Unraveling Paradoxical Theories for Rigid Body Collisions

[+] Author and Article Information
W. J. Stronge

Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, U.K.

J. Appl. Mech 58(4), 1049-1055 (Dec 01, 1991) (7 pages) doi:10.1115/1.2897681 History: Received March 30, 1990; Revised August 22, 1990; Online March 31, 2008


A collision between two rigid bodies has a normal impulsive reaction at the contact point (CP) . If the bodies are slightly rough and the contact points have a relative tangential velocity (slip), there is also a frictional force that opposes slip. Small initial slip can halt before contact terminates; when slip halts the frictional force changes and the collision process is separated into periods before and after halting. An energetically consistent theory for collisions with slip that halts is based on the work done by normal (nonfrictional) forces during restitution and compression phases. This theory clearly separates dissipation due to frictional forces from that due to internal irreversible deformation. With this theory, both normal and tangential components of the impulsive reaction always dissipate energy during collisions. In contrast, Newton’s impact law results in calculations of paradoxical increases in energy for collisions where slip reverses. This law relates normal components of relative velocity for the CP at separation and incidence by a constant (the coefficient of restitution e ). Newton’s impact law is a kinematic definition for e that generally depends on the slip process and friction; consequently it has limited applicability.

Copyright © 1991 by The American Society of Mechanical Engineers
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