  One way to select a preferred frame from gravitational radiation is via the
principal axes of < L L>, an average of the action of rotation group generators
on the Weyl tensor at asymptotic infinity. In this paper we evaluate this
time-domain average for a quasicircular binary using approximate
(post-Newtonian) waveforms. For nonprecessing unequal-mass binaries, we show
the dominant eigenvector of this tensor lies along the orbital angular
momentum. For precessing binaries, this frame is not generally aligned with
either the orbital or total angular momentum, working to leading order in the
spins. The difference between these two quantities grows with time, as the
binary approaches the end of the inspiral and both precession and higher
harmonics become more significant.
