Stability of rigid-body dynamics with sliding frictional contacts

The use of rigid body models during frictional contact i s 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 bodyto-body contacts are modeled using springs and dampers. A singular perturbation analysis reveals additional necessary conditions to ensure contact force stability an the reduced rigid-body model. Furthermore, the analysis indicates that stability depends on a damping ratio associated with the rigid contacts. dynamic equations. Other dynamic instabilities cannot be detected directly from the reduced-order rigid body models. The paper is organized as follows. Related work is described in the next section. The following section describes the assumptions and formulates the dynamic equations. In section 4, the singular perturbation analysis is presented using lumped viscoelasticity at each friction contact. The validity of the rigid model is related to the stability of the boundary layer describing the contact forces. A criteria for deciding instability is given and is related to the existence and uniqueness result of the Linear Complementarity Problem (LCP) formulation. Section 5 summarizes the results.