  In a previous investigation, a model of three-body motion was developed which
included the effects of gravitational radiation reaction. The aim was to
describe the motion of a relativistic binary pulsar that is perturbed by a
third mass and look for resonances between the binary and third mass orbits.
Numerical integration of an equation of relative motion that approximates the
binary gives evidence of such resonances. These $(m:n)$ resonances are defined
for the present purposes by the resonance condition, $m\omega=2n\Omega$, where
$m$ and $n$ are relatively prime integers and $\omega$ and $\Omega$ are the
angular frequencies of the binary orbit and third mass orbit, respectively. The
resonance condition consequently fixes a value for the semimajor axis $a$ of
the binary orbit for the duration of the resonance because of the Kepler
relationship $\omega=a^{-3/2}$. This paper outlines a method of averaging
developed by Chicone, Mashhoon, and Retzloff which renders a nonlinear system
that undergoes resonance capture into a mathematically amenable form. This
method is applied to the present system and one arrives at an analytical
solution that describes the average motion during resonance. Furthermore,
prominent features of the full nonlinear system, such as the frequency of
oscillation and antidamping, accord with their analytically derived formulae.
