On the inclination functions and a rapid stable procedure for their evaluation together with derivatives |
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| Authors: | R H Gooding C A Wagner |
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| Institution: | (1) Centre of Satellite Engineering Research, University of Surrey, Guildford, Surrey, England, UK;(2) Present address: 19 Abbot’s Ride, Farnham, Surrey, GU9 8HY, England, UK;(3) National Oceanic and Atmospheric Administration, Laboratory for Satellite Altimetry, Silver Spring, MD, USA |
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| Abstract: | The authors’ individual work on the inclination functions over a period of more than 30 years has led to the need for a joint
paper. Intervening papers by other authors have demonstrated misunderstandings needing to be corrected, in particular concerning
the key recurrence relation published by the present first author in 1971. This relation is remarkably stable, though this
has not always been recognized. The real source of error with the specific functions that are involved in the recurrence relation
arises from the possibilities for underflow (as well as overflow) in the computation. The problem exists even with normalized
versions of the functions, and is carefully addressed. Very important, for both academic and practical reasons, is a general
invariance relation that had been found earlier by the second author, for which a proof is given here for the first time.
Some numerical results from our new (and highly efficient) procedure for computing the inclination functions are tabulated,
and comparisons made with the results of other authors. Finally, Fortran code for an optimized implementation of this procedure
is in supplementary material.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. |
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| Keywords: | Inclination functions Rotation of spherical harmonics Satellite perturbations |
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