Convergence of a time-stepping scheme for rigid-body dynamics and resolution of Painlevé's problem

Abstract

This paper gives convergence theory for a new implicit time-stepping scheme for general rigid-body dynamics with Coulomb friction and purely inelastic collisions and shocks. An important consequence of this work is the proof of existence of solutions of rigid-body problems which include the famous counterexamples of PAINLEVÉ. The mathematical basis for this work is the formulation of the rigid-body problem in terms of measure differential inclusions of MOREAU and MONTEIRO MARQUES. The implicit time-stepping method is based on complementarity problems, and is essentially a particular case of the algorithm described in ANITESCU & POTRA [2], which in turn is based on the formulation in STEWART & TRINKLE [47].