Friction in collisions: Resolution of a paradox

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Abstract
The coefficient of restitution e is usually defined as an empirically determined constant of proportionality that relates normal components of incident and rebound relative velocity for contact points CPi of colliding rigid bodies. Assuming that e represents inelastic behavior, this definition results in calculated kinetic energy increases during eccentric (noncollinear) collisions for some conditions of contact point slip. These paradoxical energy increases arise only in noncollinear collisions where slip at CPi is opposed by friction. In this case e must also depend on the slip process and friction, but then the ‘‘impact law’’ is valid for only a vanishingly small range of incident velocities. To resolve this paradox, we propose a new definition where e is independent of friction; thence e specifically represents internal dissipation by irreversible deformation processes. This definition clearly separates frictional and nonfrictional sources of energy dissipation. The two definitions are only equivalent in the case of nonfrictional or central (collinear) collisions.

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