During the last four decades, the field of Mechanical Systems has developed from classical analytical mechanics to an independent and important branch in mechanics to satisfy the growing needs arising in complex practical application problems. It comprises aspects like the mechanical modeling of systems with respect to their dynamics, formalization and structuring of the dynamical equations, and their numerical implementation and evaluation. Mechanical Systems thus extends from analytical to computational mechanics with strong emphasis on applied mechanics. Classical mechanics relies on the differentiability of mappings and thus denies a proper treatment of discontinuity events as impacts or stick-slip transitions. Non-smooth dynamics, a new area of basic research that is developing and spreading at high speed, takes care of such events by fully incorporating them into general concepts on how to deal with inequalities. A central point in our research is dedicated to this kind of problems in finite freedom dynamics. In particular, we are interested in theoretical and practical questions concerning the mechanical modeling, the mathematical formulation, and the numerical treatment of systems with discontinuities, as well as their application to problems in industry.