A time - stepping method for sti + multibody dynamics with contact and friction ‡ 3

We de8ne a time-stepping procedure to integrate the equations of motion of sti+ multibody dynamics with contact and friction. The friction and non-interpenetration constraints are modelled by complemen9 tarity equations. Sti+ness is accommodated by a technique motivated by a linearly implicit Euler method. We show that the main subproblem, a linear complementarity problem, is consistent for a su=ciently 11 small time step h. In addition, we prove that for the most common type of sti+ forces encountered in rigid body dynamics, where a damping or elastic force is applied between two points of the system, 13 the method is well de8ned for any time step h. We show that the method is stable in the sti+ limit, unconditionally with respect to the damping parameters, near the equilibrium points of the springs. The 15 integration step approaches, in the sti+ limit, the integration step for a system where the sti+ forces have been replaced by corresponding joint constraints. Simulations for oneand two-dimensional examples 17 demonstrate the stable behaviour of the method. Published in 2002 by John Wiley & Sons, Ltd.