Analysis of a generalized kinematic impact law for multibody-multicontact systems, with application to the planar rocking block and chains of balls. (English) Zbl 1344.70029
Summary: 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.
MSC:
| 70F35 | Collision of rigid or pseudo-rigid bodies |
| 70H03 | Lagrange’s equations |
| 74M20 | Impact in solid mechanics |
Keywords:
multiple impacts; rocking block; kinetic angle; kinematic restitution law; Housner model; chains of balls; Moreau’s impact law; Coulomb’s frictionSoftware:
MeschachReferences:
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