Study of the Planar Rocking-Block Dynamics With Coulomb Friction: Critical Kinetic Angles

Hongjian Zhang (1) , Bernard Brogliato (2) , Caishan Liu (1)

1 State Key Laboratory for Turbulence and Complex Systems [Beijing]
2 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems

The objective of this paper is to show, through the planar rocking block example, that kinetic angles play a fundamental role in multiple impact with friction. Even in the presence of Coulomb friction, a critical kinetic angle θcr is exhibited that allows one to split the blocks into two main classes: slender blocks with a kinetic angle larger than θcr, and flat blocks with a kinetic angle smaller than θcr. The value of θcr varies with the friction value, but it is independent of the restitution coefficient (normal dissipation). Numerical results are obtained using a multiple impact law recently introduced by the authors. Some comparisons between numerical and experimental results that validate the used model and numerical scheme are presented. However, this paper is mainly based on numerical simulations.

Domaines: Optimisation et contrôle [math.OC]

Hongjian Zhang, Bernard Brogliato, Caishan Liu. Study of the Planar Rocking-Block Dynamics With Coulomb Friction: Critical Kinetic Angles. Journal of Computational and Nonlinear Dynamics, 2013, 8 (2), pp.11. ⟨10.1115/1.4007056⟩. ⟨hal-00825590⟩