On Computing Ellipsoidal Harmonics Using Jekeli´s Renormalization

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F12%3A00196251" target="_blank" >RIV/68407700:21110/12:00196251 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985815:_____/12:00388887

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00190-012-0549-4" target="_blank" >http://dx.doi.org/10.1007/s00190-012-0549-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00190-012-0549-4" target="_blank" >10.1007/s00190-012-0549-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Computing Ellipsoidal Harmonics Using Jekeli´s Renormalization

Popis výsledku v původním jazyce

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. The derived functions were tested by comparing functionals of the gravitational potential computed with both ellipsoidal and spherical harmonic syntheses. As an inp

Název v anglickém jazyce

On Computing Ellipsoidal Harmonics Using Jekeli´s Renormalization

Popis výsledku anglicky

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. The derived functions were tested by comparing functionals of the gravitational potential computed with both ellipsoidal and spherical harmonic syntheses. As an inp

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BN - Astronomie a nebeská mechanika, astrofyzika

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Geodesy

ISSN

0949-7714

e-ISSN

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Svazek periodika

86

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

14

Strana od-do

713-726

Kód UT WoS článku

000307556800003

EID výsledku v databázi Scopus

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