On the Energy of Dynamical Force Fields via Bishop Vector Fields in Minkowski Space E-1(4)

Abstract

In this study, we firstly define equations of motion based on the traditional Newtonian mechanics in terms of the parallel frame adapted to the worldline of the moving particle in Minkowski space E-1(4). Then, we compute energy on the moving timelike particle in a resultant force field by using geometrical descriptions of the curvature and the torsion of the wordline belonging to the particle in the space. We also investigate the relationship between energy on the moving timelike particle in different force fields and energy on the moving timelike particle in parallel vector fields.