Derivation of equations of circuits of electromechanical devices

Abstract

Equations of electromechanical electric and magnetic circuits are written in terms of particle derivatives where the initial point and time are independent variables (Lagrange co-ordinates). The division of the induced electric motive force (EMF) into transformer EMF and motion EMF follows from the Maxwell equations in terms of partial derivatives, where the space co-ordinates and time are independent variables (Euler co-ordinates). Commonly this is not taken into account. However, relativistic electrodynamics shows that current, voltage drop and induced EMF magnitudes are invariant with respect to the co-ordinates transformation at low speeds and the division of the induced EMF into the transformer EMF and the motion EMF is dependent on a system of coordinates. Additionally, current magnitude inside a device should be considered as a function of both space and time. For derivation of the equation it is enough to use the simplest mathematical model, considering electromagnetic processes in one moving contour of a linear electromagnetic device. This paper derives circuit equations in terms of partial derivatives and total derivatives.