An Algorithm for Rigid Body Contact with Coulomb Friction

Abstract

This paper is concerned with a numerical algorithm for the impact of rigid bodies against rigid obstacles. Some problems of this kind can be treated by specifying the quotient between the relative normal velocity of approach and separation, Newton [1], that is by introducing the classical coefficient of restitution. This is sometimes generalized to Poisson’s hypothesis, see Kilmister & Reeve [2]. In many cases, however, it is necessary to take both the normal and the tangential impulse at the impact into account to achieve reasonable agreement with observations. This class of problems has been the object of several recent studies, invariably leading to the introduction of one or more additional constitutive parameters, such as the coefficient of friction. Thus in Brach [3], a quotient between normal and tangential impulses is introduced, and several bounds based on physical assumptions, are derived for this quotient. In Stronge [4], the division of the impact process into a compression and an expansion phase is analyzed, and the problem is treated using a coefficient of restitution relating energies rather than velocities.