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Rotation in a gravitational billiard

    https://doi.org/10.1142/S0129183117500218Cited by:3 (Source: Crossref)

    Gravitational billiards composed of a viscoelastic frictional disk bouncing on a vibrating wedge have been studied previously, but only from the point of view of their translational behavior. In this work, the average rotational velocity of the disk is studied under various circumstances. First, an experimental realization is briefly presented, which shows sustained rotation when the wedge is tilted. Next, this phenomenon is scrutinized in close detail using a precise numerical implementation of frictional forces. We show that the bouncing disk acquires a spontaneous rotational velocity whenever the wedge angle is not bisected by the direction of gravity. Our molecular dynamics (MD) results are well reproduced by event-driven (ED) simulations. When the wedge aperture angle θW>π2, the average tangential velocity Rω̄ of the disk scales with the typical wedge vibration velocity vb, and is in general a nonmonotonic function of the overall tilt angle θT of the wedge. The present work focuses on wedges with θW=2π3, which are relevant for the problem of spontaneous rotation in vibrated disk packings. This study makes part of the PhD Thesis of G. G. Peraza-Mues.

    PACS Nos.: 89.65.Gh

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