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Research Papers

Generalization of the Energetic Coefficient of Restitution for Contacts in Multibody Systems

[+] Author and Article Information
Seyed Ali Modarres Najafabadi

Department of Mechanical Engineering and Centre for Intelligent Machines,  McGill University, 817 Sherbrooke St. West, Montreal, Quebec, Canada H3A 2K6smodar@cim.mcgill.ca

József Kövecses

Department of Mechanical Engineering and Centre for Intelligent Machines,  McGill University, 817 Sherbrooke St. West, Montreal, Quebec, Canada H3A 2K6jozsef.kovecses@mcgill.ca

Jorge Angeles

Department of Mechanical Engineering and Centre for Intelligent Machines,  McGill University, 817 Sherbrooke St. West, Montreal, Quebec, Canada H3A 2K6angeles@cim.mcgill.ca

The inequality relation in Eq. 1 and its counterparts in the balance of the paper are understood as shorthand notations for gi(q)0, for i=1,,m. We recall that arrays do not form ordered sets.

J. Comput. Nonlinear Dynam 3(4), 041008 (Aug 21, 2008) (14 pages) doi:10.1115/1.2960477 History: Received May 08, 2007; Revised October 11, 2007; Published August 21, 2008

This paper introduces a new interpretation of the energetic coefficient of restitution, especially applicable to contact involving multibody systems. This interpretation generalizes the concept of the energetic coefficient of restitution and allows for consideration of simultaneous multiple-point contact scenarios. Such a generalization is obtained by an analysis of energy absorption and restitution during impact, using a decomposition technique, which exactly decouples the kinetic energy associated with the normal and tangential directions of the contact pairs. The main advantages of the new definition and its potential applications are highlighted.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

General unilaterally constrained multibody system

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Figure 2

Geometrical interpretation of a planar simultaneous double-point impact

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Figure 3

Planar impact of a falling rod

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Figure 4

The constrained and admissible parts of the kinetic energy at the pre-impact instant (Nm) versus θ (deg)

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Figure 5

The partial derivative of the kinetic energy of the constrained motion with respect to θ(N m/deg) versus θ (deg)

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Figure 6

Double-point impact of a rocking rod

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