The application of quaternions in electrical circuits

This paper looks at the benefits of applying quaternions to the study and research of electrical circuits and motor/generator applications. A bottom up approach is taken. The paper shows when variables in electrical circuits are formulated as vector quantities, simple manipulation of the variables can give results which are easily interpreted, and especially so for the variables which are in quadrature with one another. The example of the force calculation in electrical motors, is also developed and extended for the case of non-ideal flux and rotor coil positioning. Other applications of quaternions are eluded to for the completeness.