Rigid Body Collisions

Abstract

A general approach is presented for solving the problem of the collision of two rigid bodies at a point. The approach overcomes the difficulties encountered by others on the treatment of contact velocity reversals and negative energy losses. A classical problem is solved; the initial velocities are presumed known and the final velocities unknown. The interaction process between the two bodies is modeled using two coefficients. These are the classical coefficient of restitution, e , and the ratio, μ, of tangential to normal impulses. The latter quantity can be a coefficient of friction as a special case. The paper reveals that these coefficients have a much broader intepretation than previously recognized in the solution of collision problems. The appropriate choice of values for μ is related to the energy loss of the collision. It is shown that μ is bounded by values which correspond to no sliding at separation and conservation of energy. Another bound on μ combined with limits on the coefficient e , provides an overall bound on the energy loss of a collision. Examples from existing mechanics literature are solved to illustrate the significance of the coefficients and their relationship to the energy loss of collisions.