2016/11/28 by Γεώργιος Πάνου, Panou, G., R. Korakitis +1
Earth and Planetary Sciences · Engineering · Social Sciences · #Computational Engineering #FOS: Computer and information sciences #Finance #Geophysics and Gravity Measurements #Historical Geography and Cartography #Inertial Sensor and Navigation #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.1612.01357
openalex publication_date 2016/11/28 · openalex created_date 2016/12/16 · openalex updated_date 2026/07/28
The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically in geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not assumed known but it is computed, allowing to check the precision of the method. An extended data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney's method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.