Equations of Motion for Continuous Matter of Special Relativity in the Lagrange Variables

Abstract

THE equations of motion for continuous matter of special relativity are usually¹ deduced by equating to zero the divergence of the material energy (the ‘Minkowski’) tensor: where ρ is the rest density and p is the pressure supposed given as a function of the x _µ. v _µ means dx _µ/ds. In this way we get the equation of continuity: dp/ds is considered small and is usually ignored; in fact, it represents the action of the pressure in creating matter². We further get for the equations of motion (ignoring dp/ds): These equations may be called the Euler equations, since the first three equations in (3) are the Euler equations of classical hydrodynamics.