Section: New Results

Multiple impacts modelling

Participants : Bernard Brogliato, Ngoc-Son Nguyen.

The work consists of studying two systems: the rocking block and tapered chains of balls, using the Darboux-Keller model of multiple impacts previously developed. The objectives are threefold: 1) show that the model predicts well the motion by careful comparisons with experimental data found in the literature, 2) study the system's dynamics and extract critical kinetic angles that allow the engineer to predict the system's gross motion, 3) develop numerical code inside the siconos platform that incorporates the model of multiple impact. Other works consist of analysing kinematic restitution laws based on the use of the kinetic energy metric. We also performed an analysis of the rocking block motion in terms of the kinetic angles between the two unilateral constraints. Results are in [21] , [22] [55] . Another work is dedicated to analysing the influence of bilateral holonomic constraints on the well-posedness of the complementarity problem obtained from the (frictionless) unilateral constraints. Gauss' principle extension to this case is also analysed [20] .