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On-axis and off-axis levitation by a rotating permanent magnet
Hugo Schreckenberg1, Zayneb El Omari El Alaoui1, Guilhem Gallot2
1Institut Polytechnique de Paris, Ecole polytechnique, Palaiseau, France.
Physical Review. E
|June 19, 2026
Summary
High-speed rotation of a tilted magnet enables stable magnetic levitation, bypassing Earnshaw's theorem. This dynamic equilibrium allows a trapped magnet to orbit, defying gravity independently.
Area of Science:
- Physics
- Magnetism
- Classical Mechanics
Background:
- Earnshaw's theorem traditionally prohibits stable static levitation of permanent magnets.
- Dynamic systems can overcome stability limitations imposed by static constraints.
Purpose of the Study:
- To theoretically and experimentally investigate a novel magnetic levitation method using a rotating magnet.
- To analyze the conditions and stability of levitation for a trapped permanent magnet.
- To explain the dynamics of the levitated magnet, including off-axis motion.
Main Methods:
- Theoretical modeling of the floater magnet's in-axis and off-axis motion.
- Experimental study of levitation stability against rotor speed and floater parameters.
- Analysis of levitation limits and extension of the dipole moment model.
Main Results:
- Achieved gravity-independent magnetic levitation by rotating a tilted permanent magnet.
- Identified stable conical orbits for the levitated magnet synchronized with the rotor.
- Determined levitation stability conditions, including dependence on rotor speed and floater size/shape.
- Observed and analyzed the lower and upper limits of stable levitation.
Conclusions:
- Dynamic stabilization through high-speed rotation provides a viable method for magnetic levitation, circumventing Earnshaw's theorem.
- The study elucidates the critical role of rotational speed and magnet geometry in achieving stable levitation.
- An extended dipole moment model successfully explains the off-axis dynamics of the levitated magnet.
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