Rotational collision dynamics of a spherical shell: frictional dissipation and stick-slip transition

Impact of a spinning shell on a wall is a common dynamic phenomenon such as table tennis. During such contact, most of the energy is dissipated by friction; however, previous studies have focused on the spinless impact problem of shell on wall rather than the tangential behavior induced by spin and friction. One difficulty is that the tangential behavior couples with the nonlinear normal contact force by friction, and thus makes predicting the tangential behavior more challenging. In the present work, considering the Coulomb friction during a rotational collision, the friction states were classified into two categories: (1) pure slip (PS) and (2) first pure slip and then stick–slip (PS-SS), depending on initial angular velocity. The primary source of energy dissipation in the system is frictional dissipation, determined predominantly by the slip magnitude and frictional force. By revisiting and refining Bao’s model, we achieved a more accurate estimation of contact time and modeled a rotational collision of a spherical shell with rigid wall model, enabling the prediction of rebound behaviors in PS cases. Additionally, we predicted the transition time from PS to PS-SS for cases where either the initial angular velocity is sufficiently small, or the friction coefficient is sufficiently large.