  The very long-term evolution of the hierarchical restricted three-body
problem with a massive perturber is analyzed analytically in the high
eccentricity regime. Perturbations on the time scale of the outer orbit can
accumulate over long timescales and be comparable to the effect of the octupole
term. These perturbations are described by Brown's Hamiltonian - having
different forms in the literature. We show that at the high eccentricity regime
- the effect of Brown's Hamiltonian is an azimuthal precesssion of the
eccentricity vector and can be solved analytically. In fact, the dynamics are
equivalent to a simple pendulum model allowing an explicit flip criterion.
