Measure-Differential Inclusions in Percussional Dynamics

We give an existence result for the dynamics of a system of particles moving on a line in a horizontal plane and subjected to friction, to percussional effects, to stiffness and to damping. The novelty in our study is that the normal reaction is expressed by a measure, incorporating a series of Dirac measures. The velocity is a function of bounded variation and the acceleration is its Stieltjes measure. Together with the tangential reaction — which is also a measure — they must satisfy a measure-differential inclusion formulation of friction. Convex analysis, variational inequalities and measure theory are used in the existence proof.