 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| A. A. Il’in, N. V. Kupriyanova, and M. Yu. Ovchinnikov, "Steady-state rotational motions of a rigid body with a strong magnet in an alternating magnetic field in the presence of dissipation," Mech. Solids. 44 (3), 341-351 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
3 |
Pages |
341-351 |
| DOI |
10.3103/S0025654409030029 |
| Title |
Steady-state rotational motions of a rigid body with a strong magnet in an alternating magnetic field in the presence of dissipation |
| Author(s) |
A. A. Il’in (Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya 4, Moscow, 125047, Russia, ilyinandrey@mail.ru)
N. V. Kupriyanova (Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudny, Moscow District, 141700, Russia, keyna@mail.ru)
M. Yu. Ovchinnikov (Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya 4, Moscow, 125047, Russia, ovchinni@keldysh.ru) |
| Abstract |
We consider steady-state rotational motions of a satellite, i.e., a rigid body with a passive magnetic attitude control system consisting of a strong constant magnet and a set of magnetic hysteresis rods. We use asymptotic methods to show that in the absence of dissipation there exists a one-parameter family of steady-state rotations of the rigid body with the strong magnet and that this one-parameter family passes into an isolated solution if a model dissipation is introduced. The motion thus obtained was discovered when processing the telemetry data from the first
Russian nano-satellite TNS-0 launched in 2005. |
| References |
| 1. | M.Yu. Ovchinnikov, V.I. Pen'kov, I.Yu. Kiryushin, et al.,
Experience of Design, Creation, and Operation of Magnetic Position Control Systems for Small Satellites.
Preprint No.53 (Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 2002) [in Russian]. |
| 2. | V.A. Sarychev and M.Yu. Ovchinnikov, Magnetic Position Control Systems for the Earth's Artificial Satellites, in Summary of Science and Technology. Series: Space Researches. Vol. 23 (VINITI, Moscow, 1985) [in Russian]. |
| 3. | G. Horn and S. Regenberg, "Zur Stabilisiering eines Satelliten mit Holfe des Erdmagnetfelds," Z. Flugwiss 14 (9), 398-413 (1966). |
| 4. | V.V. Beletskii and A.B. Novogrebel'skii, "Existence of Stable Relative Equilibria for an Artificial Satellite in a Model Magnetic Field," Astron. Zh. 50 (2), 327-335 (1973) [Sov. Astron. (Engl. Transl.) 17 (2), 213-218 (1973)]. |
| 5. | A.A. Goncharskii and A.A. Khentov, "On Some Regimes of Rotation of Magnetized Satellite-Gyrostat in the Geomagnetic Field," Izv. Vyssh. Uchebn. Zaved. Radiofiz.
15 (11), 1631-1636 (1972). |
| 6. | V.V. Beletskii, Artificial Satellite Motion about Its Center of Mass (Nauka, Moscow, 1965) [in Russian]. |
| 7. | N.N. Moiseev, Asymptotic Methods of Nonlinear Mechanics (Nauka, Moscow, 1981) [in Russian]. |
| 8. | V.V. Beletskii and A.A. Khentov, Rotational Motion of a Magnetized Satellite (Nauka, Moscow, 1985) [in Russian]. |
| 9. | A.A. Tikhonov, "Refinement of the Oblique Dipole Model in the Evolution of Rotary Motion of a Charged Body in the Geomagnetic Field," Kosmich. Issled. 40 (2), 171-177 (2002) [Cosmic Res. (Engl. Transl.) 40 (2), 157-162 (2002)]. |
| 10. | V.V. Sidorenko, Destruction of Adiabatic Invariants in Resonances: an Example from Dynamics of Solids. Preprint No. 76 (Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 1995) [in Russian]. |
| 11. | V.V. Sidorenko, "One Class of Motions for a Satellite Carrying a Strong Magnet," Kosmich. Issled. 40 (2), 147-155 (2002) [Cosmic Res. (Engl. Transl.) 40 (2), 133-141 (2002)]. |
| 12. | Yu.M. Urkich, A.S. Selivanov, Yu.M. Tuchin, et al., "Technological Nano-Satellite TNS-0 of Minimal Kitting,"
in Thesis of Report on the 3rd Conference "Microtechnologies in Aviation and Cosmonautics" (St. Petersburg, 2004), pp. 7-8. |
| 13. | N.V. Kupriyanova, M.Yu. Ovchinnikov, V.I. Pen'kov, and A.S. Selivanov, Passive Magnetic Position Control System of the First Russian Nano-Satellite TNS-0, Preprint No. 46 (Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 2005) [in Russian]. |
| 14. | D.A. Vallado and W.D. McClain, Fundamentals of Astrodynamics and Application (Kluwer, Space Technology Library, Netherland, 2001). |
|
| Received |
18 April 2007 |
| Link to Fulltext |
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