Abstract
The idea of transforming the geodetic boundary value problem into a boundary value problem with a fixed boundary dates back to the 1970s of the last century. This transformation was found by F. Sanso and was named as gravity-space transformation. Unfortunately, the advantage of having a fixed boundary for the transformed problem was counterbalanced by the theoretical as well as practical disadvantage of a singularity at the origin. In the present paper two more versions of a gravity-space transformation are investigated, where none of them has a singularity. In both cases the transformed differential equations are nonlinear. Therefore, a special emphasis is laid on the linearized problems and their relationships to the simple Hotine-problem and to the symmetries between both formulations. Finally, in numerical simulation study the accuracy of the solutions of both linearized problems is studied and factors limiting this accuracy are identified.
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Austen, G., Keller, W. Singularity free formulations of the geodetic boundary value problem in gravity-space. J Geod 83, 645–657 (2009). https://doi.org/10.1007/s00190-008-0278-x
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DOI: https://doi.org/10.1007/s00190-008-0278-x