Spin-orbit corrections in the description of motion of compact binaries I.

Description of vectors with Euler-angles

Abstract

In the research of gravitational waves, the binary systems formed by compact objects have a special role, since the waveform emitted by them, and detectable in ground-based detectors, can be described with high accuracy over a wide range of parameters. In the course of our work, we tried to take into account all the relevant effects in the description of the motion, focusing on the treatment of the eccentricity of the orbit and the effects of the spin of the bodies. In our previous research, we wrote out the series expansion of the angular quantities describing the motion as simply as possible in the post-Newtonian approximation we used, but this led to divergent contributions. To solve this problem we are using a more complex (amplitude and frequency) series expansion, but for this we need to express the relevant vector quantities with the chosen angular quantities, and calculate the equations of motion. The aim is also to explore and correct the errors of previous publications that we used as starting material.