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Hybrid Cotangent Bundle Reduction of Simple Hybrid Mechanical Systems with Symmetry
 

Summary: Hybrid Cotangent Bundle Reduction of Simple Hybrid Mechanical
Systems with Symmetry
Aaron D. Ames and Shankar Sastry
Department of Electrical Engineering and Computer Sciences
University of California at Berkeley
Berkeley, CA 94720
{adames,sastry}@eecs.berkeley.edu
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

  

Source: Ames, Aaron - Department of Mechanical Engineering, Texas A&M University

 

Collections: Engineering