Hybrid cotangent bundle reduction of simple hybrid mechanical systems with symmetry

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 minus; 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.