Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-12T18:30:40.100Z Has data issue: false hasContentIssue false
  • English
  • Français

The Use of Lie Series in The Construction of a Perturbation Theory and some Recent Results in The Theory of The Motion ofd Hyperion

Published online by Cambridge University Press:  12 April 2016

P.J. Message
P.J. Message*
Affiliation:
University of Liverpool, L69 3BX, U.K.E-mail:sx20@liverpool.ac.uk

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper begins with a brief review of a form of the Lie series transformation, and then reports some new results in the study, using Lie series methods, of the orbit of Saturn’s satellite Hyperion. In particular, improved expressions are given for the long-period perturbations of the orbital elements which describe the motion in the orbit plane, and also first results for expressions for the short-period perturbations in the apse longitude, derived from the Lie series generating function.

Type
Planets and Satellites
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999 , pp. 349 - 358
Copyright
Copyright © Kluwer 1999

References

Duriez, L., and Vienne, A.: 1997, Theory of motion and ephemerides of Hyperion, Astron. & Astrophys., 324, 366–380.Google Scholar
Message, P.J.: 1989, The use of computer algorithms m the construction of a theory of the long-period perturbations of Saturn’s satellite Hyperion, Celestial Mechanics, 45, 45–53.Google Scholar
Message, P.J.: 1993, On the second-order long-period motion of Hyperion, Celestial Mechanics, 56, 277–284.CrossRefGoogle Scholar
Newcomb, S.: 1891, Hyperion: a new case in celestial mechanics, Astron. Papers of the American Ephemeris, III.Google Scholar
Taylor, D.B.: 1992, A synthetic theory for the perturbations of Titan on Hyperion, Astron. & Astrophys., 265, 825–832.Google Scholar
Vienne, A., and Duriez, L.: 1991, A general theory of motion for the eight major satellites of Saturn, Astron. &Astrophys., 246, 619–633.Google Scholar
Woltjer, J.: 1928, The Motion of Hyperion, Annalen van de Sterrewacht te Leiden, XVI, Part 3.Google Scholar