Journal of Applied Mathematics and Mechanics (about journal) 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
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IssuesArchive of Issues2010-5pp.579-586

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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
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