On non-smooth multibody dynamics

Abstract

Contacts include the properties contact/detachment and stick/slip. In multibody systems, these features generate a combinatorial problem of large order. It can be solved by the introduction of the complementarity idea, which relates relative kinematics and constraint forces in a contact by inequality constraints in a non-smooth way. Mathematically, these complementarity inequalities can be replaced by an augmented Lagrange approach applying methods from set theory. This article gives a survey of this evolution. It presents the theoretical fundaments for such systems and considers some practical examples of industrial relevancy.