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Normal-Mode Oscillations for the Circular and Dipolar States of a Filled Hexagonal Magnetic Dipole Cluster
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
AIP Publishing LLC
NSF, Division of Chemistry (CHE) 1808225
NSF, Division of Chemistry (CHE)
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.
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.
Available for download on Thursday, June 01, 2023
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.