A study of the 1/2 retrograde resonance: Periodic orbits and resonant capture

TL;DR

This paper investigates the structure and stability of periodic orbits in the 1/2 retrograde resonance, revealing how these orbits influence resonance capture and transitions between different resonant modes.

Contribution

It provides a detailed analysis of periodic orbit families, their bifurcations, and their role in resonance capture, including the transition mechanisms between resonant modes.

Findings

Identification of stable, critical, and unstable periodic orbits.

Explanation of how proximity of orbit families affects resonance capture.

Mapping of the complex 3D resonance structure.

Abstract

We describe the families of periodic orbits in the 2-dimensional 1/2 retrograde resonance at mass ratio 0.001, analyzing their stability and bifurcations into 3-dimensional periodic orbits. We explain the role played by periodic orbits in adiabatic resonance capture, in particular how the proximity between a stable family and an unstable family with a nearly critical segment, associated with Kozai separatrices, determines the transition between distinct resonant modes observed in numerical simulations. Combining the identification of stable, critical and unstable periodic orbits with analytical modeling, resonance capture simulations and computation of stability maps helps to unveil the complex 3-dimensional structure of resonances.