On Asymmetric Zeipel–Lidov–Kozai Cycles in Mean Motion Resonances

Zeipel–Lidov–Kozai cycles is the name given to long-term interrelated changes in the inclinations and eccentricities of the orbits of natural and artificial celestial bodies. They were discovered independently by H. von Zeipel (1910), M. Lidov (1961), and Y. Kozai (1962). Originally, the existence of Zeipel–Lidov–Kozai cycles was established for nonresonant motions of celestial bodies. Approaches to studying such secular effects in the case of resonance of orbital movements appeared much later. It turned out that, at resonance, the Zeipel–Lidov–Kozai cycles may not have the symmetry that these cycles always have in nonresonant situations within the framework of the restricted three-body problem. Moreover, results of numerical studies indicate the presence of asymmetric Zeipel–Lidov–Kozai cycles in the dynamics of a number of Kuiper belt objects moving in resonance with Neptune.