Starting from the Hamiltonian model for a solid Earth with an elastic mantle previously developped by the authors, analytical expressions are derived which give the nutation series corresponding to the plane perpendicular to the angular momentum vector, to the plane perpendicular to the rotational axis and to the equator of figure, as well as the series that give the polar motion. The effects of the different perturbations -solid Earth, centrifugal and tidal potentials -are calculated separately. The corrections due to the elasticity of the mantle, which mostly correspond to the Oppolzer terms, are calculated with an accuracy of 10 -6 arc sec., given that the intrinsic observational accuracy has reached 0.0l mas.

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S U M M A R YThe canonical formalism for the rotation of an earth model composed of a rigid mantle and a liquid core, established in Getino (1995b), starting from the model of Sevilla & Romero (1987), is applied here to the study of the forced nutations caused by the perturbing lunisolar potential. The main purpose of this paper is not to get accurate values for the nutation terms, since the earth model considered does not include the effect of the elasticity. This approach should be understood as a generalization of Kinoshita's (1977) theory for a rigid earth. Under the canonical formulation, using Andoyer-like variables and following a procedure very similar to that of Kinoshita, we obtain similar expressions (to those of Kinoshita) for the nutations of the fundamental planes, the only difference being a corrector factor fc in the amplitudes of the nutation to account for the effect of the liquid core. This corrector factor is equal to 1 when particularizing for the rigid case; the results are then the same as those of Kinoshita.In this way, we develop a complete canonical theory for a non-rigid earth (not as yet including deformations) which includes the effect of the liquid core from the beginning. and which enables the amplitudes of the forced nutations to be obtained directly, unlike the usual theories for a non-rigid earth, which require the support of results for the rigid case.

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We focus on the updating of a specific contribution to the precession of the equator in longitude, usually named as "second order." It stems from the crossing of certain terms of the lunisolar gravitational potential. The IAU2006 precession theory assigns it the value of −46.8 mas/cy that was derived for a rigid Earth model. Instead of that model, we consider a two-layer Earth composed of an elastic mantle and a liquid core, working out the problem within the Hamiltonian framework developed by Getino and Ferrándiz. The targeted effect is obtained without further simplifying assumptions through Hori's canonical perturbation method applied up to the second order of perturbation. On account of using a more realistic Earth model, the revised value of the second-order contribution is significantly changed and reaches −55.29 mas/cy. That variation of the second-order contribution is larger than other contributions included in IAU2006. It must be compensated with an increase of −8.51 mas/cy in the value of the lunisolar first-order component ¢ p A of the precession of the equator rate, which is derived from the total rate by subtracting the remaining contributions accounted for in IAU2006 precession. The updating of the second-order contribution implies that the ¢ p A parameter has to be changed, from 5040684.593 to 5040693.104 mas/cy in absence of potential revisions of other contributions. It entails a proportional variation of Earth's dynamical ellipticity H d , for which the estimation associated with IAU2006, 0.00327379448, should be updated to 0.00327380001, about 1.7 ppm larger.

The IAU Working Group on Precession and the Equinox looked at several solutions for replacing the precession part of the IAU 2000A precession-nutation model, which is not consistent with dynamical theory. These comparisons show that the (Capitaine et al., Astron. Astrophys., 412, 2003a) precession theory, P03, is both consistent with dynamical theory and the solution most compatible with the IAU 2000A nutation model. Thus, the working group recommends the adoption of the P03 precession theory for use with the IAU 2000A nutation. The two greatest sources of uncertainty in the precession theory are the rate of change of the Earth's dynamical flattening, J 2 , and the precession rates (i.e. the constants of integration used in deriving the precession). The combined uncertainties limit the accuracy in the precession theory to approximately 2 mas cent −2 .Given that there are difficulties with the traditional angles used to parameterize the precession, z A , ζ A , and θ A , the working group has decided that the choice of parameters should be left to the user. We provide a consistent set of parameters that may be used with either the traditional rotation matrix, or those rotation matrices described in (Capitaine et al., Astron. Astrophys., 412, 2003a) and (Fukushima Astron. J., 126, 2003).We recommend that the ecliptic pole be explicitly defined by the mean orbital angular momentum vector of the Earth-Moon barycenter in the Barycentric Celestial Reference System (BCRS), and explicitly state that this definition is being used to avoid confusion with previous definitions of the ecliptic. 352 J. L. HILTON ET AL.Finally, we recommend that the terms precession of the equator and precession of the ecliptic replace the terms lunisolar precession and planetary precession, respectively.

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S U M M A R YThe Hamiltonian formalism was recently applied by Getino (1995a,b) for the study of the rotation of a non-rigid earth with a heterogeneous and stratified liquid core. That earth model is generalized here by including the effect of the dissipation arising from the mantle-core interaction, using a model similar to that of Sasao, Okubo 8z Saito (1980), which includes both viscous and electromagnetic coupling. First, a solution for the free nutations is obtained following a classical approach, which in our opinion is more familiar to most of the readers than the Hamiltonian treatment. This solution provides a theoretical basis clear enough to study both the qualitative and quantitative effects of the dissipations considered in the hypotheses. The main qualitative features are, besides the delays, that the free core nutation (FCN) suffers an exponential damping, while the chandler wobble (CW) is not damped at first order, by the dissipation considered. The numerical values obtained for the complex compliances agree with the most recent experimental computations.Next, the problem is studied under a Hamiltonian formalism, and a solution equivalent to the above is obtained. Besides its interest from a theoretical point of view, this formalism is necessary in order to apply canonical perturbation methods in order to obtain analytical nutation series.