Defining the coefficient of restitution for the impact between free and constrained bodies

摘要

This paper revisits the coefficient of restitution involved in the impulse-momentum balance equations for colliding rigid bodies and examines its extension to impacts between flexible bodies. The analytical solution to axial impact on a flexible rod is used to demonstrate that the coefficient of restitution is not inherent in the underlying physical process. In fact, the type of coefficient to be used in each case depends on the particu8lar model employed by the analyst to describe flexibility in the bodies concerned. It is demonstrated that the coefficient of restitution used in the generalized impulse-momentum balance for flexible bodies does not represent a physical magnitude. In any case, as shown in this paper, the ratio between the relative velocities at the contact points or surfaces of the flexible bodies before and after impact is no measure of the local loss of mechanical energy during the process.