A maximal monotone impact law for the 3-ball Newton's cradle

作者：Winandy Tom^*; Leine Remco I

来源：Multibody System Dynamics, 2017, 39(1-2): 79-94.

DOI：10.1007/s11044-016-9533-8

• Newton's cradle
• Unilateral constraints
• Impact
• Convex analysis
• Wave equation

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.

• 出版日期2017-1