Variational nonsmooth mechanics via a projected Hamilton´s principle

This paper presents a projection-based variational formulation of nonsmooth mechanics. In contrast to existing approaches, nonsmooth behavior is captured through the use of a projection mapping on the configuration space. After clearly defining a projected Hamilton´s principle, our main focus is on the existence of admissible projection mappings and variational solutions. This lays the foundation necessary for a variety of useful future developments, which includes optimization techniques, stochastic nonsmooth mechanical system models, and integrator symplecticity proofs.