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Satellite orbit integration based on canonical transformations with special regard to the resonance and coupling effects / C. Cui (1997)

Public Titre : Satellite orbit integration based on canonical transformations with special regard to the resonance and coupling effects Type de document : Monographie Auteurs : C. Cui, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1997 Collection : DGK - A Sous-collection : Theoretische Geodäsie num. 112 Importance : 128 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-8193-2 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Techniques orbitales [Termes IGN] modèle de géopotentiel [Termes IGN] orbitographie [Termes IGN] résonance [Termes IGN] transformation canonique Résumé : (Auteur) Presented are the concept and the methods to get a complete analytical solution of the system of equations describing the motion of satellites under the action of a set of body and dissipative forces with consideration of coupling and resonance effects. A solution for the perturbations due to the Earth's direct geogravitation, due to the luni-solar gravitation, due to earth tide effects as well as due to the air drag and the normal solar radiation pressure is given including the interaction of orbital perturbations due to the different perturbation effects as well as resonance effects up to the second order. The equations of motion are formulated as a canonical system of equations including dissipation force terms by using the Hill-variables. An integrable Hamiltonian of such a system has been given in a quite general form as a guidance to select suitable canonical transformations and to solve the transformed system of equations. Resonance terms of the Hamiltonian are classified into two categories: normal (medium) resonance terms and strong ones. A successive infinitesimal Lie-transformation scheme has been developed in a general form to remove all periodic terms leading either to non-resonance effects or to medium resonance effects from the Hamiltonian. This scheme has been applied to the system of equations of motion of the satellites involving also the action of non-gravitational forces. By this transformation the non-gravitational force terms are transformed too. In such a way a transformed system of equations (transformed Hamiltonian and transformed non-gravitational force terms) has been obtained. This transformed system of equations consists of a solvable major part and a minor part including both the strong resonance terms of the Hamiltonian together with the dissipation terms. The transformed system of equations has been solved by a linearisation approach usually called the Encke method. This method provides a regular solution for all orbital configurations with non-zero inclinations, among them in particular also orbits with the critical inclination, terrestrial repeating (cyclic) orbits and the polar orbits. All these kinds of orbit are of major importance for Earth observation satellites, but until now, they have only been treated insufficiently by the various existing forms of analytical solutions. Numéro de notice : 28248 Affiliation des auteurs : non IGN Thématique : IMAGERIE/POSITIONNEMENT Nature : Monographie Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63594

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Zur analytischen Bahnberechnung künstlicher Erdsatelliten mittels konformer Transformationen / R. You (1995)

Public Titre : Zur analytischen Bahnberechnung künstlicher Erdsatelliten mittels konformer Transformationen Titre original : [Sur le calcul analytique d'orbite de satellites artificiels terrestres au moyen de transformations conformes] Type de document : Thèse/HDR Auteurs : R. You, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1995 Collection : DGK - C Sous-collection : Dissertationen num. 440 Importance : 213 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-9483-3 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Techniques orbitales [Termes IGN] équation linéaire [Termes IGN] ERS-1 [Termes IGN] Lageos [Termes IGN] mécanique orbitale [Termes IGN] mouvement Képlerien [Termes IGN] orbite [Termes IGN] orbitographie [Termes IGN] satellite GPS [Termes IGN] transformation canonique Résumé : (Auteur) In this dissertation, the motions of satellites affected by conservative and nonconservative forces in the Newtonian mechanics are interpreted as geodesic motions. The dynamical geometrical properties of the motions are analyzed. In particular, the motions of satellites in the Newtonian Earth's gravitational field are explained as the minimal geodesic flows on Maupertuis' manifolds according to the Maupertuis' variational principle of least action. The Euclidean space, in which satellites move, is a conformal map of a Maupertuis' manifold. The Maupertuis' manifolds are in detail discussed. Their embedding is solved according to the Brinkmann's embedding theorem and illustrated for the elliptic Kepler motions and orbits perturbed by the Earth's oblateness. To solve analytically the problems of satellite motions, the conformal Mapping of type KS transformation is introduced. In particular, a set of canonical KS elements for elliptic Kepler motions is derived. By virtue of this conformal transformation, the equations of the Kepler motion are regularized und transformed into linear differential equations. At the same time, the equations of the elliptic Kepler motion are also stabilized. These canonical KS elements are free from all singularities which occur in the classical Kepler elements. Especially, the solutions of the perturbation computation with the KS elements keep away from the strictly resonancelike amplification. An analytical solution of first order due to perturbations of an anisotropic terrestial gravitational field, the direct lunisolar influence, the tides of the earth, the relativistic gravitational effects, the atmospheric drag and the direct solar radiation pressure is given and compared with a numerical integration on the orbits of GPS, ERS1 and LAGEOS1. Numéro de notice : 28049 Affiliation des auteurs : non IGN Thématique : IMAGERIE/POSITIONNEMENT Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63396

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Die Bewegung künstlicher Satelliten im anisotropen Gravitationsfeld einer gleichmäßig rotierenden starren Modellerde. Eine analytische Lösung 2. Ordnung / C. Cui (1990)

