Projection-based modeling and simulation of nonsmooth Hamiltonian mechanics

This paper extends projection-based formulations of nonsmooth mechanics to the Hamiltonian setting, where projection mappings may be defined in terms of phase information. The projection-based approach embeds the presence of unilateral constraints into a projection mapping and yields models with greater smoothness properties relative to classical representations. Herein, we establish sufficient conditions by which a projection-based model will remain Hamiltonian as well as conditions by which solutions will be C¹ smooth. In combination, these results identify a means to impart the geometric structure of unconstrained smooth mechanics to nonsmooth mechanical systems and enable the use of smooth simulation and control techniques.