The method of calculating the vector antenna pattern based on the algebra of quaternions

The quaternion algebra contains the algebra of real and complex numbers, as well as three-dimensional vector algebra. The algebra of quaternions finds application in describing the rotations of coordinate systems, which is also of interest in describing problems of electrodynamics, in which it is often necessary to perform a transition from the basis of sources to the basis of observation. It is shown that using the algebra of quaternions, it is possible to express Maxwell's equations and their solutions in a coordinate system invariant form. A method for calculating a vector antenna based on the algebra of quaternions is proposed. It is shown that the algebra of quaternions is applicable not only for the calculation of electromagnetic fields, radiation patterns, but also for the calculation of polarization characteristics. All transformations define products of rotation functions, for which it is enough to find trigonometric functions sinx and cosx once, and all subsequent rotation operations are performed when implementing quaternion algebra procedures. The application of the quaternion algebra also avoids errors in determining the directions of turns. The proposed methodology can be used to design antennas placed on mobile objects when solving problems of analysis and synthesis.