The assumption of the existence of rigid bodies is widely used in the field of mechanical engineering in order to simplify he mathematical equation describing the problem and to reduce computational effort. If some bilateral constraints of system are non-smooth and the friction force is determined by Coulomb's law, analytical solutions might not exist or might not be unique depending on the initial conditions, the friction force magnitude and the system geometry. This paradox was first discovered by the French scientist and prime minister Paul Painlevé in the late 19th century and is today known as Painlevé's Paradox. System like the shown Painlevé-Klein-System behave in such a paradoxical way for a certain set of parameters.

The main task of this research project is to find an explicit description and indicator for the appearance of such paradoxical situations in order to avoid misleading results. The indicator must work fro holonomic as well as non-holonomic bilateral constraints. As such problems are especially dangerous for "black box" multibody algorithms, the description must include a formalism used by such tools. In a second stage, a physical explanation for the real system behavior must be given under relaxation of either the classical Coulomb law (von Mises's Approach) or under relaxation of the assumption of rigidity (Prandtl's approach).