Dynamics of an axisymmetric body spinning on a horizontal surface. II. Self-induced jumping

Following part I of this series, the general spinning motion of an axisymmetric rigid body on a horizontal table is further analysed, allowing for slip and friction at the point of contact. Attention is focused on the case of spheroids whose density distribution is such that the centre-of-mass and centre-of-volume coincide. The governing dynamical system is treated by a multiple-scale technique in order to resolve the two time-scales intrinsic to the dynamics. An approximate solution for the high-frequency component of the motion reveals that the normal reaction can oscillate with growing amplitude, and in some circumstances will fall to zero, leading to temporary loss of contact between the spheroid and the table. The exact solution for the free motion that ensues after this 'jumping' is analysed, and the time-dependence of the gap between the spheroid and the table is obtained up to the time when contact with the table is re-established. The analytical results agree well with numerical simulations of the exact equations, both up to and after loss of contact.