  The Kozai mechanism for exponentially exciting eccentricity of a Keplerian
orbit by a distant perturber is extended to a general perturbing potential. In
particular, the case of an axisymmetric potential is solved analytically. The
analysis is applied to orbits around an oblate central object with a distant
perturber. If the equatorial plane of the central object is aligned with the
orbit of the distant perturber (axisymmetric potential), a single instability
zone, in which eccentricity grows exponentially, is found between two critical
inclinations; if misaligned (non-axisymmetric potential), a rich set of
critical inclinations separating stable and unstable zones is obtained
(Vashkoviak 1974). The analysis is also applied to a general quadratic
potential. Similarly, for non-axisymmetric cases, multiple stability and
instability zones are obtained. Here eccentricity can reach very high values in
the instability zones even when the potential's deviation from axisymmetry is
small.
