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Updated: Oct 18, 2026

Development of an Experimental Setup for the Measurement of the Coefficient of Restitution under Vacuum Conditions
Published on: March 29, 2016
Perturbation and asymptotic coefficient of restitution for the Hunt-Crossley collision under an external potential
Zijian Liang1,2, Hanbin Wang3,4
1Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China.
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.
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