Particle Motion in Static Homogeneous Electric and Magnetic Fields and its Consequences in a Typical Confinement Situation in Plasma Physics

A simple representation of the Landau-Lifshitz equation of motion for a charged particle is deduced. As a consequence of the new representation, a simple technique is developed in order to solve the equation. As an example of it, the solutions for the electric and magnetic constant field cases are found for a typical confinement in Plasma Physics. A discussion about the validity of the relativistic Larmor formulais exposed.