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Kepler Orbits in Pairs of Disks Settling in a Viscous Fluid

Chajwa, Rahul and Menon, Narayanan and Ramaswamy, Sriram (2019) Kepler Orbits in Pairs of Disks Settling in a Viscous Fluid. In: PHYSICAL REVIEW LETTERS, 122 (22).

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Official URL: https://dx.10.1103/PhysRevLett.122.224501

Abstract

We show experimentally that a pair of disks settling at negligible Reynolds number (similar to 10(-4)) displays two classes of bound periodic orbits, each with transitions to scattering states. We account for these dynamics, at leading far-field order, through an effective Hamiltonian in which gravitational driving endows orientation with the properties of momentum. This treatment is successfully compared against the measured properties of orbits and critical parameters of transitions between types of orbits. We demonstrate a precise correspondence with the Kepler problem of planetary motion for a wide range of initial conditions, find and account for a family of orbits with no Keplerian analog, and highlight the role of orientation as momentum in the many-disk problem.

Item Type: Journal Article
Additional Information: copyright for this article belongs to AMER PHYSICAL SOC
Keywords: SINGULARITY METHOD; SPHEROIDS; SEDIMENTATION; INSTABILITY; STOKES; MOTION
Department/Centre: Division of Physical & Mathematical Sciences > Physics
Depositing User: Id for Latest eprints
Date Deposited: 24 Jul 2019 11:36
Last Modified: 24 Jul 2019 11:36
URI: http://eprints.iisc.ac.in/id/eprint/63133

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