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We derive the conservative secular evolution of precessing compact binariesto second post-Newtonian order accuracy, with leading-order spin-orbit,spin-spin and mass quadrupole-monopole contributions included. The emergingclosed system of first-order differential equations evolves the pairs of polarand azimuthal angles of the spin and orbital angular momentum vectors togetherwith the periastron angle. In contrast with the instantaneous dynamics, thesecular dynamics is autonomous. This secular dynamics reliably characterizesthe system over timescales starting from a few times the radial period toseveral precessional periods, but less than the radiation reaction timescale.We numerically compare the instantaneous and secular evolutions and estimatethe number of periods for which dissipation has no significant effect, e.g. theconservative timescale. We apply the analytic equations to study the spinflip-flop effect, recently found by numerical relativity methods. Ourinvestigations show that the effect does not generalize beyond its originalparameter settings, although we reveal distinct configurations exhibiting onehalf flip-flops. In addition, we find a flip-flopping evolution of the orbitalangular momentum vector, which ventures from one pole to another throughseveral precessional periods. This is a new effect, occurring for mass ratiosmuch less than one.

Secular precessing compact binary dynamics, spin and orbital angular momentum flip-flops