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Acta Applicandae Mathematica

, Volume 67, Issue 3, pp 295–320 | Cite as

Lagrangian Mechanics on Lie Algebroids

  • Eduardo Martínez
Article

Abstract

A geometric description of Lagrangian Mechanics on Lie algebroids is developed in a parallel way to the usual formalism of Lagrangian Mechanics on the tangent bundle of a manifold. The dynamical system defined by a Lagrangian is shown to be symplectic in a generalized sense.

Lagrangian mechanics Lie algebroids 

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References

  1. 1.
    Cariñena, J. F., López, C. and Martínez, E.: A new approach to the converse of Noether's theorem, J. Phys. A: Math. Gen. 22 (1989), 4777-4786.Google Scholar
  2. 2.
    Crampin, M.: Tangent bundle geometry for Lagrangian dynamics, J. Phys. A: Math. Gen. 16 (1983), 3755-3772.Google Scholar
  3. 3.
    Grifone, J.: Structure presque tangente et connections, Ann. Inst. Fourier 22(1) (1972), 287-334.Google Scholar
  4. 4.
    Klein, J.: Espaces variationnels et mécanique, Ann. Inst. Fourier 12 (1962), 1-124.Google Scholar
  5. 5.
    Liberman, P.: Lie algebroids and mechanics, Arch. Math. (Brno) 32 (1996), 147-162.Google Scholar
  6. 6.
    Higgins, P. J. and Mackenzie, K.: Algebraic constructions in the category of Lie algebroids, J. Algebra 129 (1990), 194-230.Google Scholar
  7. 7.
    Martínez, E. and Cariñena, J. F.: Geometric characterization of linearizable second-order differential equations, Math. Proc. Cambridge Philos. Soc. 119 (1996), 373-381.Google Scholar
  8. 8.
    Martínez, E.: Hamiltonian mechanics on Lie algebroids, Preprint.Google Scholar
  9. 9.
    Nijenhuis, A.: Vector forms brackets in Lie algebroids, Arch.Math. (Brno) 32(1996), 317-323.Google Scholar
  10. 10.
    Weinstein, A.: Lagrangian mechanics and groupoids, Fields Inst. Comm. 7 (1996), 207-231.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Eduardo Martínez
    • 1
  1. 1.Departamento de Matemática Aplicada, Centro Politécnico Superior de IngenieríaUniversidad de ZaragozaZaragozaSpain

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