The period on a family of non-linear oscillations and periodic motions of a perturbed system at a critical point of the family |
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| Authors: | VN Tkhai |
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| Institution: | 1. Tokyo Metropolitan University, Department of Aerospace Engineering, 6-6 Asahigaoka, Hino, Tokyo 191-0065, Japan;2. JSAT Corporation, Japan;1. LAMIH, UMR CNRS 8530, Université de Valenciennes, Le Mont-Houy, 59313 Valenciennes Cedex 9, France;2. LAGIS, UMR CNRS 8146, Ecole Centrale de Lille, Cité Scientifique, BP 48, 59651 Villeneuve d’Ascq Cedex, France;3. Faculty of Mathematics and Computer Science, University of Sofia, 5, J. Bouchier str., 1126 Sofia, Bulgaria;1. Service de pneumologie, Nouvel Hôpital Civil, 67091 Strasbourg cedex. Groupe tuberculose de la SPLF;2. Service de Pneumologie, Centre de Lutte Antituberculeuse, CH de Chambéry, 7 square Massalaz, BP1125, 73011 Chambéry |
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| 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. |
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