Swerve During Three-Dimensional Impact of Rough Rigid Bodies

Abstract

For collisions between rough bodies, dry friction can be represented by Coulomb’s law; this relates the normal and tangential components of contact force by a coefficient of limiting friction if the contact is sliding. The friction force acts in a direction opposed to sliding. For a collision with planar changes in velocity, sliding is in either one direction or the other; the direction can reverse before separation only if the impact configuration is eccentric or noncollinear and the initial velocity of sliding is small. In general, however, friction results in nonplanar changes in velocity; for free bodies the velocity changes are three-dimensional or nonplanar unless the initial sliding velocity lies in the same plane as two principal axes of inertia for each body. Nonplanar velocity changes give a direction of sliding that continually changes or swerves during an initial phase of contact in an eccentric impact configuration. The present paper obtains changes in relative velocity during “rigid” body collisions as a function of impulse Pn of the normal component of reaction force. The method of resolving changes in relative velocity as a function of impulse is demonstrated by obtaining the solution for a spherical pendulum colliding with a rough half-space. The solution depends on two independent material parameters—the coefficient of friction and an energetic coefficient of restitution.