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