Geometric characterization of frictional impacts by means of breakable kinetic constraints

In the context of geometric impulsive mechanics of systems with a finite number of degrees of freedom, we model the roughness of a unilateral constraint S by introducing a suitable instantaneous kinetic constraint 13 c S. A constitutive characterization of 13 based only on the geometric properties of the setup and on the dry friction laws can then be introduced to model the frictional behavior of S in an impact of the system. Such a model restores determinism and avoids the analysis of frictional forces in the contact point. Furthermore, since the characterization of impulsive friction is specified solely by two numerical coefficients, the model allows for the study of a wide class of rough constraints. Three examples of increasing complexity, showing a natural stick-slip behavior of the impact, are presented.