Frictionless multiple impacts in multibody systems. II. Numerical algorithm and simulation results

Caishan Liu (1) , Zhen Zhao (2) , Bernard Brogliato (3)

1 College of Engineering [Beijing]
2 State Key Laboratory for Turbulence and Complex Systems [Beijing]
3 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems

Part I of this paper develops a framework that is an extension of the Darboux-Keller shock dynamics towards frictionless multiple impacts between bodies composed of rateindependent materials. A numerical algorithm is proposed in this paper, in which the impulsive differential equation is discretized with respect to the primary impulse corresponding to the contact with the highest potential energy, and the integration step size is estimated at the momentum level. This algorithm respects the energetic constraints and avoids the stiff ordinary differential equation problem arising by directly using the compliant model. The well-known example of Newton's cradle, as well as Bernoulli's system, is used to illustrate the developments.

Mots clés: impulse methods; Darboux-Keller's dynamics; stiff problem

Domaines: Mécanique [physics]

Caishan Liu, Zhen Zhao, Bernard Brogliato. Frictionless multiple impacts in multibody systems. II. Numerical algorithm and simulation results. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009, 465 (2101), pp.1-23. ⟨10.1098/rspa.2008.0079⟩. ⟨hal-00755948⟩