Hybrid Lagrangian and Hamiltonian Reduction of Simple Hybrid Systems
Aaron Ames, Shankar Sastry

Citation
Aaron Ames, Shankar Sastry. "Hybrid Lagrangian and Hamiltonian Reduction of Simple Hybrid Systems". Unpublished article, 2006.

Abstract
This paper extends Lagrangian and Hamiltonian reduction to a hybrid setting, i.e., to systems that display both continuous and discrete behavior. We begin by considering Lagrangians and simple mechanical systems together with unilateral constraints on the set of admissible configurations; this naturally yields the notion of a hybrid Lagrangian and a simple hybrid mechanical system. From such systems we obtain, explicitly, simple hybrid systems. We give conditions on when it is possible to reduce a hybrid system obtained from a cyclic hybrid Lagrangian, and we explicitly compute the reduced hybrid system---we perform hybrid Routhian (or Lagrangian) reduction. We then turn our attention to a more general form of reduction: hybrid Hamiltonian reduction. The main result of this paper is explicit conditions on when it is possible to reduce the phase space of simple hybrid systems due to symmetries in the system; given a Hamiltonian G-space (which is the ingredient needed to reduce a continuous system), we find conditions on the hybrid system and G-space so that reduction can be carried out in a hybrid setting.

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• HTML

  Aaron Ames, Shankar Sastry. <a
  href="http://chess.eecs.berkeley.edu/pubs/126.html"
  ><i>Hybrid Lagrangian and Hamiltonian Reduction of
  Simple Hybrid Systems</i></a>, Unpublished
  article,  2006.

• Plain text

  Aaron Ames, Shankar Sastry. "Hybrid Lagrangian and
  Hamiltonian Reduction of Simple Hybrid Systems".
  Unpublished article,  2006.

• BibTeX

  @unpublished{AmesSastry06_HybridLagrangianHamiltonianReductionOfSimpleHybridSystems,
      author = {Aaron Ames and Shankar Sastry},
      title = {Hybrid Lagrangian and Hamiltonian Reduction of
                Simple Hybrid Systems},
      year = {2006},
      abstract = {This paper extends Lagrangian and Hamiltonian
                reduction to a hybrid setting, i.e., to systems
                that display both continuous and discrete
                behavior. We begin by considering Lagrangians and
                simple mechanical systems together with unilateral
                constraints on the set of admissible
                configurations; this naturally yields the notion
                of a hybrid Lagrangian and a simple hybrid
                mechanical system. From such systems we obtain,
                explicitly, simple hybrid systems. We give
                conditions on when it is possible to reduce a
                hybrid system obtained from a cyclic hybrid
                Lagrangian, and we explicitly compute the reduced
                hybrid system---we perform hybrid Routhian (or
                Lagrangian) reduction. We then turn our attention
                to a more general form of reduction: hybrid
                Hamiltonian reduction. The main result of this
                paper is explicit conditions on when it is
                possible to reduce the phase space of simple
                hybrid systems due to symmetries in the system;
                given a Hamiltonian G-space (which is the
                ingredient needed to reduce a continuous system),
                we find conditions on the hybrid system and
                G-space so that reduction can be carried out in a
                hybrid setting.},
      URL = {http://chess.eecs.berkeley.edu/pubs/126.html}
  }
  

Posted by Aaron Ames on 15 May 2006.
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