Stability of rigid-body dynamics with sliding frictional contacts

The use of rigid body models during frictional contact is often justified by proving the existence of a unique solution to the forward dynamic equations. The implicit assumption here is that the contact forces so obtained are stable. In this paper, the rigid-body assumption is relaxed and body-to-body contacts are modelled using springs and dampers. A singular perturbation analysis reveals additional necessary conditions to ensure contact force stability in the reduced rigid-body model. Furthermore, the analysis indicates that stability depends on a damping ratio associated with the rigid contacts