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Rectangular rotation of spherical harmonic expansion of arbitrary high degree and order
https://orcid.org/0000-0001-5968-2139
Abstract 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 $$90^{\circ }$$ 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 in J Geodesy 86: 271–285, 2012a). As an example, we obtained $$2190\times 2190$$ 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.
Rectangular rotation of spherical harmonic expansion of arbitrary high degree and order
https://orcid.org/0000-0001-5968-2139
Abstract 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 $$90^{\circ }$$ 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 in J Geodesy 86: 271–285, 2012a). As an example, we obtained $$2190\times 2190$$ 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.
Rectangular rotation of spherical harmonic expansion of arbitrary high degree and order
https://orcid.org/0000-0001-5968-2139
Abstract 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 $$90^{\circ }$$ 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 in J Geodesy 86: 271–285, 2012a). As an example, we obtained $$2190\times 2190$$ 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.
Rectangular rotation of spherical harmonic expansion of arbitrary high degree and order
Fukushima, Toshio (author)
Journal of Geodesy ; 91
2017
Article (Journal)
Electronic Resource
English
Rectangular rotation of spherical harmonic expansion of arbitrary high degree and order
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