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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• HTML

  Aaron Ames, Shankar Sastry. <a
  href="http://chess.eecs.berkeley.edu/pubs/129.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-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.},
      URL = {http://chess.eecs.berkeley.edu/pubs/129.html}
  }
  

Posted by Aaron Ames on 15 May 2006.
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