Počet záznamů: 1  

On computing ellipsoidal harmonics using Jekeli's renormalization

  1. 1. 0388887 - ASU-R 2013 RIV DE eng J - Článek v odborném periodiku
    Sebera, Josef - Bouman, J. - Bosch, W.
    On computing ellipsoidal harmonics using Jekeli's renormalization.
    Journal of Geodesy. Roč. 86, č. 9 (2012), s. 713-726 ISSN 0949-7714
    Institucionální podpora: RVO:67985815
    Klíčová slova: Earth's gravitational field * spherical and ellipsoidal harmonics * hypergeometric function
    Kód oboru RIV: BN - Astronomie a nebeská mechanika, astrofyzika
    Impakt faktor: 2.808, rok: 2012

    Gravity data observed on or reduced to the ellipsoid are preferably represented using ellipsoidal harmonics instead of spherical harmonics. Ellipsoidal harmonics, however, are difficult to use in practice because the computation of the associated Legendre functions of the second kind that occur in the ellipsoidal harmonic expansions is not straightforward. Jekeli's renormalization simplifies the computation of the associated Legendre functions. We extended the direct computation of these functions-as well as that of their ratio-up to the second derivatives and minimized the number of required recurrences by a suitable hypergeometric transformation. Compared with the original Jekeli's renormalization the associated Legendre differential equation is fulfilled up to much higher degrees and orders for our optimized recurrences.
    Trvalý link: http://hdl.handle.net/11104/0217788