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

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.

final version; Remark 1 is added

References in corpus (2)

• A convex embedding for the rotating Kepler problem
• Homoclinic orbits in the Euler problem of two fixed centers

Cited by in corpus (2)

• On families of periodic orbits in the restricted three-body problem
• Reeb flows, pseudo-holomorphic curves and transverse foliations