Cotangent bundle reduction and Poincaré-Birkhoff normal forms

2012/11/25 by Ünver Çiftçi, Çiftçi, Ünver, Holger Waalkens +3
Mathematics · Physics and Astronomy · #53C80 #70F07 #70G65 #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DS #math.MP #msc:53C80 #msc:70F07 #msc:70G65 #nlin.CD

paper · pdf · doi:10.48550/arxiv.1211.5752

34 pages, 7 figures

arxiv created 2012/11/25 · arxiv updated 2012/11/27

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 Poincaré-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 Poincaré-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.

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