Jacobi-Maupertius metric and Kepler equation
Mathematical Physics
2017-04-11 v1 General Relativity and Quantum Cosmology
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1612.07395,
title = {Jacobi-Maupertius metric and Kepler equation},
author = {Sumanto Chanda and G. W. Gibbons and Partha Guha},
journal= {arXiv preprint arXiv:1612.07395},
year = {2017}
}
Comments
23 pages