Precession-tracking coordinates for simulations of compact-object binaries

Binary black hole simulations with black hole excision using spectral methods require a coordinate transformation into a corotating coordinate system where the black holes are essentially at rest. This paper presents and discusses two coordinate transformations that are applicable to precessing binary systems, one based on Euler angles, the other on quaternions. Both approaches are found to work well for binaries with moderate precession, i.e., for cases where the orientation of the orbital plane changes by << 90 degrees. For strong precession, performance of the Euler-angle parametrization deteriorates, eventually failing for a 90 degrees change in orientation because of singularities in the parametrization (gimbal lock). In contrast, the quaternion representation is invariant under an overall rotation and handles any orientation of the orbital plane as well as the Euler-angle technique handles nonprecessing binaries.