Solving problems with unilateral constraints by DAE methods

We study trajectories of mechanical systems with unilateral constraints under the additional assumption that always a given number of constraints is active. A reformulation as a problem with bilateral conditions yields a drastic reduction in the number of constraints, but in general, we are faced with regularity problems. We illustrate our approach in the special case of a dynamical rigid body contact problem. In particular, we present a regularization technique which leads to the definition of generalized solutions and a quite effective numerical method on the basis of algorithms for differential–algebraic systems. The results are applied to a wheel–rail contact problem of actual interest to railway engineers.