Haugen Peter T, Smith Andrew D P, Edwards Boyd F
Department of Physics, Utah State University, Logan, Utah 84322, USA.
St. John's College, University of Cambridge, Cambridge CB2 1TP, United Kingdom.
Chaos. 2022 Jun;32(6):063108. doi: 10.1063/5.0076147.
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.
我们分析了位于正六边形顶点处六个强度相同的磁偶极子以及位于中心处一个强度可变的磁偶极子的旋转动力学。这七个偶极子绕着垂直于六边形平面的固定轴自由旋转，其偶极矩平行于该平面。平衡偶极子取向作为中心偶极子相对强度的函数进行计算。在无摩擦的情况下计算了围绕这些平衡态的小振幅扰动，并与中心偶极子强度为零和无穷大时的解析结果进行了比较。给出了简正模式和频率。在中心偶极子强度的两个临界值处出现了分岔，在这两个值之间存在双稳性。
