A time-stepping method for stiff multibody dynamics with contact and friction

We define a time-stepping procedure to integrate the equations of motion of stiff multibody dynamics with contact and friction. The friction and non-interpenetration constraints are modelled by complementarity equations. Stiffness 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 sufficiently small time step h. In addition, we prove that for the most common type of stiff forces encountered in rigid body dynamics, where a damping or elastic force is applied between two points of the system, the method is well defined for any time step h. We show that the method is stable in the stiff limit, unconditionally with respect to the damping parameters, near the equilibrium points of the springs. The integration step approaches, in the stiff limit, the integration step for a system where the stiff forces have been replaced by corresponding joint constraints. Simulations for one- and two-dimensional examples demonstrate the stable behaviour of the method. Published in 2002 by John Wiley Sons, Ltd.