Rotation of the elastic Earth: the role of the angular-velocity-dependence of the elasticity-caused perturbation
We calculate the so-called convective term, which shows up in the expression for the angular velocity of the elastic Earth, within the Andoyer formalism. The term emerges due to the fact that the elasticity-caused perturbation depends not only on the instantaneous orientation of the Earth but also on its instantaneous angular velocity. We demonstrate that this term makes a considerable contribution into the overall angular velocity. At the same time the convective term turns out to be automatically included into the correction to the nutation series due to the elasticity, if the series is defined by the perturbation of the figure axis (and not of the rotational axis) in accordance with the current IAU resolution. Hence it is not necessary to take the effect of the convective term into consideration in the perturbation of the elastic Earth as far as the nutation is related to the motion of the figure axis.
KeywordsConvective term Elastic Earth Nutation series Andoyer variables Rotational axis Figure axis
- Efroimsky, M.: On the theory of canonical perturbations and its application to Earth rotation. In: Capitaine, N. (ed.) Proceedings of Journées 2004: Systèmes de référence spatio-temporels. l’Observatoire de Paris (2005) astro-ph/0409282Google Scholar
- Seidelmann P.K.: 1980 IAU theory of nutation: the final report of the IAU working group on nutation. Celest. Mech. Dyn. Astron. 27, 79–106 (1982)Google Scholar
- Woolard E.W.: Theory of the rotation of the Earth around its centre of mass. Astron. Papers Amer. Ephemeris 15, 1 (1953)Google Scholar