# QUATERNION ANALYSIS OF THE MODES OF ELECTRICAL SYSTEMS

S.I. Klipkov

Èlektron. model. 2019, 41(6):15-36
https://doi.org/10.15407/emodel.41.06.015

### ABSTRACT

The properties of the polygenic functions of the complex and quaternionic variables used in the problems of the electric power industry are studied from the point of view of differential calcu-lus. Based on the introduced concept of internal pseudo-derivative, expressions are obtained for the right and left quotients of the differential of an arbitrary quaternion function to the dif-ferential of its argument. The conditions for the differentiability of functions of a quaternionic variable are formulated. An example of a quaternion analysis of the modes of a simple two-node circuit of an electrical system is given.

### KEYWORDS

parametric hypercomplex numerical system, pseudo-derivative, complex num-bers, quaternions, quadriplex numbers.

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