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A theory of the impact or collision of two rigid bodies, taking account of friction, is presented. It determines how the direction of sliding varies during the impact, which must be known to calculate the direction of the frictional force and thence the frictional impulse. This is accomplished by analyzing the equations of motion of the bodies during the collision. The normal impulse is determined by using a coefficient of restitution. When the direction of sliding is constant throughout the collision, the theory agrees with that given by Whittaker, which is correct only in this case.
Joseph B. Keller (Sat,) studied this question.