Dynamic impact of a particle

Abstract

In this work, we consider a moving particle which drops down onto a stationary rigid foundation and bounces off after its contact. The equation of its motion is formulated by a second-order ordinary differential equation. The particle satisfies the Signorini contact conditions which can be interpreted in terms of complementarity conditions. The existence of weak solutions is shown by using a finite time step and the necessary a priori estimates which allow us to pass to the limit. The uniqueness of the solutions can be proved under some additional assumptions. Conservation of energy is also investigated theoretically and numerically. Numerical solutions are computed via both finite- and infinite-dimensional approaches.