  Planetary, stellar and galactic physics often rely on the general restricted
gravitational N-body problem to model the motion of a small-mass object under
the influence of much more massive objects. Here, I formulate the general
restricted problem entirely and specifically in terms of the commonly-used
orbital elements of semimajor axis, eccentricity, inclination, longitude of
ascending node, argument of pericentre, and true anomaly, without any
assumptions about their magnitudes. I derive the equations of motion in the
general, unaveraged case, as well as specific cases, with respect to both a
bodycentric and barycentric origin. I then reduce the equations to three-body
systems, and present compact singly- and doubly-averaged expressions which can
be readily applied to systems of interest. This method recovers classic
Lidov-Kozai and Laplace-Lagrange theory in the test particle limit to any
order, but with fewer assumptions, and reveals a complete analytic solution for
the averaged planetary pericentre precession in coplanar circular circumbinary
systems to at least the first three nonzero orders in semimajor axis ratio.
Finally, I show how the unaveraged equations may be used to express resonant
angle evolution in an explicit manner that is not subject to expansions of
eccentricity and inclination about small nor any other values.
