 (4), 415-429 (1986)]. |
| 5. | M. Yu. Ovchinnikov,
"Transient Motions of a Satellite with a Magnetic Attitude Control System in the Framework of a Simple Model of Hysteresis,"
Kosmich. Issled.
38 (1), 78-84 (2000)
[Cosmic Res. (Engl. Transl.)
38 (1), 73-79 (2000)]. |
| 6. | Yu. A. Sadov,
"Fast Rotation of a Satellite with Magnetic Damper.
4: Dissipative Evolution. Resonance Effects,"
Kosmich. Issled.
24 (4), 553-563 (1986)
[Cosmic Res. (Engl. Transl.)]. |
| 7. | Yu. A. Sadov,
"Secondary Resonance Effects in Mechanical Systems,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 4, 20-24 (1990)
[Mech. Solids (Engl. Transl.)]. |
| 8. | V. V. Lyubimov,
"External Stability of a Resonance in a Nonlinear System with Slowly Changing Variables,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 52-58 (2002)
[Mech. Solids (Engl. Transl.)
37 (6), 42-47 (2002)]. |
| 9. | D. E. Okhotsimskii and Yu. G. Sikharulidze,
Foundations of Spaceflight Mechanics
(Nauka, Moscow, 1990)
[in Russian]. |
| 10. | V. A. Sarychev and M. Yu. Ovchinnikov,
"Magnetic Stabilization of a Satellite with the Magnetically Anchored Spherical Damper,"
Kosmich. Issled.
24 (6), 803-815 (1986)
[Cosmic Res. (Engl. Transl.)
24 (6), 619-630 (1986)]. |
| 11. | Yu. M. Zabolotnov,
"Asymptotic Analysis of the Quasilinear Equations of Movement in an Atmosphere Spacecraft with Small Asymmetry,"
Kosmich. Issled.
31 (6), 39-50 (1993)
[Cosmic Res. (Engl. Transl.)]. |
| 12. | Yu. M. Zabolotnov and V. V. Lyubimov,
"Secondary Resonance Effects in the Rotation of a Rigid Body about a Fixed Point,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 49-59 (2002)
[Mech. Solids (Engl. Transl.)
37 (1), 39-46 (2002)]. |
| 13. | N. N. Moiseev,
Asymptotic Methods of Nonlinear Mechanics
(Nauka, Moscow, 1969)
[in Russian]. |
|
| Received |
05 December 2007 |
| Link to Fulltext |
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