 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10522 |
| In Russian (ÏÌÌ): | | 9723
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| In English (J. Appl. Math. Mech.): | | 799 |
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| A.S. Andreyev and R.B. Zainetdinov, "Stabilization of the motions of mechanical systems with variable masses," J. Appl. Math. Mech. 73 (1), 1-7 (2009) |
| Year |
2009 |
Volume |
73 |
Issue |
1 |
Pages |
1-7 |
| Title |
Stabilization of the motions of mechanical systems with variable masses |
| Author(s) |
A.S. Andreyev (Ul’yanovsk, Russia, andreevas@ulsu.ru)
R.B. Zainetdinov (Ul’yanovsk, Russia) |
| Abstract |
A holonomic mechanical system with variable masses and cyclic coordinates is considered. Such a system can have generalized steady motions in which the positional coordinates are constant and the cyclic velocities under the action of reactive forces vary according to a given law. Sufficient Routh-Rumyantsev-type conditions for the stability of such motions are determined. The problem of stabilizing a given translational-rotational motion of a symmetric satellite in which its centre of mass moves in a circular orbit and the satellite executes rotational motion about its axis of symmetry is solved. |
| References |
| 1. | E.J. Routh, A Treatise on the Stability of a Given State of Motion, Macmillan and Co, London (1877) 108p. |
| 2. | L. Salvadori, Un’osservazione su di un criterio di stabilita del Routh, Rend Accad Sci Fis e Math Soc Naz Sci Lett et Arti Napoli 20 (1/2) (1953), pp. 269–272. |
| 3. | V.V. Rumyantsev, On the Stability of Steady Motions of Satellites, Vychisl Tsentr Akad Nauk SSSR, Moscow (1967). |
| 4. | V.V. Rumyantsev, On the optimal stabilization of control systems, Prikl Mat Mekh 34 (3) (1970), pp. 440–456. |
| 5. | A.V. Karapetyan and V.V. Rumyantsev, The stability of conservative and dissipative systems, Advances in Science and Technology. General Mechanics Vol. 6, VINITI, Moscow (1983). |
| 6. | A.V. Karapetyan, The Stability of Steady Motions, Editorial URSS, Moscow (1998). |
| 7. | A.S. Andreyev, The stability of the equilibrium position of a non-autonomous mechanical system, Prikl Mat Mekh 60 (3) (1996), pp. 388–396. |
| 8. | A.S. Andreyev and K. Rizito, The stability of generalized steady motion, Prikl Mat Mekh 66 (3) (2002), pp. 339–349. |
| 9. | Andreyev A.S, Boikova T.A. Sign-definite Lyapunov functions in stability problems. In Mechanics of a Rigid Body. Donetsk: Inst Prikl Mat Mekh; 2002; 32: 109–116. |
| 10. | A.S. Andreyev and O.A. Peregudova, The comparison method in asymptotic stability problems, Prikl Mat Mekh 70 (6) (2006), pp. 965–976. |
| 11. | Andreyev A.S, Zainetdinov R.B. On the stability of the generalized steady motion of a mechanical system as a function of the acting forces. In Proc 9-th Intern Chetayev Conference "Analytical Mechanics, Stability and Control of Motion" Dedicated to the 105-th Anniversary of N. G. Chetayev. Irkutsk: Inst Dinamiki Sistem i Teor Upravleniya; 2007: 1; 5–14. |
| 12. | V.V. Rumyantsev and A.S. Andreyev, Stabilization of the motion of an unsteady controlled system, Dokl Ross Akad Nauk 416 (5) (2007), pp. 627–629. |
| 13. | V.S. Novoselov, Analytical Mechanics of Systems with Variable Masses, Izd LGU, Leningrad (1969). |
| 14. | A.P. Markeyev, Theoretical Mechanics, Nauka, Moscow (1990). |
| 15. | A.S. Andreyev, The asymptotic stability and instability of the zeroth solution of a non- autonomous system, Prikl Mat Mekh 48 (2) (1984), pp. 225–232. |
| 16. | V.V. Beletskii, The Motion of an Artificial Satellite about its Centre of Mass, Nauka, Moscow (1965). |
|
| Received |
16 April 2008 |
| Link to Fulltext |
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