Figure 1 shows the variation of the tangential and normal forces during the cycle at various values of $1. The value of x is fixed at 1.4412, corresponding to a homogeneous solid sphere with u = 0.3.
The forces are plotted on such a scale as to make F and P coincide when F = pP, i.e. in gross slip. At low angles of incidence, the tangential force shows a complete cycle of oscillation with a reversal in direction shortly after the maximum penetration is reached. In effect, the deformable surfaces act as a spring in the tangential direction which is compressed during the first quarter cycle and which overshoots its equilibrium position on recovery because of the inertia of the sphere. At the midpoint of the cycle, the local tangential velocity is opposite in direction to that at incidence.
This tangential oscillation is cut short by the occurrence of gross slip when F reaches the value -pP and the direction‘of slip is opposite to the relative tangential velocity at incidence. The surface of the half-space, having passed through a nearly complete cycle of oscillation, is now moving in thesame direction as the local incident tangential velocity of the sphere and at a greater speed than the sphere itself (which has been retarded during the impact).
When a larger angle of incidence is used, the start of the cycle is delayed by the initial period of gross slip, but the same general type of behaviour is observed.