The rotor: A new method to derive rotation between two reference frames

Abstract

The paper presents a study of two techniques to derive the relative orientation of two reference frames: the Standard Method, based on the least squares procedure, and a new method - the ROTOR, based on the representation of systematic differences in terms of orthogonal functions. It is shown that the ROTOR is preferable over the Standard Method since it (a) takes into account only the harmonics which are responsible for rotation, (b) tests them for pure rotation, (c) discovers the existence of quasi-rotational terms which may smear the rotation, (d) in the absence of quasirotational terms, reconstructs the rotation exactly. Numerical experiments with the 1535 fundamental stars of the FK5 show that the ROTOR may be used to obtain rotation of any reference frame (including the HIPPARCOS catalogue) with respect to the FK5.