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Reduction of Lagrangian mechanics on Lie algebroids

Authors
Journal
Journal of Geometry and Physics
0393-0440
Publisher
Elsevier
Publication Date
Volume
57
Issue
3
Identifiers
DOI: 10.1016/j.geomphys.2006.08.001
Keywords
  • Reduction
  • Lie Algebroids
  • Lagrangian Mechanics
Disciplines
  • Mathematics

Abstract

Abstract We prove that if a surjective submersion which is a homomorphism of Lie algebroids is given, then there exists another homomorphism between the corresponding prolonged Lie algebroids and a relation between the dynamics on these Lie algebroid prolongations is established. We also propose a geometric reduction method for dynamics on Lie algebroids defined by a Lagrangian and the method is applied to regular Lagrangian systems with nonholonomic constraints.

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