Reduction by Symmetries of Simple Hybrid Mechanical Systems

Abstract

Abstract This paper investigates reduction by symmetries in simple hybrid mechanical systems, in particular, symplectic and Poisson reduction for simple hybrid Hamiltonian and Lagrangian systems. We give general conditions for whether it is possible to perform a symplectic reduction for simple hybrid Lagrangian system under a Lie group of symmetries and we also provide sufficient conditions for performing the reduction by symmetries of hybrid Poisson manifolds for simple hybrid Hamiltonian systems.