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arXiv · 1910.06681

On the minimality of Keplerian arcs with fixed negative energy

Vivina Barutello·Alberto Boscaggin·Walter Dambrosio
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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.

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Vivina Barutello, Alberto Boscaggin, Walter Dambrosio. 2019-10-15. On the minimality of Keplerian arcs with fixed negative energy. https://arxiv.org/abs/1910.06681

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