On a convex embedding of the Euler problem of two fixed centers
Symplectic Geometry
2018-07-04 v4 Dynamical Systems
Abstract
In this article, we study a convex embedding for the Euler problem of two fixed centers for energies below the critical energy level. We prove that the doubly-covered elliptic coordinates provide a 2-to-1 symplectic embedding such that the image of the bounded component near the lighter primary of the regularized Euler problem is convex for any energy below the critical Jacobi energy. This holds true if the two primaries have the equal mass, but does not holds near the heavier body.
Cite
@article{arxiv.1701.07258,
title = {On a convex embedding of the Euler problem of two fixed centers},
author = {Seongchan Kim},
journal= {arXiv preprint arXiv:1701.07258},
year = {2018}
}
Comments
final version; Remark 1 is added