Indirect effect of the triaxiality in the Hamiltonian theory for the rigid Earth nutations

Escapa, Alberto; Getino, Juan; Ferrándiz, José M.

doi:10.1051/0004-6361:20020734

Cited by 16 publications

(19 citation statements)

References 8 publications

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“…taken A 0 = B 0 since B 0 /A 0 − 1 10 −5 (e.g. Escapa et al 2002); kept only first order terms in the angle J , and denoted the moments of inertia A 0 and C 0 as A and C, respectively. These relations are the same as those reported in Kubo (1991Kubo ( , 2009.…”

Section: Hamiltonian Of the Systemmentioning

confidence: 99%

“…On the one hand, some works have improved the rotational model of the rigid Earth, establishing a truncation level in the nutation series of the figure axis of 0.1 micro-arcsecond (e.g. Souchay et al 1999 and references therein, Escapa et al 2002;Getino et al 2010). On the other hand, Kinoshita's method has been properly modified and extended to consider more realistic non-rigid Earth models.…”

Section: Introductionmentioning

confidence: 99%

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Corrections stemming from the non-osculating character of the Andoyer variables used in the description of rotation of the elastic Earth

Escapa

2011

Celest Mech Dyn Astr

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We explore the evolution of the angular velocity of an elastic Earth model, within the Hamiltonian formalism. The evolution of the rotation state of the Earth is caused by the tidal deformation exerted by the Moon and the Sun. It can be demonstrated that the tidal perturbation to spin depends not only upon the instantaneous orientation of the Earth, but also upon its instantaneous angular velocity. Parameterizing the orientation of the Earth figure axis with the three Euler angles, and introducing the canonical momenta conjugated to these, one can then show that the tidal perturbation depends both upon the angles and the momenta. This circumstance complicates the integration of the rotational motion. Specifically, when the integration is carried out in terms of the canonical Andoyer variables (which are the rotational analogues to the orbital Delaunay variables), one should keep in mind the following subtlety: under the said kind of perturbations, the functional dependence of the angular velocity upon the Andoyer elements differs from the unperturbed dependence (Efroimsky in Proceedings of Journées 2004: Systèmes de référence spatio-temporels. l'Observatoire de Paris, pp 74-81, 2005; Efroimsky and Escapa in Celest. Mech. Dyn. Astron. 98:251-283, 2007). This happens because, under angular velocity dependent perturbations, the requirement for the Andoyer elements to be canonical comes into a contradiction with the requirement for these elements to be osculating, a situation that parallels a similar antinomy in orbital dynamics. Under the said perturbations, the expression for the angular velocity acquires an additional contribution, the so called convective term. Hence, the time variation induced on the angular velocity by the tidal deformation contains two parts. The first one comes from the direct terms, caused by the action of the elastic perturbation on the torque-free expressions of the angular velocity. The second one arises from the convective terms. We compute the variations of the angular velocity through the approach developed in Getino and Ferrándiz (Celest. Mech. Dyn. Astron. 61:117-180, 1995), but considering the contribution of the convective terms. Specifically, we 123 100 A. Escapa derive analytical formulas that determine the elastic perturbations of the directional angles of the angular velocity with respect to a non-rotating reference system, and also of its Cartesian components relative to the Tisserand reference system of the Earth. The perturbation of the directional angles of the angular velocity turns out to be different from the evolution law found in Kubo (Celest. Mech. Dyn. Astron. 105:261-274, 2009), where it was stated that the evolution of the angular velocity vector mimics that of the figure axis. We investigate comprehensively the source of this discrepancy, concluding that the difference between our results and those obtained in Ibid. stems from an oversimplification made by Kubo when computing the direct terms. Namely, in his computations Kubo disregarded the motion of the tide rai...

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Section: Hamiltonian Of the Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Corrections stemming from the non-osculating character of the Andoyer variables used in the description of rotation of the elastic Earth

Escapa

2011

Celest Mech Dyn Astr

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“…These values are 1 order of magnitude larger than the value that is used by Mathews and Bretagnon [] or Escapa et al . [] when they tried to estimate the influence of the core triaxiality on the prograde diurnal polar motion. Both of these two studies assumed that β f is around 1.0 × 10 −5 .…”

Section: Discussionmentioning

confidence: 92%

Influence of dynamical equatorial flattening and orientation of a triaxial core on prograde diurnal polar motion of the Earth

Sun

Shen

2016

JGR Solid Earth

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The noise floor of empirical models of the prograde diurnal Earth rotation could reach as low as 1 µas as shown by several recent studies. In another aspect, the differences between these empirical models with the theoretical model predictions given by International Earth Rotation and Reference Systems Service (IERS) Conventions (2010) for certain diurnal frequencies are more than 10 µas (e.g., K1). The triaxiality of the core is ignored in the theoretical model given by IERS Conventions (2010) because it is highly uncertain. To explain the differences between the empirical models and the theoretical model, we consider the possible influence of a triaxial core. We use the differences between the empirical models and the theoretical model predictions given by IERS Conventions (2010) as inputs to invert the triaxiality parameter of the core. In the inversion, we assume the ocean tide response is subjected to the admittance theory. So extra six admittance parameters are introduced to model the differences between the smooth responses inferred from the empirical models and that given by theoretical model predictions from IERS Conventions (2010). The results show that adding core triaxiality into the theoretical model could narrow the differences between the empirical models and the theoretical model at the prograde diurnal band. As for the dynamical equatorial flattening of the core, the estimates inverted based on the different empirical models are consistent within standard deviation. The results also suggest that the principal axes of the triaxial core do not coincide with the principal axes of the whole Earth.

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“…There are still many difficult open problems, such as magnetic effects (HUANG et al 2011), motions of inner layers (BARKIN and VILKE 2004), relativistic effects (KLIONER et al 2009), consistent and comprehensive treatment of a more realistic time-varying earth model, etc. Clearer separation of nutations and polar motion is also sought as we approach the EOP determination at a sub-diurnal rate (NILSSON et al 2010) and non-predictable constituents are accounted in the nutation angles like the free core nutation (FCN) (LAMBERT 2007;KRASNA et al 2013), whereas some short periodic predictable astronomical effects are included into PM ESCAPA et al 2002, BRZEZINSKI 2001.…”

Section: Present State Of the Earth Rotation Modelling And Outlookmentioning

confidence: 99%

Earth’s Rotation: A Challenging Problem in Mathematics and Physics

Ferrándiz

Navarro

Escapa

et al. 2014

Pure Appl. Geophys.

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Indirect effect of the triaxiality in the Hamiltonian theory for the rigid Earth nutations

Cited by 16 publications

References 8 publications

Corrections stemming from the non-osculating character of the Andoyer variables used in the description of rotation of the elastic Earth

Corrections stemming from the non-osculating character of the Andoyer variables used in the description of rotation of the elastic Earth

Influence of dynamical equatorial flattening and orientation of a triaxial core on prograde diurnal polar motion of the Earth

Earth’s Rotation: A Challenging Problem in Mathematics and Physics

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