Keywords: Lorentz covariance, Lorentz force, accelerated motion of particles, particle accelerators, relativistic covariant Hooke law, particle dynamics, elastic body dynamics, Lorentz covariant equations
Lorentz covariant formulation for the laws of physics – particle and elastic body dynamics
An equation representing a law of physics is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities. The key property of Lorentz covariant equations is that if they hold in one inertial frame, then they hold in any inertial frame. This condition is a requirement according to the principle of relativity, that is, all non–gravitational laws must make the same predictions for identical experiments taking place at the same space–time event in two different inertial frames of reference. We divided the presentation into three main sections: introduction for a simple case, the analysis of complex motion under electromagnetic Lorentz force in particle accelerators and we end with a covariant formulation for the Hooke law.