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arxiv: 1612.07395 · v1 · submitted 2016-12-22 · 🧮 math-ph · gr-qc· math.MP

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Jacobi-Maupertius metric and Kepler equation

Sumanto Chanda , G.W. Gibbons , Partha Guha
Authors on Pith no claims yet
classification 🧮 math-ph gr-qcmath.MP
keywords keplermetrictransformationhourijacobiliftmilnorsystems
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This article studies the application of the Jacobi-Eisenhart lift, Jacobi metric and Maupertius transformation to the Kepler system. We start by reviewing fundamentals and the Jacobi metric. Then we study various ways to apply the lift to Kepler related systems: first as conformal description and Bohlin transformation of Hooke's oscillator, second in contact geometry, third in Houri's transformation (Houri, Liouville integrability of Hamiltonian systems and spacetime symmetry, http://www.geocities.jp/football\_physicien/publication.html), coupled with Milnor's construction (Milnor, The American Mathematical Monthly 90 (1983) 353-365) with eccentric anomaly.

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  1. The Bohlin variant of the Eisenhart lift

    nlin.SI 2026-02 unverdicted novelty 7.0

    The Bohlin variant of the Eisenhart lift embeds Lagrangian systems into timelike geodesics of conformally flat (d+2)-dimensional metrics and yields novel examples of such metrics admitting higher-rank Killing tensors.