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The period on a family of non-linear oscillations and periodic motions of a perturbed system at a critical point of the family

✍ Scribed by V.N. Tkhai

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
307 KB
Volume
74
Category
Article
ISSN
0021-8928

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✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

First integrals and families of symmetri
First integrals and families of symmetric periodic motions of a reversible mechanical system
✍ V.N. Tkhai πŸ“‚ Article πŸ“… 2006 πŸ› Elsevier Science 🌐 English βš– 297 KB

A reversible mechanical system which allows of first integrals is studied. It is established that, for symmetric motions, the constants of the asymmetric integrals are equal to zero. The form of the integrals of a reversible linear periodic system corresponding to zero characteristic exponents and t