Orbits in the problem of two fixed centers on the sphere
Mathematical Physics
2017-10-03 v2 math.MP
Exactly Solvable and Integrable Systems
Abstract
A trajectory isomorphism between the two Newtonian fixed center problem in the sphere and two associated planar two fixed center problems is constructed by performing two simultaneous gnomonic projections in . This isomorphism converts the original quadratures into elliptic integrals and allows the bifurcation diagram of the spherical problem to be analyzed in terms of the corresponding ones of the planar systems. The dynamics along the orbits in the different regimes for the problem in is expressed in terms of Jacobi elliptic functions.
Cite
@article{arxiv.1704.00030,
title = {Orbits in the problem of two fixed centers on the sphere},
author = {M. A. Gonzalez Leon and J. Mateos Guilarte and M. de la Torre Mayado},
journal= {arXiv preprint arXiv:1704.00030},
year = {2017}
}
Comments
Revised version with minor changes and references added. 29 pages, 25 figures