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Title: Lagrangian Lie subalgebroids generating dynamics for second-order mechanical systems on Lie algebroids
Author: Abrunheiro, Lígia
Colombo, Leonardo
Keywords: Higher order mechanics
Lagrangian mechanics
Lagrangian submanifolds
Mechanics on Lie algebroids
Issue Date: 1-Apr-2018
Publisher: Springer Verlag
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”
Peer review: yes
DOI: 10.1007/s00009-018-1108-x
ISSN: 1660-5446
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Appears in Collections:CIDMA - Artigos

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