On nonlinear motions of a Hamiltonian system in the case of external resonance
type: Item
instance of: scholarly article
title: On nonlinear motions of a Hamiltonian system in the case of external resonance
zbMATH Open document ID: 1016.37027
DOI: 10.1016/S0034-4877(02)80013-1
author: Boris S. Bardin
published in: Reports on Mathematical Physics
publication date: 2003-01-22T00:00:00Z
review text: A nonlinear conservative Hamiltonian system with one degree of freedom subjected to a small periodic perturbation with external resonance is considered. It is investigated the case of \(2\pi\)-periodic solutions bifurcation together with stability of bifurcating solutions. The normal forms method and KAM theory is used. The obtained results are applied to the problem of satellite planar motions in an elliptic orbit.
Mathematics Subject Classification ID: 37J20
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 70K30
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 70H12
zbMATH DE Number: 1857350
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: periodic solutions
zbMATH Keywords: nonlinear oscillations
zbMATH Keywords: stability
zbMATH Keywords: perturbation with external resonance
zbMATH Keywords: normal forms
zbMATH Keywords: KAM theory
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
cites work: Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
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cites work: The motion of a system close to Hamiltonian with one degree of freedom when there is resonance in forced vibrations
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description: scientific article; zbMATH DE number 1857350