On a Fortran procedure for rotating spherical-harmonic coefficients

Authors: Gooding, R.1; Wagner, C.2

Source: Celestial Mechanics and Dynamical Astronomy, Volume 108, Number 1, September 2010 , pp. 95-106(12)

Publisher: Springer

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Abstract:

The authors describe a Fortran subroutine that rotates the coefficients of a given spherical-harmonic model (in particular the geopotential). It is based on a paper by T. Risbo, working with the d-functions fundamental to axis rotations in Quantum Mechanics, his approach being equally applicable to the inclination functions of satellite geodesy (which we obtain as an option in the procedure). The subroutine applies Risbo’s approach to evaluate, for a given inclination, stably and accurately, the necessary d-functions up to a specified degree, whilst at the same time ‘rotating’ (for each degree in turn) the values of the harmonic coefficients. We follow Risbo’s helpful example by including a listing of the new subroutine.

Keywords: Inclination functions; Risbo’s approach; Rotation Matrices; Rotation of spherical harmonics

Document Type: Research Article

DOI: http://dx.doi.org/10.1007/s10569-010-9293-3

Affiliations: 1: Centre of Satellite Engineering Research, University of Surrey, Guildford, Surrey, England, UK, Email: family.gooding@virgin.net 2: National Oceanic and Atmospheric Administration, Laboratory for Satellite Altimetry, Silver Spring, MD, USA, Email: carl.wagner@noaa.gov

Publication date: September 1, 2010

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