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Prediction and Control of Slip-Free Rotation States in Sphere Assemblies

D. V. Stäger, N. A. M. Araújo, and H. J. Herrmann
Phys. Rev. Lett. 116, 254301 – Published 24 June 2016
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Abstract

We study fixed assemblies of touching spheres that can individually rotate. From any initial state, sliding friction drives an assembly toward a slip-free rotation state. For bipartite assemblies, which have only even loops, this state has at least four degrees of freedom. For exactly four degrees of freedom, we analytically predict the final state, which we prove to be independent of the strength of sliding friction, from an arbitrary initial one. With a tabletop experiment, we show how to impose any slip-free rotation state by only controlling two spheres, regardless of the total number.

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  • Received 15 February 2016

DOI:https://doi.org/10.1103/PhysRevLett.116.254301

© 2016 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsNonlinear Dynamics

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Balls as 3D Gears

Published 24 June 2016

Spinning a few spheres among a large collection of them can lead to a predictable state where each sphere rotates in synch with the others.

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Authors & Affiliations

D. V. Stäger1,*, N. A. M. Araújo2,†, and H. J. Herrmann1,3,‡

  • 1Computational Physics for Engineering Materials, IfB, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland
  • 2Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal, and Centro de Física Teórica e Computacional, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
  • 3Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil

  • *staegerd@ethz.ch
  • nmaraujo@fc.ul.pt
  • hans@ifb.baug.ethz.ch

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Issue

Vol. 116, Iss. 25 — 24 June 2016

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