Analysis of a generalized kinematic impact law for multibody-multicontact systems, with application to the planar rocking block and chains of balls

Bernard Brogliato 1, * Zhang Hongjian 2 Caishan Liu 2
* Corresponding author
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 State Key Laboratory for Turbulence and Complex Systems [Beijing]
Abstract : In this paper, we analyze the capabilities of a generalized kinematic (Newton's like) restitution law for the modeling of a planar rigid block that impacts a rigid ground. This kinematic restitution law is based on a specific state transformation of the Lagrangian dynamics, using the kinetic metric on the configuration space. It allows one to easily derive a restitution rule for multiple impacts. The relationships with the classical angular velocity restitution coefficient r for rocking motion are examined in detail. In particular, it is shown that r has the interpretation of a tangential restitution coefficient. The case when Coulomb's friction is introduced at the contact impulse level together with an angular velocity restitution is analyzed. A simple chain of aligned balls is also examined, illustrating that the impact law applies to various types of multibody systems.
Keywords : Moreau's impact law Coulomb's friction Chains of balls Multiple impacts Rocking block Kinetic angle Kinematic restitution law Housner model
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Bernard Brogliato, Zhang Hongjian, Caishan Liu. Analysis of a generalized kinematic impact law for multibody-multicontact systems, with application to the planar rocking block and chains of balls. Multibody System Dynamics, Springer Verlag, 2012, 27 (3), pp.351-382. ⟨10.1007/s11044-012-9301-3⟩. ⟨hal-00825573⟩

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