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Hierarchy of Periodic Solutions for Hamiltonian Systems and their Applications to Celestial Mechanics

Published online by Cambridge University Press:  12 April 2016

Yu.V. Barkin
Yu.V. Barkin*
Affiliation:
Moscow State Technical University, Chair of Theoretical Mechanics, 52nd Bauman Street, Moscow, Russia

Abstract

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A systematic investigation has been carried out for periodic solutions for standard-form Hamiltonian systems containing a small parameter/the principal problem of dynamics/. An efficient method of investigation of conditions for periodicity of solutions has been developed. Besides fitting the initial conditions of the action-angle variables, the idea of fitting the values of the parameters of the problem is used. Constructive conditions are obtained for the existence of periodic solutions in both principal and degenerate cases, as well as necessary conditions for their stability; algorithms have been developed for constructing these solutions as series in integer powers of the small parameter. To study particular periodic solutions /by high order resonances/, canonical transformations of the initial equations to a special form are used.

Type
Part V General Celestial Mechanics and Stellar Dynamics
Information
International Astronomical Union Colloquium , Volume 132: Instability, Chaos and Predictability in Celestial Mechanics and Stellar Dynamics , 1993 , pp. 323 - 337
Copyright
Copyright © Nova Science Publishers 1993

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