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Non-Holonomic Systems with Symmetry Allowing a Conformally Symplectic Reduction

In: New Advances in Celestial Mechanics and Hamiltonian Systems

Author

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  • Pedro de M. Rios

    (Laboratório Nacional de Computaçāo Cientifica)

  • Jair Koiller

    (Laboratório Nacional de Computaçāo Cientifica)

Abstract

Non-holonomic mechanical systems can be described by a degenerate almostPoisson structure [10] (dropping the Jacobi identity) in the constrained space. If enough symmetries transversal to the constraints are present, the system reduces to a nondegenerate almost-Poisson structure on a “compressed” space. Here we show, in the simplest non-holonomic systems, that in favorable circumnstances the compressed system is conformally symplectic, although the “noncompressed” constrained system never admits a Jacobi structure (in the sense of Marie et al. [4] [9]).

Suggested Citation

  • Pedro de M. Rios & Jair Koiller, 2004. "Non-Holonomic Systems with Symmetry Allowing a Conformally Symplectic Reduction," Springer Books, in: J. Delgado & E. A. Lacomba & J. Llibre & E. Pérez-Chavela (ed.), New Advances in Celestial Mechanics and Hamiltonian Systems, pages 239-252, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-9058-7_15
    DOI: 10.1007/978-1-4419-9058-7_15
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