Jacobi’s solution for geodesics on a triaxial ellipsoid
Abstract
Abstract On Boxing Day, 1838, Jacobi found a solution to the problem of geodesics on a triaxial ellipsoid, with the course of the geodesic and the distance along it given in terms of one-dimensional integrals. Here, a numerical implementation of this solution is described. This entails accurately evaluating the integrals and solving the resulting coupled system of equations. The inverse problem, finding the shortest path between two points on the ellipsoid, can then be solved using a similar method as for biaxial ellipsoids.
Fields of Study & Subjects
Historical Geography and Cartography
Mathematics and Applications
Analytic and geometric function theory
Publication details
- Journal / source
- Journal of Geodesy
- Publisher
- Springer Science and Business Media LLC
- Volume
- 100
- Issue
- 2
- Publication date
- 1 February 2026
- Language
- EN