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Normal-Mode Oscillations For The Circular And Dipolar States Of A Filled Hexagonal Magnetic Dipole Cluster, Peter T. Haugen, Andrew D. P. Smith, Boyd F. Edwards

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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 …