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 $\mathcal{S}\text{/}$ by introducing a suitable instantaneous kinetic constraint $\mathcal{B}\text{/}\subset \mathcal{S}\text{/}$. A constitutive characterization of $\mathcal{B}\text{/}$ 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 $\mathcal{S}\text{/}$ in an impact of the system. Such a model restores determinism and avoids the analysis of frictional forces in the contact point, with all its associated theoretical problems of causality. Three examples of increasing complexity, showing a natural stick–slip behavior of the impact, are presented.