Skip to main content
Log in

Obtaining the free frequencies of the non‐rigid Earth

  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript

Abstract

In this paper, the mathematical algorithm elaborated by González, Getino and Farto (1998) is applied to four different non‐rigid Earth models, in order to obtain the analytical expressions of the corresponding free frequencies. The solutions are studied, and the contributions of the different considered effects are evaluated. A numerical integration is also carried out, showing the validity of the obtained analytical solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Abhyankar, S. S.: 1955, 'On the ramification of algebroid functions', Amer. J. Math. 77, 575–592.

    Google Scholar 

  2. Dziewonski, A. M. and Anderson D. L.: 1981, 'Preliminary reference earth model', Phys. Earth planet. Inter. 25, 297–356.

    Google Scholar 

  3. González, A. B., Getino, J. and Farto, J. M.: 1998, An algorithm for an eigenvalues problem in the Earth rotation theory, J. Comput. Appl. Math. (submitted).

  4. Getino, J.: 1995a, 'An interpretation of the core–mantle interaction problem', Geophys. J. Int. 120, 693–705.

    Google Scholar 

  5. Getino, J.: 1995b, 'Forced nutations of a rigid mantle–liquid core Earth model in canonical formulation', Geophys. J. Int. 122, 803–814.

    Google Scholar 

  6. Getino, J. and Ferrándiz, J. M.: 1995, 'On the effect of the elastic mantle on the Earth rotation', Celest. Mech. 61, 117–180.

    Google Scholar 

  7. Getino, J. and Ferrándiz, J. M.: 1996a, 'Canonical treatment of dissipative forces between Earth mantle and core', in: S. Ferraz-Mello et al. (eds), Dynamics Ephemerides and Astrometry of the Solar System, Proc. IAU Symp. No. 172 (Paris), 233–238.

  8. Getino, J. and Ferrándiz, J. M.: 1996b, 'Canonical approach for the free nutations of a nonrigid Earth with solid inner core', in: in Proc. Fourth Int.Workshop on Positional and Celestial Mechanics, Peñíscola, Spain, (in press).

  9. Getino, J. and Ferrándiz, J. M.: 1997, 'A Hamiltonian approach to dissipative phenomena between Earth mantle and core, and effects on free nutation', Geophys. J. Int. 130, 326–334.

    Google Scholar 

  10. Getino, J. and Ferrándiz, J. M.: 1998, 'The effect of the solid inner core on the free nutations of the Earth', Preprint.

  11. González, A. B. and Getino, J.: 1997, 'The rotation of non-rigid, non-symmetrical Earth I: Free nutations', Celest. Mech. 68(2), 139–149.

    Google Scholar 

  12. Hori, G.: 1966, 'Theory of general perturbations with unspecified canonical variables', Publ. Astron. Soc. Japan 18, 287.

    Google Scholar 

  13. Kinoshita, H.: 1977, 'Theory of the rotation of the rigid Earth', Celest. Mech. 15, 277–326.

    Google Scholar 

  14. Mathews, P. M., Buffet, B. A., Herring, T. A. and Shapiro, I. I.: 1991, 'Forced nutations of the Earth: Influence of solid inner core Dynamics 2. Numerical results and comparisons', J. Geophys. Res. 96, 8243–8257.

    Google Scholar 

  15. Sasao T., Okubo, S. and Saito, M.: 1980, 'A simple theory on the dynamical effects of a stratified fluid core upon nutational motion of the Earth', in: Proc. IAU Symp. No. 78, p. 165.

    Google Scholar 

  16. Walker, R. J.: 1962, Algebraic Curves, Dover, New York.

    Google Scholar 

  17. Woolard, E. W.: 1953, Astron. Papers Amer. Ephemeris 15, pt. 1.

    Google Scholar 

  18. Zurro, M. A.:1993, 'The Abhyankar–Jung theorem revisited', J. Pure Appl. Algebra 90, 275–82.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Getino, J., Farto, J.M. & Ferrándiz, J.M. Obtaining the free frequencies of the non‐rigid Earth. Celestial Mechanics and Dynamical Astronomy 71, 95–108 (1998). https://doi.org/10.1023/A:1008358808146

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008358808146

Navigation