  Three transiting circumbinary planets (Kepler-16 b, Kepler-34 b, and
Kepler-35 b) have recently been discovered from photometric data taken by the
Kepler spacecraft. Their orbits are significantly non-Keplerian because of the
large secondary-to-primary mass ratio and orbital eccentricity of the binaries,
as well as the proximity of the planets to the binaries. We present an analytic
theory, with the planet treated as a test particle, which shows that the
planetary motion can be represented by the superposition of the circular motion
of a guiding center, the forced oscillations due to the non-axisymmetric
components of the binary's potential, the epicyclic motion, and the vertical
motion. In this analytic theory, the periapse and ascending node of the planet
precess at nearly equal rates in opposite directions. The largest forced
oscillation term corresponds to a forced eccentricity (which is an explicit
function of the parameters of the binary and of the guiding center radius of
the planet), and the amplitude of the epicyclic motion (which is a free
parameter of the theory) is the free eccentricity. Comparisons with direct
numerical orbit integrations show that this analytic theory gives an accurate
description of the planetary motion for all three Kepler systems. We find that
all three Kepler circumbinary planets have nonzero free eccentricities.
