Çiftçi, ÜnverWaalkens, HolgerBroer, Henk W.2022-05-112022-05-1120140167-27891872-8022https://doi.org/10.1016/j.physd.2013.10.007https://hdl.handle.net/20.500.11776/7377In 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.en10.1016/j.physd.2013.10.007info:eu-repo/semantics/openAccessSymplectic reductionHamiltonian systemsRelative equilibriaRelative EquilibriaPhase-SpaceInternal MotionsSystemsStabilitySymmetryOrbitsEnergyArticle268113Q1WOS:0003299577000012-s2.0-84896506248Q1