Geodesics on an ellipsoid (English Wikipedia)

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If $c ⁄ a < 1 ⁄ 2$ , there are other simple closed geodesics similar to those shown in Figs. 11 and 12 (Klingenberg 1982, §3.5.19). Klingenberg, W. P. A. (1982). Riemannian Geometry. de Gruyer. ISBN 978-3-11-008673-7. MR 0666697. OCLC 8476832.

Laplace (1799a) showed that a particle constrained to move on a surface but otherwise subject to no forces moves along a geodesic for that surface. Thus, Clairaut's relation is just a consequence of conservation of angular momentum for a particle on a surface of revolution. Laplace, P. S. (1829) [1799a]. "Book 1, §8.". Treatise on Celestial Mechanics. Vol. 1. Translated by Bowditch, N. Boston: Hillard, Gray, Little, & Wilkins. OCLC 1294937.

This section is adapted from the documentation for GeographicLib (Karney 2015, Geodesics on a triaxial ellipsoid) Karney, C. F. F. (2015). "GeographicLib". Version 1.44.

Laplace (1799a) showed that a particle constrained to move on a surface but otherwise subject to no forces moves along a geodesic for that surface. Thus, Clairaut's relation is just a consequence of conservation of angular momentum for a particle on a surface of revolution. Laplace, P. S. (1829) [1799a]. "Book 1, §8.". Treatise on Celestial Mechanics. Vol. 1. Translated by Bowditch, N. Boston: Hillard, Gray, Little, & Wilkins. OCLC 1294937.
If $c ⁄ a < 1 ⁄ 2$ , there are other simple closed geodesics similar to those shown in Figs. 11 and 12 (Klingenberg 1982, §3.5.19). Klingenberg, W. P. A. (1982). Riemannian Geometry. de Gruyer. ISBN 978-3-11-008673-7. MR 0666697. OCLC 8476832.