The study presents approaches to both electrostatic and magnetostatic levitations. For anisotropic balls, both dielectric and magnetic field distributions are derived in analytical forms by means of the variable separation method. Distributions are given by power functions and polynomials either Legendre's (for the electrostatic problem) or the associated polynomials (for the magnetostatic problem). The levitation forces are evaluated by means of four methods, i.e. Maxwell stress tensor generalised method, co-energy method, material force density, and equivalent dipole analysis for both levitations. Levitation forces versus either electric permittivity or magnetic permeability are presented. The stability of the equilibrium points is investigated. The frequencies of free and damped oscillations are evaluated.

中文翻译：

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球的静电和静磁悬浮–力，稳定性和振荡频率

该研究提出了静电和静磁悬浮的方法。对于各向异性球，通过变量分离法以解析形式导出了介电和磁场分布。分布由幂函数和多项式给出，要么是勒让德式（针对静电问题），要么是相关联的多项式（针对静磁问题）。悬浮力通过四种方法评估，即麦克斯韦应力张量广义方法，协能方法，材料力密度和两种悬浮的等效偶极分析。呈现了相对于介电常数或磁导率的悬浮力。研究了平衡点的稳定性。评估自由振荡和阻尼振荡的频率。