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

In this paper a new-time-stepping method for simulating systems of rig id bodies is given which incorporates Coulomb friction and inelastic i mpacts and shocks. Unlike-other methods which take an instantaneous po int of view, this method does not need to identify explicitly impulsiv e forces. instead, the treatment is similar to that of J. J. Moreau an d Monteiro-Marques, except that the numerical formulation used here en sures; that there is no inter-penetration of rigid bodies, unlike thei r velocity-based formulation. Numerical results are given for the meth od presented here for a spinning rod impacting a table in two dimensio ns, and a system of four balls colliding on a table in a fully three-d imensional way. These numerical results also show the practicality of the method, and convergence of the method as the step size becomes sma ll.