### Abstract

The true-and eccentric-anomaly parameterizations of the Kepler motion are generalized to quasi-periodic orbits, by considering perturbations of the radial part of the kinetic energy in the form of a series of negative powers of the orbital radius. A toolbox of methods for averaging observables as functions 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 in the theory of gravitational radiation, involve integrals of these functions over a period of motion. These integrals are evaluated by using the residue theorem. In the course of this work, two important questions emerge: (1) When do the true-and eccentric-anomaly parameters exist? (2) Under what circumstances, and why, are the poles in the origin? The purpose of this paper is to find the answer to these queries.

Original language | English |
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Pages (from-to) | 79-84 |

Number of pages | 6 |

Journal | Astrophysical Journal, Supplement Series |

Volume | 126 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2000 |

### Keywords

- Binaries: close
- Gravitation
- Relativity

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science