Existence results for non-smooth second order differential inclusions, Convergence result for a numerical scheme and applications for modelling inelastic collisions

TL;DR

This paper establishes existence results for non-smooth second order differential inclusions with unilateral constraints, extends a numerical scheme with convergence proof, and applies these findings to model inelastic collisions between rigid particles.

Contribution

It provides new existence results for differential inclusions with unilateral constraints, extends a numerical scheme with proven convergence, and applies these methods to inelastic collision modeling.

Findings

Proved existence of solutions for non-smooth second order differential inclusions.

Extended and validated a numerical scheme with convergence guarantees.

Applied the theoretical framework to model inelastic collisions in rigid particles.

Abstract

We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal normal cone to a time-dependent set. Moreover we extend a numerical scheme, introduced in [8] and proved a convergence result. We propose applications in modelling inelastic collisions between rigid particles too.