Evolution of the Earth's principal axes and moments of inertia: the canonical form of solution |
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Authors: | A N Marchenko O A Abrikosov |
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Institution: | (1) State University `Lviv Polytechnic', Faculty of Geodesy, S. Bandera St. 12, 290646 Lviv, Ukraine e-mail: march@polynet.lviv.ua; Tel.: +38 0322 39 84 56; Fax: +38 0322 74 43 00/+38 0322 74 41 43, UA |
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Abstract: | Harmonic coefficients of the 2nd degree are separated into the invariant quantitative (the 2nd-degree variance) and the qualitative
(the standardized harmonic coefficients) characteristics of the behavior of the potential V
2(t). On this basis the evolution of the Earth's dynamical figure is described as a solution of the time-dependent eigenvalues–eigenvectors
problem in the canonical form. Such a canonical quadratic form is defined only by temporal variations of the harmonic coefficients
and always remains finite, even within an infinite time interval. An additional condition for the correction or the determination
of temporal variations of the 2nd degree is obtained. Temporal variations of the fully normalized sectorial harmonic coefficients
are estimated in addition to ˙Cˉ
20, ˙Cˉ
21, and ˙Sˉ
21 of the EGM96 gravity model. In addition, a non-linear hyperbolic model for Cˉ
2m
(t), Sˉ
2m
(t) is constructed. The trigonometric form of the hyperbolic model leads to the consideration of the potential V
2(ψ) instead of V
2(t) within the closed interval −π/2≤ψ≤+π/2. Thus, it is possible to evaluate the global trend of V
2(t), the Earth's principal axes and the differences of the moments of inertia within the whole infinite time interval.
Received: 25 September 1998 / Accepted: 28 June 2000 |
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Keywords: | : Potential Gravitational quadrupole Harmonic coefficients Temporal variations |
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