A systematic study about orbit flips of test particles caused by eccentric von Zeipel-Lidov-Kozai effects

TL;DR

This paper systematically investigates orbit flips caused by eccentric von Zeipel-Lidov-Kozai effects using multiple approaches, revealing the underlying dynamical structures and boundaries of flipping regions in parameter space.

Contribution

It introduces a comprehensive analysis combining Poincaré sections, dynamical systems theory, and perturbation methods to understand orbit flips and delineate flipping regions.

Findings

Orbit flips are linked to libration islands at 90° inclination.

Polar periodic orbits and invariant manifolds are key to orbit flips.

Resonant trajectories and their widths define flipping region sizes.

Abstract

The problem of orbit flips caused by eccentric von Zeipel-Lidov-Kozai effects is systematically investigated by means of three approaches, including Poincar\'e sections, dynamical system theory (periodic orbits and invariant manifolds) and perturbation treatments. Poincar\'e sections show that orbit flips are due to the existence of islands of libration centered at inclination of $90^{\circ}$, dynamical system theory shows that orbit flips are due to the existence of polar periodic orbits and invariant manifolds, and perturbative treatments indicate that orbit flips are due to the libration of a certain critical argument. Using these approaches, the boundaries of flipping regions in the entire parameter space are produced and they are in excellent agreement with each other. Through analysis, the essence of flipping orbits is reached: (a) flipping orbits are a kind of quasi-periodic trajectories around polar periodic orbits and invariant manifolds at the same level of Hamiltonian provide boundaries of flipping regions, and (b) flipping orbits are a kind of resonant trajectories and resonant width measures the size of flipping regions.