Perturbation and asymptotic coefficient of restitution for the Hunt-Crossley collision under an external potential field
Phys. Rev. E 114, 034212 – Published 15 September, 2026
DOI: https://doi.org/10.1103/gcd1-jc6s
Abstract
We generalize the Hunt-Crossley (HC) model to the case compatible with external potential fields, attributing to a small dimensionless parameter, and employ the perturbation method to derive the perturbation and asymptotic solutions of the coefficient of restitution. The numerical results reveal that the perturbation solution decreases with the impact velocity for higher velocities and asymptotically approaches the case without any external force, while dropping into a critical sticking velocity for lower velocities. Finally, we analyze the dissipative properties of the bouncing ball system and demonstrate that a localized dispersive structure consistent with experiments appears after mapping the chaotic phase diagram to the perturbation solution. The proposed model and its solutions may be applied to study other collision-related nonlinear dynamic systems.
