AN IMPLICIT TIME-STEPPING SCHEME FOR RIGID BODY DYNAMICS WITH INELASTIC COLLISIONS AND COULOMB FRICTION

TLDR

The method builds on Moreau and Monteiro‑Marques’ framework but uses a numerical formulation that guarantees no inter‑penetration of rigid bodies, unlike their velocity‑based approach. This paper introduces a new time‑stepping scheme for rigid‑body simulations that incorporates Coulomb friction and inelastic impacts and shocks. The scheme avoids explicit identification of impulsive forces by treating collisions implicitly, thereby eliminating the need for instantaneous force calculations. Numerical experiments on a spinning rod and a four‑ball system confirm the method’s practicality and show convergence as the time step is reduced.

Abstract

In this paper a new time-stepping method for simulating systems of rigid bodies is given which incorporates Coulomb friction and inelastic impacts and shocks. Unlike other methods which take an instantaneous point of view, this method does not need to identify explicitly impulsive forces. Instead, the treatment is similar to that of J. J. Moreau and Monteiro-Marques, except that the numerical formulation used here ensures that there is no inter-penetration of rigid bodies, unlike their velocity-based formulation. Numerical results are given for the method presented here for a spinning rod impacting a table in two dimensions, and a system of four balls colliding on a table in a fully three-dimensional way. These numerical results also show the practicality of the method, and convergence of the method as the step size becomes small.