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  4. On the transformation of the harmonic coefficients of the geopotential for small rotations of the coordinate system

On the transformation of the harmonic coefficients of the geopotential for small rotations of the coordinate system

ISTCGCAP.
2004;
Volume 65, 2004, Number 65, 2004
: 64-72
Authors:
  1. Alexander N. Marchenko
  2. N.P. Yarema
1
Department of Geodesy, Institute of Geodesy, Lviv Polytechnic National University
2
Lviv Polytechnic National University

The rigorous transformation of harmonic coefficients of the geopotential from the fixed at given epoch reference frame to some close system was considered. This problem was solved in the dosed form for the 2-nd degree harmonic coefficients with additional condition to save zero trace of the deviatoric part of the planet’s tensor of inertia that leads to a simple algorithm of the transformation based on the use of orthogonal matrices in the case of finite rotations.

1. Lambeck К. Determination of the Earth's pole of rotation from laser range observations to satellites II Bulletin Geodesique, 101, 1971. - pp. 263-281. 
2. Lemoine, F.G., S.C. Kenyon, J.K. Factor, R.G. Trimmer, N.K. Pavlis, D.S. Chinn, C.M. Cox, S.M. Klosko, S.B. Lulhcke, M.H. Torrence, Y.M. Wang, R.G. Williamson, E.C. Pavlis, R.ll. Rapp, and T.R. Olson. The Development of the Joint NASA GSFC and the National IMagery> and Mapping Agency (NIMA) Geopotential Model EGM96 U NASA Technical Paper NASA/TP-1998-206861, Goddard Space Flight Center, Greenbelt, USA, 1998. 
3. Madelund E. Die Mathematischen Hilfsmittel des Physikers // Berlin, Gottingen, Heidelberg, Springer-Verlag, 1957. 
4. Marchenko A., Schwinlzer P. Estimation of the Earth's tensor of inertia from recent global gravity field solutions // Journal of Geodesy, 76(9-10), 2003. - pp. 495-509.
5. Reigber Ch., Jochmann H., Wunsch J., Neumayer K.H., Schwintzer P. First Insight into Temporal Gravity Variability from CHAMP, // "First CHAMP Mission Results for Gravity, Magnetic and Atmospheric Studies". Springer-Verlag Berlin¬Heidelberg, 2003. - pp. 128-133.