The Idea of Complementarity in Multibody Dynamics

Considered in a straightforward manner multibody systems with many multiple unilateral contacts involve a combinatorial problem of huge dimensions, which can only be solved reasonably by the introduction of the complementarity idea. It states that for unilateral contacts either relative kinematics is zero and the corresponding constraint forces are not zero, or vice versa. This leads to a complementarity problem which is somehow related to linear programming problems. Paper discusses the theoretical and practical background.