Related papers: Quaternion Mathematics in Electromagnetic Modeling…
The duality relation between the electric and magnetic fields, in the presence of an additional axion-like field, is considered. We derive the new equations that describe the electrodynamics in this model, and we discuss the implications…
Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a…
A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to…
We applied an effective approximation into Maxwell's equations with an axion interaction for haloscope searches. A set of Maxwell's equations acquired from this approximation describes just the reacted fields generated by the anomalous…
This paper revisits the little-known Gibbs-Rodrigues representation of rotations in a three-dimensional space and demonstrates a set of algorithms for handling it. In this representation the rotation is itself represented as a…
It is shown that the groups of Euclidian rotations, rigid motions, proper, orthochronous Lorentz transformations, and the complex rigid motions can be represented by the groups of unit-norm elements in the algebras of real, dual, complex,…
Future developments of lighter, more compact and powerful motors-driven by environmental and sustainability considerations in the transportation industry-involve higher stresses, currents and electromagnetic fields. Strong couplings between…
A transverse multipole expansion is derived, including the longitudinal components necessarily present in regions of varying magnetic field profile. It can be used for exact numerical orbit following through the fringe field regions of…
Within the framework of exterior algebra, the concept of time-like quaternions has been previously established. This paper advances beyond the existing structure by elucidating the procedure for constructing time-like quaternions with the…
New electrodynamics with quaternionic mass is found to yields interesting results. The quaternionic mass involves longitudinal as well as transverse (vector) masses. Because of these two masses, an application of a magnetic field in a…
This article is an exhaustive revision of concepts and formulas related to quaternions and rotations in 3D space, and their proper use in estimation engines such as the error-state Kalman filter. The paper includes an in-depth study of the…
The paper aims to explore the impact of composite operators containing a few physical quantities on the gravitational and electromagnetic fields, studying the influencing factors and physical properties of octonion field equations. J. C.…
We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two…
We give a simple and self contained introduction to quaternions and their practical usage in dynamics. The rigid body dynamics are presented in full details. In the appendix, some more exotic relations are given that allow to write more…
Following a previous proposition of quaternity spacetime for electronic orbitals in neon shell, this paper describes the geometrical course each electron takes as it oscillates harmonically within a certain quaternity space dimension and…
Maxwell's equations are formulated in arbitrary moving frames by means of tetrad fields, which are interpreted as reference frames adapted to observers in space-time. We assume the existence of a general distribution of charges and currents…
A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped with the matrix product rule and chain rule and it is able to…
Electromagnetism is the energy originating from an electric charge. Our purpose is to enlarge Maxwell. Include the charge transfer phenomenology. A four bosons electromagnetism is derived. An EM completeness is achieved. The charge's set…
Polarization wiggling is an observational effect of a gravitational field on the polarization of electromagnetic radiation traversing it. We find that in linear gravity, the polarization wiggle rate contributions from scalar, vector and…
The paper aims to apply the complex-octonions to explore the variable gravitational mass and energy gradient of several particles in the external ultra-strong magnetic fields. J. C. Maxwell was the first to introduce the algebra of…