  The true- and eccentric-anomaly parametrizations of the Kepler motion are
generalized to quasiperiodic orbits by considering perturbations of the radial
part of kinetic energy as a series in the negative powers of the orbital
radius. A toolbox of methods for averaging observables in terms of the energy
$E$ and angular momentum $L$ is developed. A broad range of systems governed by
the generic Brumberg force, as well as recent applications of the theory of
gravitational radiation involve integrals over a period of motion. These
integrals are evaluated by using the residue theorem. It is shown that the pole
of the integrand is located in the origin and that under certain circumstances
an additional pole emerges.
