Instability of Vehicles Levitated by Eddy Current Repulsion-Case of an Infinitely Long Current Loop

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Abstract
The coordinates which will assure translational and rotational equilibrium of an infinitely long current loop moving parallel to a metallic sheet of thickness d are found. It is found that two distinct equilibrium positions exist for a given loop velocity, current, and weight. It is also found that the equilibrium positions are unstable. The primary manifestation of this instability appears to be a run away in velocity coupled with oscillations in height and angle of tilt. End effects of the current loop and aerodynamic drag forces could hopefully stabilize a real vehicle supported by magnetic levitation.