On the minimality of Keplerian arcs with fixed negative energy
Classical Analysis and ODEs
2019-10-16 v1
Abstract
We revisit a classical result by Jacobi on the local minimality, as critical points of the corresponding energy functional, of fixed-energy solutions of the Kepler equation joining two distinct points with the same distance from the origin. Our proof relies on the Morse index theorem, together with a characterization of the conjugate points as points of geodesic bifurcation.
Keywords
Cite
@article{arxiv.1910.06681,
title = {On the minimality of Keplerian arcs with fixed negative energy},
author = {Vivina Barutello and Alberto Boscaggin and Walter Dambrosio},
journal= {arXiv preprint arXiv:1910.06681},
year = {2019}
}