Two Interpretations of Rigidity in Rigid-Body Collisions

[+] Author and Article Information
A. Chatterjee

Department of Engineering Science and Mechanics, The Pennsylvania State University, University, PA 16802

A. Ruina

Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853

J. Appl. Mech 65(4), 894-900 (Dec 01, 1998) (7 pages) doi:10.1115/1.2791929 History: Received March 18, 1996; Revised July 15, 1998; Online October 25, 2007


We distinguish between, and discuss the applicability of, two levels of rigidity in rigid-body collision modeling. For rigidity in the strong force-response sense, collisional contact deformations must be highly localized. The bodies then move according to second-order rigid-body mechanics during the collision. Incremental collision laws and most collision models using continuum mechanics for the contact region depend on force-response rigidity. For rigidity in the weaker impulse-response sense, the deformations need not be localized but displacements during the collision need to be small everywhere. Only the time-integrated rigid-body equations, involving before-collision and after-collision velocities, then need apply. Although a force-response rigid body is also impulse-response rigid the converse is not true. Algebraic collision laws depend only on impulse-response rigidity. Elastic vibration models of collisions are also generally consistent with impulse-response rigidity.

Copyright © 1998 by The American Society of Mechanical Engineers
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