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Rolling contacts are usual in various technical systems and yield usually non-holonomic constraints. A new regularization method motivated by physical considerations is investigated in the present paper. The convergence of the spring-damper regularization for the so called principal damping, which is motivated by the critical damping in the linear case, is proven. The solutions of the DAEs and the corresponding ODEs converge if a certain condition on the regularization parameters is fulfilled. A rolling disc on the flat plane and a skate on an inclined plane are analyzed as numerical examples. It is demonstrated firstly that the optimal choice of the regularization parameters corresponds to the principle damping and secondly that the sufficient convergence condition obtained in the proof is valid for the numeric simulations.

Regularization, Nonholonomic constraints, DAEs, Convergence