7 Remarks and conclusion

In the present study we have carried out the final step of a complete reconstruction of the tables of nutation for a rigid Earth model REN-2000 (Rigid Earth Nutation), whose one of the main purpose was to catch all the coefficients up to $0.1 ~\rm\mu as$. We have detailed the calculations and given the coefficients of rigid Earth nutation related to two different kinds of second-order effects, which are the crossed-nutation effects and the spin-orbit coupling effect. We can observe that the Hamiltonian approach used here enabled to separate very easily these two kinds of contributions. Moreover we have given a complete overview of the contributions to the leading 18.6 y nutation with argument $\Omega$, with precise explanations for their origin.

As our results here can be considered as definitive ones following the four other specific studies which lead to the establishment of the tables REN-2000 (Souchay & Kinoshita 1996, 1997; Folgueira et al. 1998a; Folgueira et al. 1998b), we have listed here the leading coefficients of rigid Earth nutation for the axis of angular momentum and the axis of figure, with the related Oppolzer terms. Also we have made a final review of all the different contributions to the tables REN-2000, with some explanations on their origin, their way of calculations, their amplitudes and other remarks.

A numerical integration (Souchay 1998) has been done in order to check our analytical results, which is accompanied by a comparison with recent works which have also lead to the establishment of other series of nutation for a rigid Earth model (Bretagnon et al. 1997; Roosbeek & Dehant 1997).

Acknowledgements

We are very thankful to Dr. N. Capitaine for giving us some important and decisive clarification concerning a delicate theoretical part, and Dr. J. Williams to give us various comments to improve the quality of the paper.