Epitrochoidal angular oscillation patterns are common in experiments where a dipole magnet gets trapped in a rotating dipole field. These patterns are also seen on other particle trapping schemes and likely attributed to instability of the circular motion possibly to nonlinearities in these interactions. These are mentioned in my published article (https://doi.org/10.3390/sym13030442) however not analysed. Normally a trapped dipole body performs angular motion where its dipole axis orientation traces a circle. In many cases, also depending mainly on the moment of inertia tensor and to configuration parameters this circular motion persists. In other cases these epitrochoidal patterns slowly develop.They might be linked to harmonics of the motion. Beside the angular motion, the body also can gain spin around its dipole axis. The reason of the torque resulting on this spin is likely induction currents produced in the magnet body. Anyway, this spin is a main factor in development of epitrochoidal motions.
Here I would like to ask is there any analysis where these epitrochoidal patterns can be predicted?
I recently uploaded new experiments videos on my youtube channel where these patterns can be seen (http://youtube.com/user/sudanamaru/videos)
Attached is a picture where a epitrochoidal angular motion of a trapped magnet in air is shown by a light trace.
Keywords: Classical mechanics, magnetic levitation, magnetodynamics, magnetic bound state, maglev, driven harmonic motion, epitrochoid
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