On a convex embedding of the Euler problem of two fixed centers

2017/01/31 by Seongchan Kim · 1 citation
Mathematics · #math.DS #math.SG

paper · pdf · doi:10.1134/s1560354718030061

published as Regular and Chaotic Dynamics, 2018, vol.23, no.3, pp.304-324 · final version; Remark 1 is added

arxiv created 2018/05/24 · arxiv updated 2018/07/04

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.

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