Forced nutations of a two-layer Earth model

Abstract

In this paper we present a theory of the Earth rotation for a model composed of an inelastic mantle and a liquid core, including the dissipation in the core–mantle boundary (CMB). The main features of the theory are: (i) to be Hamiltonian, therefore the computation of some complex inner torques can be avoided; (ii) to be self‐consistent and non‐dependent on a previous rigid Earth theory, so there is no need to use transfer functions; (iii) to be analytical, the solution being derived by perturbation methods. Numerical nutation series deduced from the theory are compared with the IERS 96 empirical series, an accuracy better than 0.8 mas in providing celestial ephemeris pole (CEP) offsets.

Hamiltonian theory for the non-rigid Earth: Semidiurnal terms

“…Values of BEP, taken from Getino and Ferrándiz (2000b) With these parameters the amplitudes of the nutation series can be evaluated. First of all, we show in Table 1 the amplitudes corresponding to the dissipative terms in obliquity (depending on functionF b 1 ), where only the main terms are listed.…”

A note on the periodic orbits of a self excited rigid body

“…This idea has been used in previous works as an integrability criterium and for obtaining approximation solutions to real problems, see for instance [3,4,5,6]. In order to present our results we need some preliminary definitions and notation.…”

Hamiltonian of a Second Order Two-Layer Earth Model

“…and C , A are the principal moments of inertia , and the generating function which produced through the first order solution by Getino and Ferrandiz (2001), after some calculations, we can deduce w 2B as follows…”

“…In view of dynamical formation of structures at the core-mantle boundary, Hansen & Stemmer (2006) apply fully three dimensional models in cartesian and spherical geometry, in order to study the evolving patterns at the lower boundary in convection with strongly temperature-dependent viscosity at high Rayleigh number. Getino & Ferrandiz (2001) calculated the nutation series of a 2-layer Earth model (at a first order), Ferrandiz et al (2004) calculated precession for a free core nutation (FCN),they mentioned the computation of precession due to secular part of a second order term of the transformed Hamiltonian. In this work, we will deduce a second order Hamiltonian of a 2-layer Earth model including the tidal effect produces by the attraction of Moon and Sun.…”