Public Titre : Die Bewegung künstlicher Satelliten im anisotropen Gravitationsfeld einer gleichmäßig rotierenden starren Modellerde. Eine analytische Lösung 2. Ordnung Titre original : [Le mouvement d'un satellite artificiel dans un champ de pesanteur anisotrope d'une Terre modèle fixe à rotation régulière : une solution analytique de second ordre] Type de document : Thèse/HDR Auteurs : C. Cui, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1990 Collection : DGK - C Sous-collection : Dissertationen num. 357 Importance : 106 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-9405-5 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Techniques orbitales [Termes IGN] champ de pesanteur terrestre [Termes IGN] compensation [Termes IGN] itération [Termes IGN] mécanique céleste [Termes IGN] mouvement Képlerien [Termes IGN] satellite artificiel [Termes IGN] transformation canonique [Termes IGN] transformation de Lie Résumé : (Auteur) A second order analytical solution of the equation of motion of artificial satellites in the gravitational field of a uniformly rotating non-symmetrical solid earth has been derived using canonical transformations. The solution is consistent in the linear terms with solutions by Brouwer and by Kaula. The numerical tests show an accuracy of the solution of the order 10-10 for the zonal perturbations and of the order 10-8 for the tesseral perturbations. The solution can be employed to evaluate the perturbations from arbitrary harmonic terms. To derive the analytical solution an intermediate orbit has been developed ; a quasi-mean-value method and an iterative method for solving the Lie-Hori equation to determine the generating function of the Lie-transformation have been developed. A formula of the inverse of the product of two Lie-transformations has been derived. An application of the solution to determine the harmonic coefficients of the geopotential using the satellite-to-satellite-tracking data of the low- low-mode has been outlined. The inclination function by Kaula and the excentricity function by Lelgemann have been investigated in detail. A set of recurrence formulas and symmetrical properties of both functions have been derived. Numéro de notice : 59536 Affiliation des auteurs : non IGN Thématique : IMAGERIE/POSITIONNEMENT Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=60589

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A contribution to 3D-operational geodesy, Part 4. The observation equations of satellite geodesy in the model of integrated geodesy / Bernd Eissfeller (1986)

Public Titre de série : A contribution to 3D-operational geodesy, Part 4 Titre : The observation equations of satellite geodesy in the model of integrated geodesy Type de document : Monographie Auteurs : Bernd Eissfeller, Auteur ; Günter W. Hein, Auteur Editeur : Munich : Universität der Bundeswehr Année de publication : 1986 Collection : Schriftenreihe des Instituts für Geodäsie, ISSN 0173-1009 num. 17 Importance : 187 p. Format : 21 x 30 cm Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale [Termes IGN] accélération [Termes IGN] élément orbital [Termes IGN] équation de Hamilton-Jacobi [Termes IGN] géodésie tridimensionnelle [Termes IGN] matrice de rotation [Termes IGN] orbitographie [Termes IGN] système de référence géodésique [Termes IGN] transformation canonique Index. décimale : 30.60 Géodésie spatiale Résumé : (Auteur) This work is the fourth part of a series on the development of operational or integrated geodesy. After having published the observation equations for geodetic measurements of terrestrial type (Hein, 1982a), the concept of a solution (Hein,1982b), the first operational software OPERA on the processing of terrestrial data in the integrated adjustment model (Hein and Landau,1983), we have tried to outline here in detail the observation equations of satellite geodesy including orbit determination in that unified model. Thereby we refer to the main principle outlined already by Moritz (1980, p225 to 230) and other developments of the Stuttgart school on a slightly different approach to operational geodesy, e.g. (Grafarend, 1979; 1981 1982), in particular (Grafarend and Livieratos, 1978 ; Grafarend and Heinz, 1978) - to mention only some of the publications. The present state-of-the-art in integrated geodesy is summerized in Hein (1986). Numéro de notice : 62044 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Monographie Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=61028

Voir aussi

• A contribution to 3D-operational geodesy, Part 3. OPERA, A multi-purpose program for operational adjustment of geodetic observations of terrestrial type / Günter W. Hein (1983)

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Les fondements de la mécanique céleste / Y. Thiry (1970)

Public Titre : Les fondements de la mécanique céleste Type de document : Guide/Manuel Auteurs : Y. Thiry, Auteur Editeur : New York, Amsterdam : Gordon and Breach Année de publication : 1970 Collection : Cours et documents de mathématiques et de physique Importance : 198 p. Format : 15 x 23 cm ISBN/ISSN/EAN : 978-0-677-50270-0 Langues : Français (fre) Descripteur : [Vedettes matières IGN] Astronomie fondamentale [Termes IGN] distribution de Poisson [Termes IGN] équation [Termes IGN] équation de Lagrange [Termes IGN] équation de Poisson [Termes IGN] force de gravitation [Termes IGN] intégrale de Jacobi [Termes IGN] intégrale de Laplace [Termes IGN] mécanique céleste [Termes IGN] mécanique de Hamilton [Termes IGN] mécanique de Lagrange [Termes IGN] mouvement Képlerien [Termes IGN] orbite [Termes IGN] orbite circulaire [Termes IGN] orbite képlerienne [Termes IGN] problème des trois corps [Termes IGN] transformation canonique Index. décimale : 31.10 Astronomie fondamentale Numéro de notice : 49773 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Manuel de cours Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=48010

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Mécanique classique / H. Goldstein (1964)

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