Geometric characterization of frictional impacts by means of breakable kinetic constraints

TL;DR

This paper introduces a geometric approach to model frictional impacts in mechanical systems using breakable kinetic constraints, simplifying analysis by avoiding complex friction force calculations.

Contribution

It proposes a novel geometric characterization of frictional impacts through breakable kinetic constraints, enhancing determinism and simplifying impact analysis.

Findings

Model captures stick-slip behavior naturally

Restores determinism in impact analysis

Avoids complex friction force calculations

Abstract

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 ${\mathcal S\/}$ by introducing a suitable instantaneous kinetic constraint ${\mathcal B\/}\subset {\mathcal S\/}$. A constitutive characterization of ${\mathcal B\/}$ 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 ${\mathcal S\/}$ 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.