Model of Oscillations of Earth’s Poles Based on Gravitational Tides

  • S. A. Kumakshev
Conference paper
Part of the Springer Geology book series (SPRINGERGEOL)


A model of oscillations of Earth’s poles is constructed on the basis of the analysis of the gravitational torques from Sun and Moon. The model reflects physical processes and does not imply using curve fitting techniques, based, for example, on the polynomial approximation. Within the framework of this model, the Chandler frequency is interpreted as the fundamental frequency of oscillations of the mechanical system and the annual frequency as the frequency of the excitation force. A fine mechanism of excitation of the oscillations based on the combination of natural and forced frequencies is revealed. The model has only six parameters that can be identified by applying the least squares technique to the experimental data of the International Earth Rotation and Reference Systems Service. The prediction provided by the proposed model has high degree of accuracy for an interval of several years.


Earth’s pole oscillations Gravitational torques 



This study was partly supported by the Russian Foundation for Basic Research (project 17-01-00538).


  1. 1.
    Munk, W.H., Macdonald, G.T.F.: The Rotation of the Earth. Cambridge University Press, New York (1960)zbMATHGoogle Scholar
  2. 2.
    IERS Annual Reports, 1990 July 1991 bis 2000 July 2001. Central Bureau of IERS. Observatoire de ParisGoogle Scholar
  3. 3.
    Moritz, H., Mueller, I.I.: Earth Rotation: Theory and Observation. Ungar, New York (1987)Google Scholar
  4. 4.
    Avsyuk, Y.N.: Tidal forces and natural processes. Inst. Physics of the Earth RAS, Moscow (1996). (in Russian)Google Scholar
  5. 5.
    Ishlinskiy, A.Y.: Orientation, Gyroscopes and Inertial Navigation. Nauka, Moscow (1976)Google Scholar
  6. 6.
    Ilyushin, A.A.: Continuum Mechanics. Moscow University Press, Moscow (1990)Google Scholar
  7. 7.
    Akulenko, L.D., Kumakshev, S.A., Markov, Y.G., Rykhlova, L.V.: A gravitational-tidal mechanism for the Earth’s polar oscillations. Astron. Rep. 49(10), 847–857 (2005)ADSCrossRefGoogle Scholar
  8. 8.
    Beletskii, V.V.: Satellite motion about the center of mass in gravitational field. Izdat. MGU, Moscow (1975). (in Russian)Google Scholar
  9. 9.
    Klimov, D.M., Akulenko, L.D., Kumakshev, S.A.: Mechanical model of the perturbed motion of the Earth with respect to the barycenter. Dokl. Phys. 58(11), 505–509 (2013)ADSCrossRefGoogle Scholar
  10. 10.
    Linnik, J.W.: Method of Least Squares and Principles of the Theory of Observations. Pergamon Press, New York, Oxford, London, Paris (1961)zbMATHGoogle Scholar
  11. 11.
    Kalarus, M., Schuh, H., Kosek, W., Akyilmaz, O., Bizouard, C., Gambis, D., Gross, R., Jovanovirc, B., Kumakshev, S., Kutterer, H., Mendes Cerveira, P.J., Pasynok, S., Zotov, L.: Achievements of the Earth orientation parameters prediction comparison campaign. J. Geod. 84, 587–596 (2010)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Problems in Mechanics of the Russian Academy of SciencesMoscowRussia

Personalised recommendations