Rocking Newton’s cradle

Abstract

In textbook descriptions of Newton's cradle, it is generally claimed that displacing one ball will result in a collision that leads to another ball being ejected from the line, with all others remaining motionless. Hermann and Schmälzle, Hinch and Saint-Jean, and others have shown that a realistic description is more subtle. We present a simulation of Newton's cradle that reproduces the break-up of the line of balls at the first collision, the eventual movement of all the balls in phase, and is in good agreement with our experimentally obtained data. The first effect is due to the finite elastic response of the balls, and the second is a result of viscoelastic dissipation in the impacts. We also analyze a dissipation-free ideal Newton's cradle which displays complex dynamics.

Breather Solutions of the Discrete p-Schrödinger Equation

“…The DpS equation was recently introduced to describe small amplitude oscillations in a class of mechanical systems consisting of a chain of touching beads confined in smooth local potentials [12,13,26], the most well known example of such systems being Newton's cradle [10]. In this context, the p-Laplacian involved in (1) accounts for the fully-nonlinear character of Hertzian interactions between beads (with p = 5/2 in the case of contacting spheres).…”

Onset of rigidity for stretched string networks

“…It was originally conceived as a variation on the theme of soft disk and sphere packings, as formulated by Liu and others [4][5][6]. That work is mainly founded on Hooke's law interactions which act under compression only (similar to those found for example in the interaction between the spheres in a Newton's cradle [7]). It has proved to be extremely rich in subtle phenomena, such as non-integer indices that relate contact number variations with compression.…”

Toying with physics

“…th and early 20 th century in mathematics and physics, respectively, who collaborated on "Über die Theorie des Kreisels", publishing all four volumes in Leipzig between 1897 and 1910; H. Bondi, J. L. Synge, and K. Stewartson all wrote about spinning tops and so on. This tradition of studying toys seriously has, fortunately, survived to the present day, and we find in the current literature and in premier journals contributions on the "Levitron" [8], on "Newton's cradle" [9] (and references therein), and on "Euler's disk" [10].…”

“…Recognizing this, we see that the subsequent motion cannot long conform to what is expected (and taught by many). Indeed it does not, and several papers address this motion; see [9] and references therein. To observe it unmodified by air drag, build a big Cradle, and rock it.…”