Lumped Electromechanical Elements In the design of rotating machines, especially for operation on alternating currents, it is desirable to have a system similar to that in Fig. 2.1.3 but to modify it in such a way that the mutual inductance varies cosinusoidally with O(L, = Mcos 0). This is accomplished by putting additional slots and windings at different positions around the periphery of both members. By using a proper distribution of slots and numbers of turns the dependence of L, can be made the cosinusoidal function shown by the dashed curve in Fig. 2.1.4. In many later examples we assume that this design process has been followed. When the two currents i. and i, and the angular position 0 are functions of time and the mutual inductance is expressed as Lm = M cos 0, we can write the terminal voltages as dir dil di-di V 1 = = L 1 "-+ M cos d -i-M sin 0dt dt dt dt d)a, di di de v= L, -+ M cos 0 --ilM sin -. dt dt dt dt Note that the first term in each expression is a derivative with a constant coefficient, whereas the last two terms are derivatives with time-varying coefficients.
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