Symmetry and reduction in implicit generalized Hamiltonian systems

In this paper we study the notion of symmetry for implicit generalized Hamiltonian systems, which are Hamiltonian systems with respect to a generalized Dirac structure. We investigate the reduction of these systems admitting a symmetry Lie group with corresponding quantities. Main features in this a...

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Bibliographic Details
Published in:Reports on mathematical physics 2001-02, Vol.47 (1), p.57-100
Main Authors: Blankenstein, G., van der Schaft, A.J.
Format: Article
Language:English
Subjects:
constraints
Dirac structures
Hamiltonian systems
implicit systems
reduction
symmetry
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Summary:In this paper we study the notion of symmetry for implicit generalized Hamiltonian systems, which are Hamiltonian systems with respect to a generalized Dirac structure. We investigate the reduction of these systems admitting a symmetry Lie group with corresponding quantities. Main features in this approach concern the projection and restriction of Dirac structures, generalizing the corresponding theory for symplectic forms and Poisson brackets. The results are applied to the theory of symmetries and reduction in nonholonomically constrained mechanical systems. The main result extends the reduction theory for explicit Hamiltonian systems and constrained mechanical systems to a general unified reduction theory for implicit generalized Hamiltonian systems.
ISSN:0034-4877
1879-0674
DOI:10.1016/S0034-4877(01)90006-0