Post-Newtonian dynamics basing on Mathisson-Papapetrou equations with Corinaldesi-Papapetrou condition in Kerr spacetime

We derive the post-Newtonian dynamics for a spinning body with Corinaldesi-Papapetrou spin supplementary condition in Kerr spacetime. Both the equations of motion for the center-of-mass of body and the spin evolution are obtained. For the non-relativistic case, our calculations show that the magnitude of spin measured in the rest frame of the body's center-of-mass does not change with time, though the center-of-mass does not move along the geodesic. Moreover, we find that the effects of the spin-orbit and spin-spin couplings will be suppressed by the Lorentz factor when the body has a relativistic velocity.