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arXiv · 1211.5752

Cotangent bundle reduction and Poincar\'e-Birkhoff normal forms

Ünver Çiftçi·Holger Waalkens·Henk Broer
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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 Poincar{\'e}-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 Poincar{\'e}-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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Ünver Çiftçi, Holger Waalkens, Henk Broer. 2012-11-25. Cotangent bundle reduction and Poincar\'e-Birkhoff normal forms. https://arxiv.org/abs/1211.5752

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