Relativistic theory of direct interactions and a gravitational two-body problem in the second post-Newtonian approximation

Three-dimensional Lagrangian formulation of relativistic theory of direct interactions is applied to the problem of two-body motion in the second post-Newtonian approximation. On the basis of the Poincare-invariance, taking into account the requirements of agreement with the scalar-tensor theory in linear approximation by gravitational constant and with the Lagrangian of test particle in the Schwarzschild field in the approximation of one-body problem, the Lagrangian function of the system of two gravitating point particles is plotted. The efficiency of application of direct interaction theory general methods is shown, which permits to proceed to the Hamiltonian description of the system mentioned