Dynamics of a particle with friction and delay

We are interested in the motion of a simple mechanical system having a finite number of degrees of freedom subjected to a unilateral constraint with dry friction and delay effects (with maximal duration $\tau >0$). At the contact point, we characterize the friction by a Coulomb law associated with a friction cone. Starting from a formulation of the problem that was given by Jean-Jacques Moreau in the form of a second-order differential inclusion in the sense of measures, we consider a sweeping process algorithm that converges towards a solution to the dynamical contact problem. The mathematical machinery as well as the general plan of the existence proof may seem much too heavy in order to treat just this simple case, but they have proved useful in more complex settings.