PPAP (Problem of Pen-Apple-Pen)

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Александр Устинов
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PPAP (Problem of Pen-Apple-Pen)

Сообщение Александр Устинов » 07 фев 2017, 10:01

Ученые идут в ногу со временем;)

PPAP (Problem of Pen-Apple-Pen)

Toshio Fukushima. National Astronomical Observatory of Japan

In order to move the polar singularity of arbitrary spherical harmonic expansion to a point on the equator, we rotate the expansion around the $y$-axis by 90 degrees such that the $x$-axis becomes a new pole. The expansion coefficients are transformed by multiplying a special value of Wigner $D$-matrix and a normalization factor. The transformation matrix is unchanged whether the coefficients are $4 \pi$ fully-normalized or Schmidt quasi-normalized. The matrix is recursively computed by the so-called X-number formulation (Fukushima, 2012, J. Geodesy, 86, 271--285). As an example, we obtained 2,190$\times$2,190 coefficients of the rectangular rotated spherical harmonic expansion of EGM2008. A proper combination of the original and the rotated expansions will be useful in (i) integrating the polar orbits of artificial satellites precisely, and (ii) synthesizing/analyzing the gravitational/geomagnetic potentials and their derivatives accurately in the high latitude regions including the arctic and antarctic area. (Reference: Fukushima, 2017, J. Geodesy, accepted, DOI: 10.1007/s00190-017-1004-3)
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