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

We de ne 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 complementarity 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 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, the method is well de ned 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 The integration step approaches, in the sti limit, the integration step for a system where the sti forces have been replaced by corresponding joint constraints.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 one- and two-dimensional examples demonstrate the stable behaviour of the method