On the Manev spatial isosceles three-body problem

TL;DR

This paper investigates the Manev three-body problem with an isosceles configuration, analyzing collision singularities, the impact of angular momentum, and the global flow dynamics using a McGehee-type blow-up technique.

Contribution

It introduces a novel application of McGehee-type blow-up to the Manev three-body problem, revealing how the collision manifold's topology varies with angular momentum.

Findings

Orbits near total collision are common across many angular momenta.

The collision manifold's topology changes as angular momentum increases.

The study characterizes equilibria and homographic motions near the collision manifold.

Abstract

We study the isosceles three-body problem with Manev interaction. Using a McGehee-type technique, we blow up the triple collision singularity into an invariant manifold, called the collision manifold, pasted into the phase space for all energy levels. We find that orbits tending to/ejecting from total collision are present for a large set of angular momenta. We also find that as the angular momentum is increased, the collision manifold changes its topology. We discuss the flow near-by the collision manifold, study equilibria and homographic motions, and prove some statements on the global flow.