In the case of continuously distributed substance throughout the entire volume of space in the gravitational and electromagnetic fields, we shall use the Lagrangian function L, which in the covariant theory of gravitation (CTG) has the form :
3-vector Vgv in the left side of (21) is equivalent in its meaning to action of Christoffel symbols, which are used to write the equations of motion in Riemannian space in four-dimensional notation, both in the general theory of relativity and in the covariant theory of gravitation.
Thus, from the variation of action (1) with the Lagrangian (4) in the framework of the covariant theory of gravitation (CTG), we can obtain the equation of motion of a particle (22), which is valid in the special theory of relativity (SRT).
In this case, the density ratio [[rho].sub.0q]/[[rho].sub.0] will be unchanged, the covariant derivative [[nabla].sub.[delta]] [[rho].sub.0q]/[[rho].sub.0] is zero, and (80) turns into the equation of motion of substance in gravitational and electromagnetic fields, taken in the covariant theory of gravitation under these conditions (see the equation (35) in ).
Difference in positions of the covariant theory of gravitation (CTG) and the general theory of relativity (GTR) describing the motion of a small test particle in an external field is demonstrated in equations (21) and (23).
The Principle of Least Action in Covariant Theory of Gravitation.