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Inspired by the turf-ball interaction in golf, this paper seeks to understandthe bounce of a ball that can be modelled as a rigid sphere and the surface assupplying an elasto-plastic contact force in addition to Coulomb friction. Ageneral formulation is proposed that models the finite time interval of bouncefrom touch-down to lift-off. Key to the analysis is understanding transitionsbetween slip and roll during the bounce. Starting from the rigid-body limitwith a an energetic or Poisson coefficient of restitution, it is shown thatslip reversal during the contact phase cannot be captured in this case, whichresult generalises to the case of pure normal compliance. Yet, the introductionof linear tangential stiffness and damping, does enable slip reversal. Thisresult is extended to general weakly nonlinear normal and tangentialcompliance. An analysis using Filippov theory of piecewise-smooth systems leadsto an argument in a natural limit that lift-off while rolling is non-genericand that almost all trajectories that lift off, do so under slip conditions.Moreover, there is a codimension-one surface in the space of incoming velocityand spin which divides balls that lift off with backspin from those that liftoff with topspin. The results are compared with recent experimentalmeasurements on golf ball bounce and the theory is shown to capture the mainfeatures of the data.

Analysis of point-contact models of the bounce of a hard spinning ball on a compliant frictional surface