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Impact-contact dynamics in a disc-ball system

Caishan Liu 1 Hongjian Zhang 1 Zhao Zhen 2 Bernard Brogliato 3, *
* Corresponding author
3 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
Abstract : This paper concerns a disc-ball system, in which a moving ball collides against a disc resting on a rough, fixed horizontal surface. The complexity in such a simple object is due to the presence of the line contact between the disc and the fixed plate, which significantly influences the impact-generated state of the disc. We deal with this problem in a uniform framework that encapsulates different structures of the mathematical model, including contacts, impacts, stick-slip in friction, as well as the transitions among different states of the variable-structure dynamics. We design specific experiments that provide useful information to help determine the macroscopic parameters in impact and friction. Other complicated cases concerned with the couplings between impacts and friction are theoretically and experimentally investigated. Excellent agreements between numerical and experimental results support our theoretical developments.
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Caishan Liu, Hongjian Zhang, Zhao Zhen, Bernard Brogliato. Impact-contact dynamics in a disc-ball system. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2013, 469 (2152), pp.20. ⟨10.1098/rspa.2012.0741⟩. ⟨hal-00825597⟩

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