Didactic study on classical dynamics of an electrically charged particle under influence of a constant and uniform magnetic field

The main task of this work is to study, by means of algebraic methods, the influence of a constant and uniform magnetic field on the classical dynamics of an electrically charged particle. In this text, we initially deal with the Lorentz equation in 4-dimensional Minkowski spacetime. Also, the Taylor series expansion of the relativistic factor and its behavior in Galileo's regime of relativity are presented. Finally, the equations of motion of a charged classical particle under the influence of the classical electromagnetic field configuration of the constant magnetic field type in time and uniformly distributed in 3-dimensional space are presented.