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

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 c ounterexamples of PAINLEVE. The mathematical basis for this work is the for mulation of the rigid-body problem in terms of measure differential inclusi ons of MOREAU and MONTEIRO MARQUES. The implicit time-stepping method is ba sed on complementarity problems, and is essentially a particular case of th e algorithm described in ANITESCU & POTRA [2], which in turn is based on th e formulation in STEWART Sr TRINKLE [47].