NDLI: On nonlinear motions of Hamiltonian system in case of fourth order resonance

Content Provider	Springer Nature Link
Author	Bardin, B. S.
Copyright Year	2007
Abstract	We deal with an autonomous Hamiltonian system with two degrees of freedom. We assume that the Hamiltonian function is analytic in a neighborhood of the phase space origin, which is an equilibrium point. We consider the case when two imaginary eigenvalues of the matrix of the linearized system are in the ratio 3: 1. We study nonlinear conditionally periodic motions of the system in the vicinity of the equilibrium point. Omitting the terms of order higher then five in the normalized Hamiltonian we analyze the so-called truncated system in detail. We show that its general solution can be given in terms of elliptic integrals and elliptic functions. The motions of truncated system are either periodic, or asymptotic to a periodic one, or conditionally periodic. By using the KAM theory methods we show that most of the conditionally periodic trajectories of the truncated systems persist also in the full system. Moreover, the trajectories that are not conditionally periodic in the full system belong to a subset of exponentially small measure. The results of the study are applied for the analysis of nonlinear motions of a symmetric satellite in a neighborhood of its cylindric precession.
Starting Page	86
Ending Page	100
Page Count	15
File Format	PDF
ISSN	15603547
Journal	Regular and Chaotic Dynamics
Volume Number	12
Issue Number	1
e-ISSN	14684845
Language	English
Publisher	Nauka/Interperiodica
Publisher Date	2007-01-01
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hamiltonian system periodic orbits normal form resonance action-angle variables KAM theory Dynamical Systems and Ergodic Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Statistical and Nonlinear Physics Mathematical Physics Mechanical Engineering Modeling and Simulation

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