A mechanical analysis of a special class of rebound phenomena

An analytical method is presented for determining the post-impact motion of a rough elastic ball which collides with and rebounds from an arbitrarily oriented rough inertial surface. Pre-impact ball motion is completely general, and the contact interface is assumed to be sufficiently rough to provide a no-slip condition during the restitution phase of the short impact interval. A solution to the impulse-momentum equations is obtained by using Newton's linear coefficient of restitution, and by introducing a torsional coefficient of restitution to account for changes in the magnitude and direction of the component of the ball's angular velocity vector perpendicular to the inertial surface. This method is used to analyze the hop or hook-serve used in advanced-level handball play. An expression for the hop angle gamma is derived, which depends on the components of the mass center velocity and angular velocity vectors imparted to the ball by the server. These results are consistent with the natural tendency for right- and left-handed servers to generate characteristic hops to the left and right, respectively. These same results also indicate, however, that many handball authorities are not giving proper instructions when teaching hop servers how the ball should be spinning after hand impact.