Henri Poincaré, 1912–2012

Duplantier, Bertrand; Rivasseau, Vincent

doi:10.1007/978-3-0348-0834-7

Cited by 4 publications

(1 citation statement)

References 33 publications

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“…Readers can consult Boccaletti and Pucacco (1998, their Section 6.6 on p. 33) or Marinca and Herisanu (2011, their Chapter 2 on p. 9) for brief but excellent reviews about what the Lindstedt series is, as well as how it was developed in the history of perturbation theory studies. As for the interrelationship of the Lindstedt series to Poincaré's work, a long review (Chenciner, 2015) in a book (Duplantier and Rivasseau, 2015) is very thorough and worth a read.…”

Section: The Lindstedt Seriesmentioning

confidence: 99%

The Lidov-Kozai Oscillation and Hugo von Zeipel

Ito,

Ohtsuka

2019

Preprint

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The circular restricted three-body problem, particularly its doubly averaged version, has been very well studied in celestial mechanics. Despite its simplicity, circular restricted three-body systems are suited for modeling the motion of various objects in the solar system, extrasolar planetary systems, and in many other dynamical systems that show up in astronomical studies. In this context, the so-called Lidov-Kozai oscillation is well known and applied to various objects. This 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 also causes a libration of the perturbed body's argument of pericenter around stationary points. 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). Since then, the theory has been extensively studied and developed. 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 von Zeipel. In this monograph, we first outline the basic framework of the circular restricted three-body problem including typical examples where the Lidov-Kozai 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 von Zeipel's work, and show that his achievements in the early twentieth century already comprehended most of the fundamental and necessary formulations that the Lidov-Kozai oscillation requires. By comparing the works of Lidov, Kozai, and von Zeipel, we assert that the prefix "von Zeipel-Lidov-Kozai" should be used for designating this theoretical framework, and not just Lidov-Kozai or Kozai-Lidov. This justifiably shows due respect and appropriately commemorates these three major pioneers who made significant contributions to the progress of modern celestial mechanics.

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Section: The Lindstedt Seriesmentioning

confidence: 99%