Spinning compact binary inspiral II: Conservative angular dynamics
  We establish the evolution equations of the set of independent variables
characterizing the 2PN rigorous conservative dynamics of a spinning compact
binary, with the inclusion of the leading order spin-orbit, spin-spin and mass
quadrupole - mass monopole effects, for generic (noncircular, nonspherical)
orbits. More specifically, we give a closed system of first order ordinary
differential equations for the orbital elements of the osculating ellipse and
for the angles characterizing the spin orientations with respect to the
osculating orbit. We also prove that (i) the relative angle of the spins stays
constant for equal mass black holes, irrespective of their orientation, and
(ii) the special configuration of equal mass black holes with equal, but
antialigned spins, both laying in the plane of motion (leading to the largest
recoil found in numerical simulations) is preserved at 2PN level of accuracy,
with leading order spin-orbit, spin-spin and mass quadrupolar contributions
included.
