For three-phase currents ( i_a = I_m \cos(\omega t) ), ( i_b = I_m \cos(\omega t - 120^\circ) ), ( i_c = I_m \cos(\omega t - 240^\circ) ) in windings spaced ( 120^\circ ) apart, the resultant magnetomotive force (MMF) is: [ F(\phi, t) = \frac32 F_\textmax \cos(\omega t - \phi) ] where ( \phi ) is the spatial angle. This represents a wave traveling at angular velocity ( \omega ).
Unlike many modern textbooks that rely heavily on simulation software and simplified models, Langsdorf’s approach is rigorous and mathematical. He believed that to truly understand an AC machine, one must master the —the idea that induction motors, synchronous machines, and even DC machines can be understood through a unified set of principles revolving around rotating magnetic fields and equivalent circuits. Theory-alternating-current-machines-alexander-langsdorf-pdf