Variational methods in the representation of the gravitational potential

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Variational methods in the representation of the gravitational potential

Popis výsledku v původním jazyce

The determination of the gravity field of the Earth is approached from the mathematical point of view. We discuss the integration of Laplace's equation under given boundary data. In particular we focus on the solution of a gravimetric boundary value problem. An approach is applied that follows the concept of variational methods and the notion of the weak solution. A system of elementary potentials is used as a function basis. We then construct Galerkin's system of linear equations for the coefficients in the approximation of the disturbing potential by means of linear combinations of basis functions. Elements of the matrix of this system are computed for the exterior of an ellipsoid of revolution. Ellipsoidal harmonics are used as a natural tool in these computations. The effects caused by the flattening of the ellipsoid are expressed up to terms multiplied by the square of the numerical eccentricity. A reference is also made which concerns effects caused by the topography.

Název v anglickém jazyce

Variational methods in the representation of the gravitational potential

Popis výsledku anglicky

The determination of the gravity field of the Earth is approached from the mathematical point of view. We discuss the integration of Laplace's equation under given boundary data. In particular we focus on the solution of a gravimetric boundary value problem. An approach is applied that follows the concept of variational methods and the notion of the weak solution. A system of elementary potentials is used as a function basis. We then construct Galerkin's system of linear equations for the coefficients in the approximation of the disturbing potential by means of linear combinations of basis functions. Elements of the matrix of this system are computed for the exterior of an ellipsoid of revolution. Ellipsoidal harmonics are used as a natural tool in these computations. The effects caused by the flattening of the ellipsoid are expressed up to terms multiplied by the square of the numerical eccentricity. A reference is also made which concerns effects caused by the topography.

Druh

D - Stať ve sborníku

CEP obor

DE - Zemský magnetismus, geodesie, geografie

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2003

Kód důvěrnosti údajů

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

Název statě ve sborníku

Cahiers du Centre Européen de Géodynamique et de Séismologie

ISBN

2-9599804-9-2

ISSN

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e-ISSN

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Počet stran výsledku

9

Strana od-do

3-11

Název nakladatele

Centre Européen de Géodynamique et de Séismologie

Místo vydání

Luxembourg

Místo konání akce

Muensbach

Datum konání akce

23. 10. 2001

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

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