 | | 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 (ΟΜΜ): | | 9723
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| In English (J. Appl. Math. Mech.): | | 799 |
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| V.N. Tkhai, "The period on a family of non-linear oscillations and periodic motions of a perturbed system at a critical point of the family," J. Appl. Math. Mech. 74 (5), 579-586 (2010) |
| Year |
2010 |
Volume |
74 |
Issue |
5 |
Pages |
579-586 |
| Title |
The period on a family of non-linear oscillations and periodic motions of a perturbed system at a critical point of the family |
| Author(s) |
V.N. Tkhai (Moscow, Russia, tkhaivn@yandex.ru) |
| Abstract |
Single-frequency oscillations of a reversible mechanical system are considered. It is shown that the oscillation period of a non-linear system usually only depends on a single parameter and it is established that, at a critical point of the family, at which the derivative of the period with respect to the parameter vanishes, due to the action of perturbations two families of symmetrical resonance periodic motions are produced. The oscillations of a satellite in an elliptic orbit, due to the action of gravitational and aerodynamic moments, are considered as an example. The operations in a circular orbit are investigated in detail initially, and then in an elliptical orbit of small eccentricity. |
| Received |
02 November 2009 |
| Link to Fulltext |
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