A Method for stability analysis of magnetic bearings : Basic stability   criteria
  In this work I outline a general procedure for dynamic modeling and stability analysis of a magnetic bearing, which is a rotating shaft confined inside a chamber through electromagnetic forces alone. I consider the simplest type of self-propelled bearing, namely a permanent magnet synchronous motor and an induction motor rotor freely suspended inside the corresponding stator, and having no eccentricity-fedback control algorithm. Writing Euler's equations for the rotor mechanics and Maxwell's equations for the electromagnetic field leads to a systematic technique for analysing the dynamics of the complete system. Physical arguments indicate that that two essential components for rotor confinement are a spatial gradient in the stator magnetic field and a torque angle lying in the second quadrant. These predictions are confirmed through the linear stability analysis. The direct practical utility of the results is mitigated by the presence of a repeated eigenvalue in the linearized equations. Despite this limitation, the analysis presented can act as a good starting point for more accurate treatments of other magnetic bearing configurations. 
B Shayak
physics.class-ph