  Binary systems subject to generic perturbations evolve on quasiperiodic
orbits. We derive the most generic class of perturbations, which allow to
evaluate secular effects via generalized complex true and eccentric anomaly
parameters, by use of the residue theorem. Such perturbations include both the
generic Brumberg force and various linear contributions to the conservative
dynamics of compact binaries, up to the second post-Newtonian order. As an
example, we compute the self-spin contribution to the luminosity due to
gravitational radiation of a compact binary consisting of galactic black holes,
the most important type of source for LISA. This translates to simply calculate
the residue of the instantaneous energy loss in the origin of the complex
parameter plane, which illustrates the power of the presented method.
