  Binary black hole simulations with black hole excision using spectral methods
require a coordinate transformation into a co-rotating 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 much less than 90 degrees. For
strong precession, performance of the Euler-angle parameterization
deteriorates, eventually failing for a 90 degree change in orientation because
of singularities in the parameterization ("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 non-precessing binaries.
