The Lidov-Kozai Oscillation and Hugo von Zeipel

Abstract

The so-called oscillation is very well known and applied to various problems in solar system dynamics. This mechanism makes the orbital inclination and eccentricity of the perturbed body in the circular restricted three-body system oscillate with a large amplitude under certain conditions. It is widely accepted that the theoretical framework of this phenomenon was established independently in the early 1960s by a Soviet Union dynamicist (Michail L'vovich Lidov) and by a Japanese celestial mechanist (Yoshihide Kozai). A large variety of studies has stemmed from the original works by Lidov and Kozai, now having the prefix of Lidov-Kozai or Kozai- Lidov. However, from a survey of past literature published in late nineteenth to early twentieth century, we have confirmed that there already existed a pioneering work using a similar analysis of this subject established in that period. This was accomplished by a Swedish astronomer, Edvard Hugo Zeipel. In this monograph, we first outline the basic framework of the circular restricted three-body problem including typical examples where the oscillation occurs. Then, we introduce what was discussed and learned along this line of studies from the early to mid-twentieth century by summarizing the major works of Lidov, Kozai, and relevant authors. Finally, we make a summary of Zeipel's work, and show that his achievements in the early twentieth century already comprehended most of the fundamental and necessary formulations that the oscillation requires. By comparing the works of Lidov, Kozai, and Zeipel, we assert that the prefix von Zeipel-Lidov-Kozai should be used for designating this theoretical framework, and not just or Kozai-Lidov.