On the Tetrad Formulation of the Equations of Motion in General Relativity

It is shown that the equation of motion Du _j/Ds = (e/mc ²)F _ji u ⁱ , a natural generalization to the curved spacetime of the Heaviside-Lorentz law of ponderomotive force, is equivalent to the metric independent and covariant Van Dantzig's equations of motion dx ^j _jpi] = 0 or L _v p _i = 0, where p _i is the conjugate momentum 4-vector and v a vector determined by the condition p _i v ⁱ, only with respect to holonomic coordinates. With respect to an anholonomic system, the Heaviside-Lorentz equation is a particular case of the VD equations valid for a privileged class of anholonomic frames, those consisting of orthogonal unit vectors.