Abstract

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.

中文翻译：

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平均运动共振中的不对称Zeipel–Lidov–Kozai循环

摘要

Zeipel–Lidov–Kozai周期是对自然和人造天体轨道的倾角和偏心率进行长期相互关联的更改的名称。它们由H.von Zeipel（1910），M。Lidov（1961）和Y. Kozai（1962）独立发现。最初，Zeipel–Lidov–Kozai循环的存在是为天体的非共振运动建立的。研究在轨道运动共振的情况下这种长期影响的方法出现得很晚。事实证明，在共振条件下，Zepel-Lidov-Kozai循环可能不具有在受限三体问题框架内非共振情况下这些循环始终具有的对称性。此外，