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Lagrangian Lie Subalgebroids Generating Dynamics for Second-Order Mechanical Systems on Lie Algebroids

  • Lígia Abrunheiro
  • Leonardo Colombo
Article
  • 32 Downloads

Abstract

The study of mechanical systems on Lie algebroids permits an understanding of the dynamics described by a Lagrangian or Hamiltonian function for a wide range of mechanical systems in a unified framework. Systems defined in tangent bundles, Lie algebras, principal bundles, reduced systems, and constrained are included in such description. In this paper, we investigate how to derive the dynamics associated with a Lagrangian system defined on the set of admissible elements of a given Lie algebroid using Tulczyjew’s triple on Lie algebroids and constructing a Lagrangian Lie subalgebroid of a symplectic Lie algebroid, by building on the geometric formalism for mechanics on Lie algebroids developed by M. de León, J.C. Marrero and E. Martínez on “Lagrangian submanifolds and dynamics on Lie algebroids”.

Keywords

Mechanics on Lie algebroids Higher order mechanics Lagrangian mechanics Lagrangian submanifolds 

Mathematics Subject Classification

Primary 53D12 70H50 53D17 Secondary 70H03 37J15 53D05 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Research and Development in Mathematics and ApplicationsISCA, Universidade de AveiroAveiroPortugal
  2. 2.Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM)MadridSpain

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