The rotor: Rotation of frames via representation of systematic differences in terms of spherical functions

The paper presents a method to derive rotational angles between two reference frames from the systematic differences represented in terms of spherical functions - hereafter referred to as the ROTOR (ROTation by Orthogonal Representation). It is shown that the ROTOR is preferable over the least-squares technique since it (a) takes into account only the harmonics which correspond to rotation, (b) tests them for pure rotation, and (c) discovers the existence of quasi-rotational terms which may smear rotation. Due to these properties the ROTOR yields realistic results even in the case when the observational data contain not only noise but other systematic terms that have nothing to do with rotation. Numerical experiments with the FK5 and three catalogs of radio sources are described.