  The method of averaging is used to investigate the phenomenon of capture into
resonance for a model that describes a Keplerian binary system influenced by
radiation damping and external normally incident periodic gravitational
radiation. The dynamical evolution of the binary orbit while trapped in
resonance is elucidated using the second order partially averaged system. This
method provides a theoretical framework that can be used to explain the main
evolutionary dynamics of a physical system that has been trapped in resonance.
