Summary: Hybrid Geometric Reduction of Hybrid Systems
Aaron D. Ames and Shankar Sastry
Abstract-- This paper presents a unifying framework in
which to carry out the hybrid geometric reduction of hybrid
systems, generalizing classical reduction to a hybrid setting.
The reduction of mechanical systems with symmetries
plays a fundamental role in understanding the many im-
portant and interesting properties of these systems. Given a
Hamiltonian on a symplectic manifold (the phase space) on
which a Lie group acts symplectically, the main geometric re-
duction theorem  states that under certain conditions one
can reduce the phase space to another symplectic manifold by
"dividing out" by the symmetries. In addition, trajectories of
the Hamiltonian on the phase space determine corresponding
trajectories on the reduced space.
The goal of this paper is to generalize this result to a
hybrid setting--a formidable obstacle to which is the copi-
ous mathematical framework needed to perform reduction.
Such a generalization of reduction, therefore, requires a