Equations of Electrical Machines with a Rotating Permanent Magnet Playing the Role of the Stator and Their Nonlocal Analysis

A complete mathematical model is developed for the motion of a current loop powered from a constant voltage source and placed in the field of a permanent magnet rotating with a constant angular velocity. Local analysis of this model shows that it is unstable in the absence of external load, which contradicts the practice of motor operation. Therefore, the motor rotor model considered is incorrect although it is frequently used. The detected contradiction is eliminated by introducing an additional loop, which is orthogonal to the initial one and has the same parameters but is shortcircuited. The complete mathematical model of such a system is unstable in the absence of external load. For the case of an induction motor, the conditions of dichotomy, global asymptotic stability, and instability are formulated.