All Physics Faculty Publications

Document Type

Article

Journal/Book Title/Conference

Chaos

Author ORCID Identifier

Peter T. Haugen https://orcid.org/0000-0003-3779-1806

Andrew D. P. Smith https://orcid.org/0000-0002-3142-2105

Boyd F. Edwards https://orcid.org/0000-0002-2309-1350

Volume

32

Issue

6

Publisher

AIP Publishing LLC

Publication Date

6-1-2022

Award Number

NSF, Division of Chemistry (CHE) 1808225

Funder

NSF, Division of Chemistry (CHE)

First Page

1

Last Page

9

Abstract

We analyze the rotational dynamics of six magnetic dipoles of identical strength at the vertices of a regular hexagon with a variable-strength dipole in the center. The seven dipoles spin freely about fixed axes that are perpendicular to the plane of the hexagon, with their dipole moments directed parallel to the plane. Equilibrium dipole orientations are calculated as a function of the relative strength of the central dipole. Small-amplitude perturbations about these equilibrium states are calculated in the absence of friction and are compared with analytical results in the limit of zero and infinite central dipole strength. Normal modes and frequencies are presented. Bifurcations are seen at two critical values of the central dipole strength, with bistability between these values.

Comments

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Haugen, P. T., Smith, A. D., & Edwards, B. F. (2022). Normal-mode oscillations for the circular and dipolar states of a filled hexagonal magnetic dipole cluster. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(6), 063108. and may be found at https://aip.scitation.org/doi/10.1063/5.0076147.

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