Physical Restrictions on the Impulse Acting During Three-Dimensional Impact of Two “Rigid” Bodies

Abstract

It is well known that the impulse of the contact force acting during impact of two rigid bodies determines the abrupt change in the motions of the two bodies. Much recent work has been focused on determining a constitutive equation for this impulse which models the complicated phenomena occurring during the actual deformations of the two bodies. The objective of this paper is to discuss a set of physical conditions which impose nontrivial restrictions on general constitutive equations for the impulse. Due to the general nature of these restrictions they can be used to determine the range of validity of various proposals for the impulse. For the general case of three-dimensional impact, the impulse depends on an energetic coefficient of restitution and two angles defining its direction. However, when there are no directional properties of the roughness of the two impacting bodies, it is reasonable to propose a simpler form for the direction of the impulse which depends only on this coefficient of restitution and a single friction angle. An example of impact of two finite spheres is considered which shows that the condition that the two bodies have a tendency to separate after impact imposes nontrivial bounds on this friction angle.