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Non-singular expressions for vector and gradient tensor of gravitation in a geocentric spherical frame
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för data-, elektro- och lantmäteriteknik.ORCID-id: 0000-0003-0067-8631
2008 (engelsk)Inngår i: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 34, nr 12, s. 1762-1768Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

The traditional expressions of the gravitational vector (GV) and the gravitational gradient tensor (GGT) have complicated forms depending on the first- and the second-order derivatives of associated Legendre functions (ALF), and also singular terms when approaching the poles. This article presents alternative expressions for the GV and GGT, which are independent of the derivatives, and are also non-singular. By using such expressions, it suffices to compute the ALF to two additional degrees and orders, instead of computing the first and the second derivatives of all the ALF. Therefore, the formulas are suitable for computer programming. Matlab software as well as an output of a numerical computation around the North Pole is also presented based on the derived formulas.

sted, utgiver, år, opplag, sider
2008. Vol. 34, nr 12, s. 1762-1768
Emneord [en]
Non-singularity, associated Legendre functions, normalization
HSV kategori
Forskningsprogram
TEKNIK
Identifikatorer
URN: urn:nbn:se:hv:diva-7902DOI: 10.1016/j.cageo.2008.02.022OAI: oai:DiVA.org:hv-7902DiVA, id: diva2:845884
Tilgjengelig fra: 2015-08-13 Laget: 2015-08-13 Sist oppdatert: 2017-12-04bibliografisk kontrollert

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