The transition from equations presented in matrix form for the perturbed Earth’s rotation to excitation equations

A convenient method for studying the influence of disturbing factors on Earth’s rotation, such as influence of oceans, atmosphere and hydrology, is representation of the Earth’s rotation equations in the excitation equations form, which was introduced by W. Munc and G. Macdonald. Traditionally, these factors are taken into account in two stages: first, an exact solution is found for an equation of the unperturbed rotation for given Earth’s model, and then the influence of small perturbation factors is taken into account in the form of corrections to the exact solution of unperturbed Earth’s rotation. The equations of unperturbed rotation for most modern theories of Earth’s rotation (and, possible, futures too) can be written in the form of matrix linear differential equations. The purpose of this study is to take into account the influence of small perturbations such as oceans, atmosphere and hydrology on Earth’s rotation in newly created theories of Earth’s rotation. A fairly general algorithm of converting perturbed equations in matrix form to the form of the excitation equations has been developed and presented. As an example, this method was applied to the relatively simple equations of the Sasao, Okubo and Saito theory based on the original Earth’s model of Molodenskii. The equations for finding corrections to the original solution are reduced to the form of excitation equations. The developed algorithm is proposed to be used to transition to equations in the form of excitation in newly created theories of the Earth’s rotation.

1. Pasynok S. L. Ocenka metrologicheskikh kharakteristik mezhdunarodnykh opornykh znachenij parametrov vrashсheniya Zemli. Almanac of Modern Metrology (10), 151–166 (2017). (In Russ.)

2. W. H. Munk and G. J. F. MacDonald. The Rotation of the Earth. Cambridge University Press, London (1960).

3. Helmut Moritz, Ivan I. Mueller. Earth rotation: theory and observation. Ungar, New York (1987).

4. Sasao T., Okubo S., Saito M. A simple theory on the dynamical effects of a stratified fluid core upon nutational motion of the Earth. In: Fedorov E. P., Smith M. L., Bender P. L. (eds). Nutation and the Earth’s Rotation. International Astronomical Union / Union Astronomique Internationale, 78, (1980). https://doi.org/10.1007/978-94-010-9568-6_27

5. Dehant V., Mathews P. M. Precession, nutation, and Wobble of the Earth, Cambridge University Press, Cambridge (2015). https://doi.org/10.1017/CBO9781316136133

6. Sidorenkov Nikolay S. The interaction between Earth’s rotation and geophysical processes. Wiley, Weinheim (2009).

7. Saynisch J., Wenzel M., Schröter J. Assimilation of Earth rotation parameters into a global ocean model: excitation of polar motion. Nonlinear Processes in Geophysics, 18(5), 581–585 (2011). https://doi.org/10.5194/npg-18-581-2011

8. Pasynok S. L. Metody opredeleniya opornykh znachenij uglov nutacii Zemli. Doctoral dissertation Technical Sciences, Mendeleevo, VNIIFTRI (2014). (In Russ.)

9. Zharov V. E., Vrashhenie Zemli i dinamika atmosfery. Doctoral dissertation Physical and Mathematical Sciences, St. Petersburg University (1998). (In Russ.)

10. Zharov V. E., Pasynok S. L. Theory of nutation of the non-rigid Earth with the atmosphere. Journees 2002 “Astrometry from ground and from space”, 25–28 September 2002, pp. 140–145, Bucharest (2002).