To conclude, the non-smooth approach changes the underlying mathematical structure if required and leads to a proper description of mechanical systems with unilateral contacts and friction. As a consequence of the changing mathematical structure, impacts can occur, and the time evolutions of the positions and the velocities can not be assumed to be smooth anymore. As a consequence, additional impact equations and impact laws have to be defined. In order to handle the changing mathematical structure, the set-valued force laws are commonly written as inequality or inclusion problems. The evaluation of these inequalities/inclusions is commonly done by solving linear (or nonlinear) complementarity problems, by quadratic programming or by transforming the inequality/inclusion problems into projective equations which can be solved iteratively by Jacobi or Gauss–Seidel techniques. The non-smooth approach provides a new modeling approach for mechanical systems with unilateral contacts and friction, which incorporates also the whole classical mechanics subjected to bilateral constraints. The approach is associated to the classical DAE theory and leads to robust integration schemes.