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"Relativistic equations of motion in electromagnetic theory"
P. R. Wallace, Am. J. Math. Vol. 63 (1941) p.729

"On the motion of particles in general relativity theory"
A. Einstein and L. Infeld, Can. J. Math. Vol. 1 (1949) p.209

"Obtaining equations of motion for charged particles in the (v/c)3-approximation by the Einstein-Infeld-Hoffmann method"
M.V.Gorbatenko, Theor. Math. Phys. (Springer-Verlag), Vol. 142, (2005), p. 138

Here is one of my papers where the EIH method is applied: Gen. Rel. Grav. version, arxiv.org version.