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].
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
(Accepted January 26, 1998)
Rights and permissions
About this article
Cite this article
Stewart, D. Convergence of a Time‐Stepping Scheme for Rigid‐Body Dynamics and Resolution of Painlevé's Problem. Arch Rational Mech Anal 145, 215–260 (1998). https://doi.org/10.1007/s002050050129
Issue Date:
DOI: https://doi.org/10.1007/s002050050129