Cotangent bundle reduction and Poincare-Birkhoff normal forms
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Date
2014
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Access Rights
info:eu-repo/semantics/openAccess
Abstract
In this paper we study a systematic and natural construction of canonical coordinates for the reduced space of a cotangent bundle with a free Lie group action. The canonical coordinates enable us to compute Poincare-Birkhoff normal forms of relative equilibria using standard algorithms. The case of simple mechanical systems with symmetries is studied in detail. As examples we compute Poincare-Birkhoff normal forms for a Lagrangian equilateral triangle configuration of a three-body system with a Morse-type potential and the stretched-out configuration of a double spherical pendulum. (C) 2013 Elsevier B.V. All rights reserved.
Description
Keywords
Symplectic reduction, Hamiltonian systems, Relative equilibria, Relative Equilibria, Phase-Space, Internal Motions, Systems, Stability, Symmetry, Orbits, Energy
Journal or Series
Physica D-Nonlinear Phenomena
WoS Q Value
Q1
Scopus Q Value
Q1
Volume
268
