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We revisit the problem of the equations of motion of a system of $N$self-interacting massive particles (without spins) in the firstpost-Minkowskian (1PM) approximation of general relativity. We write theequations of motion, gravitational field and associated conserved integrals ofthe motion in a form suitable for comparison with recently publishedpost-Newtonian (PN) results at the 4PN order. We show that the Lagrangianassociated with the equations of motion in harmonic coordinates is ageneralized one, and compute all the terms linear in $G$ up to 5PN order. Wediscuss the Hamiltonian in the frame of the center of mass and exhibit acanonical transformation connecting it to previous results directly obtainedwith the Hamiltonian formalism of general relativity. Finally we recover theknown result for the gravitational scattering angle of two particles at the 1PMorder.

Equations of motion of self-gravitating $N$-body systems in the first post-Minkowskian approximation