Analysis of Motion of Magnetic Levitation Systems: Implications for High-Speed Vehicles

Abstract

To study the motion of a magnetically suspended high‐speed vehicle, a simple example (the long wire above a thin conducting plate) is considered in detail. The lift and drag forces on the magnet (long wire) are derived for arbitrary motion above the plate. The stability of the system is analyzed for typical parameters (velocity = 300 mph, height = 0.1 m). By using a Laplace‐transform technique, it is shown that two types of modes occur (in the linearized equations of motion). One mode is a vertical oscillation with an amplitude that grows slowly in time. The other mode is an unbounded increase in the horizontal velocity error. This latter instability results from the fact that the drag force decreases with increasing velocity at high speeds. In this connection, an error is pointed out in a recent publication in which it was claimed that the system is stable. Detailed consideration of the effects of horizontal acceleration and vertical velocity on the magnetic forces is given. The effects of aerodynamic drag and the need for active control of the system are also discussed.