Lagrangian classical relativistic mechanics of a system of directly interacting particles. II

On the basis of the approach developed in the first part of the work the general expressions for interaction Lagrangians of particle system up to the second order in $c^{-2}$ including accelerations are found. They include all known approximate Lagrangian functions as particular cases. In the framework of Lagrangian formalism with higher derivatives a method for building up the relativistic second order equations of motion is considered. An explicit form of these equations for $N$ particles in the first approximation in $c^{-2}$ and for two particles in the second approximation in $c^{-2}$ are obtained. The realisation of the Currie–Hill conditions in the approximations considered is established. Corresponding expressions for motion integrals with usual transformation properties with respect to the Poincare group are written down.