Estimation of coefficients of differential equations modeling the polar motion

Details Estimation of coefficients of differential equations modeling the polar motion Estimation of coefficients of differential equations modeling the polar motion

Apr 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008jsrs.meet..202a&link_type=abstract

"Proceedings of the "Journées Systèmes de Référence Spatio-temporels 2007". Observatoire de Paris, 17-19 September 2007. Editor:

Physics

Scientific paper

We dealt with Liouville equations which describes the polar motion and presents a system of first-order equations with coefficients depending on T (period of free nutation) and Q (mantle quality factor). The actual problem is to evaluate these coefficients (i.e. T and Q) by:1) excitation functions series used for constructing right hand-side of Liouville equations and 2) polar coordinates series which one can interpret as a solution of the equations. Validity of this task which is typical inverse problem is shown. Practically we solved a number of “direct” ones under different meanings of T and Q. The preferred values of parameters to be estimated are: T=425-440 days and Q=20-60. Disagreement between our model based on Liouville equations and data series is conditioned by physical reasons, as far as mathematical problem is valid. Possible causes of such disagreement are discussed. In this work, we attempted to find optimal values T and Q as parameters fitted by the numerical integration of the Liouville equations with simultaneous modeling of the yearly and Chandlerian components of the pole motion. Also, the stability of values (T and Q) depending on time, length of data sets and different variants of excitation functions (right-hands sides of equations) was investigated.

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