Post-Newtonian Approximation for Spinning Particles

Using an energy-momentum tensor for spinning particles due to Dixon and Bailey-Israel, we develop the post-Newtonian approximation for N spinning particles in a self-contained manner. The equations of motion are derived directly from this energy-momentum tensor. Following the formalism of Epstein- Wagoner, we also obtain the waveform and the luminosity of the gravitational wave generated by these particles.