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Transformation of amplitudes and frequencies of precession and nutation of the earth’s rotation vector to amplitudes and frequencies of diurnal polar motion / Bernd Richter in Journal of geodesy, vol 84 n° 1 (January 2010)  

Public [article]  inJournal of geodesy > vol 84 n° 1 (January 2010) . - pp 1 - 18 Titre : Transformation of amplitudes and frequencies of precession and nutation of the earth’s rotation vector to amplitudes and frequencies of diurnal polar motion Type de document : Article/Communication Auteurs : Bernd Richter, Auteur ; J. Engels, Auteur ; Erik W. Grafarend, Auteur Année de publication : 2010 Article en page(s) : pp 1 - 18 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] équation différentielle [Termes IGN] mouvement du pôle [Termes IGN] nutation [Termes IGN] précession [Termes IGN] rotation de la Terre Résumé : (Auteur) The temporal change of the rotation vector of a rotating body is, in the first order, identical in a space-fixed system and in a body-fixed system. Therefore, if the motion of the rotation axis of the earth relative to a space-fixed system is given as a function of time, it should be possible to compute its motion relative to an earth-fixed system, and vice versa. This paper presents such a transformation. Two models of motion of the rotation axis in the space-fixed system are considered: one consisting only of a regular (i.e., strictly conical) precession and one extended by circular nutation components, which are superimposed upon the regular precession. The Euler angles describing the orientation of the earth-fixed system with respect to the space-fixed system are derived by an analytical solution of the kinematical Eulerian differential equations. In the first case (precession only), this is directly possible, and in the second case (precession and nutation), a solution is achieved by a perturbation approach, where the result of the first case serves as an approximation and nutation is regarded as a small perturbation, which is treated in a linearized form. The transformation by means of these Euler angles shows that the rotation axis performs in the earth-fixed system retrograde conical revolutions with small amplitudes, namely one revolution with a period of one sidereal day corresponding to precession and one revolution with a period which is slightly smaller or larger than one sidereal day corresponding to each (prograde or retrograde) circular nutation component. The peculiar feature of the derivation presented here is the analytical solution of the Eulerian differential equations. Copyright Springer Numéro de notice : A2010-032 Affiliation des auteurs : IGN+Ext (1940-2011) Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-009-0339-9 Date de publication en ligne : 16/09/2009 En ligne : https://doi.org/10.1007/s00190-009-0339-9 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30228 [article]

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266-2010011	SL	Revue	Centre de documentation	Revues en salle	Disponible

Eine approximative Lösung der fixen gravimetrischen Randwertaufgabe im Innen- und Außenraum der Erde / J. Engels (1991)

Public Titre : Eine approximative Lösung der fixen gravimetrischen Randwertaufgabe im Innen- und Außenraum der Erde Titre original : [Solution approximative au problème des valeurs aux limites fixes gravimétriques sur terre et dans l'espace] Type de document : Thèse/HDR Auteurs : J. Engels, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1991 Collection : DGK - C Sous-collection : Dissertationen num. 379 Importance : 115 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-9425-3 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] géoïde terrestre [Termes IGN] harmonique sphérique [Termes IGN] masse de la Terre [Termes IGN] modèle de géopotentiel [Termes IGN] potentiel de pesanteur terrestre [Termes IGN] problème des valeurs limites [Termes IGN] système linéaire Index. décimale : 30.40 Géodésie physique Résumé : (Auteur) In order to determine the geoïd, which is situated partially in the interior, partially in the exterior of the Earth's body, it is common practice to calculate the gravity potential of the Earth by solving the geodetic boundary value problem in the exterior space. By means of a density hypothesis for the topographic masses the potential is "continued downwards" into the Earth's interior. This thesis constructs the geoïd from the solution of an exterior as well as an interior boundary value problem, i. e. it does not employ reductions. It is well known that the gravitational part of the potential fulfills the Laplacian differential equation in mass free points. On the other hand, in the interior the potential obeys the Poisson differential equation, whereby the inhomogeneity is only known approximately (mainly from seismic observations). Thus we are led to the inverse problem of geophysics. We ensure that the mass density function is compatible with the boundary function as prescribed by the Newtonian gravitational law. This is achieved by adding a correction function to the model density and the model potential, respectively. A correction potential function is chosen which fulfills the bipotential equation. Gravity values at the Earth's surface are taken to be boundary values; the geometry of the surface is considered as known. In the first chapter the boundary value problem (especially that of the interior domain) are mathematically formulated. In the second chapter we consider the boundary value problem in the exterior space; we quote uniqueness and existence theorems and discuss several solution methods. We present in detail the method of series expansions with spherical harmonies, which is well suited for global calculations; we derive a linear equation System, which bas to be solved for the unknown series coefficients. Accordingly the third chapter deals with the interior boundary value problem. In the fourth chapter a reference potential for both domains is constructed. In the last chapter numerical simulation amputations are presented, whereby a good agreement with the reduction methods is found. Numéro de notice : 28092 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63439

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