Formulary of geodesics of the projected averaged Kepler Hamiltonian

Jean-Baptiste Caillau (1)

1 IRIT-APO - Algorithmes Parallèles et Optimisation

This short note gives the quadratures of the geodesics of the averaged Hamiltonian of the controlled Kepler equation (energy criterion) projected on $\SS^2$. The endpoints of the corresponding cut locus are also deduced, as well as the injectivity radius of the associated Riemannian metric on the $2$-sphere.

Mots clés: averaged Kepler equation; geodesics on $\SS^2$; cut locus

Domaines: Optimisation et contrôle [math.OC]

Jean-Baptiste Caillau. Formulary of geodesics of the projected averaged Kepler Hamiltonian. 2007. ⟨hal-00130214v3⟩