NONLINEAR OSCILLATIONS OF REVERSIBLE-SYSTEMS

Authors
Citation
Vn. Tkhai, NONLINEAR OSCILLATIONS OF REVERSIBLE-SYSTEMS, Journal of applied mathematics and mechanics, 59(1), 1995, pp. 35-45
Citations number
8
Categorie Soggetti
Mathematics,Mathematics,Mechanics
ISSN journal
00218928
Volume
59
Issue
1
Year of publication
1995
Pages
35 - 45
Database
ISI
SICI code
0021-8928(1995)59:1<35:NOOR>2.0.ZU;2-Z
Abstract
A reversible system with a small parameter mu is considered. When mu = 0 the generating system has a periodic motion, symmetric to a fixed s et of the system automorphism. It is shown that this periodic motion i s continued with respect to a small parameter in the Poincare-unisolat ed case when certain conditions are satisfied only on the generating s ystem. Symmetric periodic solutions are constructed both for a non-res onant and for a resonant system. In the plane unrestricted three-body problem the small parameter is chosen to be the quantity characterizin g the interaction between two bodies chosen from the three. It is show n that in this problem there are solutions in which the body moves alo ng curves close to circles. The problem of the applicability of the re sult to a sun-earth-moon type is discussed.