Hybrid Routhian reduction of Lagrangian hybrid systems

This paper extends Routhian reduction to a hybrid setting, i.e., to systems that display both continuous and discrete behavior. We begin by considering a Lagrangian together with a configuration space with unilateral constraints on the set of admissible configurations. This naturally yields the notion of a hybrid Lagrangian, from which we obtain a Lagrangian hybrid system in a way analogous to the association of a Lagrangian vector field to a Lagrangian. We first give general conditions on when it is possible to reduce a cyclic Lagrangian hybrid system, and explicitly compute the reduced Lagrangian hybrid system in the case when it is obtained from a cyclic hybrid Lagrangian