Peter Reinhardt has also made a set of movies that illustrates the orbital dynamics of black holes that have nearly equal masses. More will be posted as Peter develops additional models; for now, the one shown below is nicely illustrative of what we can show. The left-hand panel shows the orbital tracks of the binary's members; the smaller black hole (1 million solar masses) orbits at large radius, the larger one (3 million solar masses) at large radius. As the evolution proceeds, notice that both orbital radii shrink. The right-hand side is in a frame that co-rotates with the overall orbit, and the slow shrinking of the orbital radii is taken out.
In both panels, the various rods illustrate angular momentum vectors. The magenta rod shows us the direction of the orbital angular momentum vector; the orange rods show us the spin angular momenta of the two black holes; and the green rod is the direction of the system's total angular momentum. Notice that the orange vectors whip around quite a bit. This is thanks to the general relativistic precession of the spin vector, which is rather pronounced in this strong-field regime. The orbital angular momentum precesses so that the sum of spin and orbit remains nearly constant. This is reflected in the fact that the green vectors remain very nearly fixed. Their slight motion toward the end is actually an artifact of the breakdown of the post-Newtonian equations of motion and the fact that defined angular momenta for the individual black holes is not well posed at this point.