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Rotation of the elastic Earth: the role of the angular-velocity-dependence of the elasticity-caused perturbation

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Abstract

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.

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References

  • Efroimsky M., Goldreich P.: Gauge symmetry of the N-body problem in the Hamilton-Jacobi approach. J. Math. Phys. 44, 5958–5977 (2003) astro-ph/0305344

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • 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/0409282

  • Efroimsky M., Escapa A.: The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables. Celest. Mech. Dyn. Astron. 98, 251–283 (2007) astro-ph/0506427

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Getino J., Ferrándiz J.M.: On the effect of the mantle elasticity on the Earth’s rotation. Celest. Mech. Dyn. Astron. 61, 117–180 (1995)

    Article  ADS  Google Scholar 

  • Kinoshita H.: Theory of the rotation of the rigid Earth. Celest. Mech. Dyn. Astron. 15, 277–326 (1977)

    MathSciNet  Google Scholar 

  • Krasinsky G.A.: Earth’s precession-nutation motion: the error analysis of the theories IAU 2000 and IAU 2006 applying the VLBI data of the years 1984–2006. Celest. Mech. Dyn. Astron. 101, 325–336 (2008)

    Article  MATH  ADS  Google Scholar 

  • Kubo Y.: A core-mantle interaction in the rotation of the Earth. Celest. Mech. Dyn. Astron. 19, 215–241 (1979)

    MATH  MathSciNet  Google Scholar 

  • Kubo Y.: Solution to the rotation of the elastic Earth by method of rigid dynamics. Celes. Mech. Dyn. Astron. 50, 165–187 (1991)

    Article  MATH  ADS  Google 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 

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  1. 5-8-3 Higashi-gotanda, Shinagawa-ku, Tokyo, 141-0022, Japan

    Yoshio Kubo

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  1. Yoshio Kubo
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Correspondence to Yoshio Kubo.

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Kubo, Y. Rotation of the elastic Earth: the role of the angular-velocity-dependence of the elasticity-caused perturbation. Celest Mech Dyn Astr 105, 261–274 (2009). https://doi.org/10.1007/s10569-009-9225-2

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  • DOI: https://doi.org/10.1007/s10569-009-9225-2

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