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A Study on Geodetic Boundary Value Problems in Ellipsoidal Geometry

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In this thesis, special geodetic problems are treated as boundary value problems. The geodesic problem, the gravity field due to a homogeneous ellipsoid and the linear fixed altimetry-gravimetry problem are thoroughly studied in ellipsoidal geometry. The study is not limited on a biaxial ellipsoid (oblate spheroid), which is the wellknown mathematical model used in geodesy, but is extended on a triaxial ellipsoid. The key issue in the current analysis is the expression of the above problems in the suitable ellipsoidal coordinate system. The ellipsoidal coordinate system is described in some detail. For a one-to-one correspondence between ellipsoidal and Cartesian coordinates two variants of ellipsoidal coordinates are introduced. The transformation between ellipsoidal and Cartesian coordinates on a triaxial ellipsoid is presented in these two variants. Also, the element of distance and Laplace’s equation are expressed in these coordinates. The classical transformation between ellipsoidal and Cartesian coordinates on a biaxial ellipsoid is presented as a degenerate case.
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  NATIONAL TECHNICAL UNIVERSITY OF ATHENS   DEPARTMENT OF SURVEYING ENGINEERING A Study on Geodetic Boundary Value Problems in Ellipsoidal Geometry  by Georgios Panou  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Supervisor : Associate Professor D. Delikaraoglou Athens, June 2014   ii    iii NATIONAL TECHNICAL UNIVERSITY OF ATHENS   DEPARTMENT OF SURVEYING ENGINEERING A Study on Geodetic Boundary Value Problems in Ellipsoidal Geometry  by Georgios Panou  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Evaluation Committee : 1. Associate Prof. D. Delikaraoglou, Department of Surveying Engineering, NTUA. 2. Professor R. Korakitis, Department of Surveying Engineering, NTUA. 3. Professor V.-G. Papanicolaou, Department of Mathematics, NTUA. 4. Professor K. Papazissi, Department of Surveying Engineering, NTUA. 5. Professor D. Tsoulis, Department of Geodesy and Surveying, AUTH. 6. Professor I.N. Tziavos, Department of Geodesy and Surveying, AUTH. 7. Assistant Prof. N. Yannakakis, Department of Mathematics, NTUA. Athens, June 2014     iv «  Η    έγκριση   της    διδακτορικής    διατριβής    από   την    Ανώτατη    Σχολή    Αγρονόμων   και   Τοπογράφων    Μηχανικών   του    Ε  .  Μ  .  Π  . δεν   υποδηλώνει   αποδοχή   των   γνωμών   του   συγγραφέα  (  Ν . 5343/1932, Άρθρο  202)».
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