NDLI: A maximal monotone impact law for the 3-ball Newton’s cradle

Content Provider	Springer Nature Link
Author	Winandy, Tom Leine, Remco I.
Copyright Year	2016
Abstract	The 3-ball Newton’s cradle is used as a stepping stone to divulge the structure of impact laws. A continuous conewise linear impact law that maps the preimpact contact velocities to the postimpact contact velocities is proposed for the 3-ball Newton’s cradle. The proposed impact law is kinematically, kinetically, and energetically consistent. It reproduces the outcomes of experimental observation. Moreover, it is in accordance with the outcome of the collision of three identical linear-elastic thin rods for which the impact process is governed by the one-dimensional wave equation. The proposed impact law is shown to be nonexpansive. Therefore, the relationship between the mean contact velocity and its dual, the impulsive force, is maximal monotone. A counterexample to maximal cyclical monotonicity of this relationship allows us to conclude that no dissipation function exists for the proposed impact law.
Starting Page	79
Ending Page	94
Page Count	16
File Format	PDF
ISSN	13845640
Journal	Multibody System Dynamics
Volume Number	39
Issue Number	1-2
e-ISSN	1573272X
Language	English
Publisher	Springer Netherlands
Publisher Date	2016-08-31
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Newton’s cradle Unilateral constraints Impact Convex analysis Wave equation Vibration, Dynamical Systems, Control Optimization Electrical Engineering Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Mechanical Engineering Aerospace Engineering Modeling and Simulation Computer Science Applications

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