Space gradiometry: tensor-valued ellipsoidal harmonics, the datum problem and application of the Lusternik-Schnirelmann category to construct a minimum atlas. (English) Zbl 1301.86016
Summary: Our contribution deals with three topics, namely (1) the tensor of gravity gradients in ellipsoidal harmonics, (2) the corresponding datum problem and (3) the construction of a minimum atlas in terms of ellipsoidal harmonics of Jacobi type following the basic result of the theory of the Lusternik-Schnirelmann category.
MSC:
| 86A30 | Geodesy, mapping problems |
| 35Q86 | PDEs in connection with geophysics |
| 00A69 | General applied mathematics |
| 34A26 | Geometric methods in ordinary differential equations |
Keywords:
ellipsoidal harmonics; minimum atlas; tensor-valued ellipsoidal harmonics; downward continuation; Somigliana-Pizzetti gravity fieldReferences:
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