Planar dynamics of a rigid body system with frictional impacts. II Qualitative analysis and numerical simulations

Abstract : The objective of this paper is to implement and test the theory presented in a companion paper for the non-smooth dynamics exhibited in a bouncing dimer. Our approach revolves around the use of rigid body dynamics theory combined with constraint equations from the Coulomb's frictional law and the complementarity condition to identify the contact status of each contacting point. A set of impulsive differential equations based on Darboux-Keller shock dynamics is established that can deal with the complex behaviours involved in multiple collisions, such as the frictional effects, the local dissipation of energy at each contact point, and the dispersion of energy among various contact points. The paper will revisit the experimental phenomena found in Dorbolo et al. (Dorbolo et al. 2005 Phys. Rev. Lett. 95, 044101), and then present a qualitative analysis based on the theory proposed in part I. The value of the static coefficient of friction between the plate and the dimer is successfully estimated, and found to be responsible for the formation of the drift motion of the bouncing dimer. Plenty of numerical simulations are carried out, and precise agreements are obtained by the comparisons with the experimental results.
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2009, 465 (2107), pp.2267-2292. 〈http://rspa.royalsocietypublishing.org/content/465/2107/2267.full〉. 〈10.1098/rspa.2008.0520〉
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Zhen Zhao, Caishan Liu, Bernard Brogliato. Planar dynamics of a rigid body system with frictional impacts. II Qualitative analysis and numerical simulations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2009, 465 (2107), pp.2267-2292. 〈http://rspa.royalsocietypublishing.org/content/465/2107/2267.full〉. 〈10.1098/rspa.2008.0520〉. 〈hal-00755926〉

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