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

Abstract

The problem of orbit flips caused by eccentric von Zeipel-Lidov-Kozai effects is systematically investigated by means of three approaches, including Poincaré sections, dynamical system theory (periodic orbits and invariant manifolds) and perturbation treatments. Poincaré 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.

arXiv comment20 pages, accepted for publication in AJ

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Cited by in corpus (6)

• Extremely Inclined Orbit of S-type Planet $\gamma$ Cep Ab Induced by Eccentric Kozai-Lidov Mechanism
• Librating Kozai-Lidov Cycles with a Precessing Quadrupole Potential are Analytically Approximately Solved
• Dynamical essence of the eccentric von Zeipel-Lidov-Kozai effect in restricted hierarchical planetary systems
• Quadrupole and octupole order resonances in non-restricted hierarchical planetary systems
• Short-Range Forces Can Catalyze Extreme Orbital Evolution in Hierarchical Triples
• Secular dynamics of stellar spin driven by planets inside Kozai-Lidov resonance