The magnetic analogue of the inverted pendulum

An inverted pendulum can be balanced using an oscillating system which provides stability. One such system involves a magnet supported by an ac magnetic field. More recent designs of this oscillating system uses both ac and dc magnetic fields to support the magnet. The floating magnet can be regarded as a short dipole, with the ac coil providing a vertical oscillating field. The geometry and symmetrical filamentry of the turns in an optimum ac coil are presented.