Journal
MULTIBODY SYSTEM DYNAMICS
Volume 27, Issue 3, Pages 351-382Publisher
SPRINGER
DOI: 10.1007/s11044-012-9301-3
Keywords
Multiple impacts; Rocking block; Kinetic angle; Kinematic restitution law; Housner model; Chains of balls; Moreau's impact law; Coulomb's friction
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Funding
- NSFC/ANR [ANR-08-BLAN-0321-01]
- China Scholarship Council [2009601276]
- ANR project Multiple Impact [ANR-08-BLAN-0321-01]
- Agence Nationale de la Recherche (ANR) [ANR-08-BLAN-0321] Funding Source: Agence Nationale de la Recherche (ANR)
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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.
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