Earth rotation based on the celestial coordinates of the celestial intermediate pole - I. The dynamical equations

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We present a study of the Earth's rotational motion in terms of the Earth Orientation Parameters (EOP) of the new paradigm that is recommended by the IAU 2000 resolutions to transform between the celestial and terrestrial reference systems. This paper presents the first part of the study whose purpose is to establish the dynamical equations of the rotation of a rigid Earth as a function of these new parameters. Starting from Euler dynamical equations for a rigid Earth, and using expressions for the components of the instantaneous rotation vector as functions of the celestial coordinates X, Y of the Celestial intermediate pole (CIP) and of the Earth rotation angle (ERA), the equations of Earth rotation were obtained explicitly in terms of those parameters. Taking into account the order of magnitude of the terms of these equations, we obtain the most appropriate form of the equations for a practical integration. We then investigated the possible methods of integration for providing semi-analytical solutions for the X and Y variables in the axially symmetric case. We also perform a number of tests regarding the efficiency of these methods, based on the IAU 2000 precession-nutation. We extended this approach to a deformable Earth, based on integration constants compliant with the new P03 precession model.
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