Non-Holonomic Systems with Symmetry Allowing a Conformally Symplectic Reduction

Pedro de M. Rios () and Jair Koiller ()
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Pedro de M. Rios: Laboratório Nacional de Computaçāo Cientifica
Jair Koiller: Laboratório Nacional de Computaçāo Cientifica

A chapter in New Advances in Celestial Mechanics and Hamiltonian Systems, 2004, pp 239-252 from Springer

Abstract: 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]).

Keywords: Non-holonomic systems; almost Poisson structures (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-9058-7_15

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DOI: 10.1007/978-1-4419-9058-7_15

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