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Hybrid Cotangent Bundle Reduction of Simple Hybrid Mechanical Systems with Symmetry
Aaron Ames, Shankar Sastry

Citation
Aaron Ames, Shankar Sastry. "Hybrid Cotangent Bundle Reduction of Simple Hybrid Mechanical Systems with Symmetry". American Control Conference, June, 2006.

Abstract
This paper begins by introducing the notion of a simple hybrid mechanical system, which generalizes mechanical systems to include unilateral constraints on the configuration space. From such a system we obtain, explicitly, a simple hybrid system. The main contribution of this paper is to provide conditions on when it is possible to reduce the phase space of hybrid systems obtained from simple hybrid mechanical systems, and general simple hybrid systems, due to symmetries in the systems. Specifically, given a Hamiltonian G-space—-which is the ingredient needed to reduce continuous systems—-we find conditions on the hybrid system and the G-space so that reduction can be carried out in a hybrid setting—-conditions that are explicitly related to conditions on the original hybrid mechanical system.

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Citation formats  
  • HTML
    Aaron Ames, Shankar Sastry. <a
    href="http://chess.eecs.berkeley.edu/pubs/258.html"
    >Hybrid Cotangent Bundle Reduction of Simple Hybrid
    Mechanical Systems with Symmetry</a>, American Control
    Conference, June, 2006.
  • Plain text
    Aaron Ames, Shankar Sastry. "Hybrid Cotangent Bundle
    Reduction of Simple Hybrid Mechanical Systems with
    Symmetry". American Control Conference, June, 2006.
  • BibTeX
    @inproceedings{AmesSastry06_HybridCotangentBundleReductionOfSimpleHybridMechanical,
        author = {Aaron Ames and Shankar Sastry},
        title = {Hybrid Cotangent Bundle Reduction of Simple Hybrid
                  Mechanical Systems with Symmetry},
        booktitle = {American Control Conference},
        month = {June},
        year = {2006},
        abstract = {This paper begins by introducing the notion of a
                  simple hybrid mechanical system, which generalizes
                  mechanical systems to include unilateral
                  constraints on the configuration space. From such
                  a system we obtain, explicitly, a simple hybrid
                  system. The main contribution of this paper is to
                  provide conditions on when it is possible to
                  reduce the phase space of hybrid systems obtained
                  from simple hybrid mechanical systems, and general
                  simple hybrid systems, due to symmetries in the
                  systems. Specifically, given a Hamiltonian
                  G-spaceâ-which is the ingredient needed to
                  reduce continuous systemsâ-we find conditions on
                  the hybrid system and the G-space so that
                  reduction can be carried out in a hybrid
                  settingâ-conditions that are explicitly related
                  to conditions on the original hybrid mechanical
                  system.},
        URL = {http://chess.eecs.berkeley.edu/pubs/258.html}
    }
    

Posted by Aaron Ames on 16 May 2007.
Groups: chess
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