@ARTICLE{Spałek_Dariusz_Levitation_Early,
 author={Spałek, Dariusz},
 journal={Bulletin of the Polish Academy of Sciences Technical Sciences},
 pages={e154719},
 howpublished={online},
 year={Early Access},
 abstract={The paper presents approaches to levitation of permanent magnet levitation in a forced inhomogeneous magnetostatic field. For a permanent magnet ball, the magnetic field distribution is derived in analytical forms using the separation of variables separation method. Distribution is given by power functions and Legendre polynomials. The force (i.e. material force) is caused by the vertical magnetization of a permanent magnet and reluctivity change at the magnet boundary. The levitation force is evaluated using the generalized Maxwell stress tensor, coenergy, material force density, and equivalent magnetic dipole methods. The levitation forces are presented in terms of both magnetic permeabilities. The stability of equilibrium point is investigated. The frequencies of free and damped oscillations are evaluated.},
 type={Article},
 title={Levitation of Permanent Magnet Ball},
 URL={http://ochroma.man.poznan.pl/Content/135112/PDF/BPASTS-04956-EA.pdf},
 doi={10.24425/bpasts.2025.154719},
 keywords={permanent magnet, levitation force, material force},
}