2016/12/22 by Sumanto Chanda, G. W. Gibbons, Partha Guha · 1 citation
Physics and Astronomy · Mathematics · #math-ph #gr-qc #math.MP #msc:70H06 #msc:53D25 #msc:53B20 #msc:70F16
paper · pdf · doi:10.1142/s0219887817300021
23 pages
arxiv created 2016/12/22 · arxiv updated 2017/04/11
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.