  A test particle in a noncoplanar orbit about a member of a binary system can
undergo Kozai-Lidov oscillations in which tilt and eccentricity are exchanged.
An initially circular highly inclined particle orbit can reach high
eccentricity. We consider the nonlinear secular evolution equations previously
obtained in the quadrupole approximation. For the important case that the
initial eccentricity of the particle orbit is zero, we derive an analytic
solution for the particle orbital elements as a function of time that is exact
within the quadrupole approximation. The solution involves only simple
trigonometric and hyperbolic functions. It simplifies in the case that the
initial particle orbit is close to being perpendicular to the binary orbital
plane. The solution also provides an accurate description of particle orbits
with nonzero but sufficiently small initial eccentricity. It is accurate over a
range of initial eccentricity that broadens at higher initial inclinations. In
the case of an initial inclination of pi/3, an error of 1% at maximum
eccentricity occurs for initial eccentricities of about 0.1.
