Lie-series for orbital elements: I. The planar case

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Lie-integration is one of the most efficient algorithms for numerical integration of ordinary differential equations if high precision is needed for longer terms. The method is based on the computation of the Taylor coefficients of the solution as a set of recurrence relations. In this paper, we present these recurrence formulae for orbital elements and other integrals of motion for the planar N-body problem. We show that if the reference frame is fixed to one of the bodies-for instance to the Sun in the case of the Solar System-the higher order coefficients for all orbital elements and integrals of motion depend only on the mutual terms corresponding to the orbiting bodies.

Original languageEnglish
Pages (from-to)45-54
Number of pages10
JournalCelestial Mechanics and Dynamical Astronomy
Volume119
Issue number1
DOIs
Publication statusPublished - 2014

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orbital elements
solar system
many body problem
coefficients
numerical integration
sun
differential equations
method

Keywords

  • Lie-integration
  • N-body problems
  • Numerical methods
  • Planetary systems
  • Recurrence relations
  • Taylor coefficients

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

Lie-series for orbital elements : I. The planar case. / Pál, A.

In: Celestial Mechanics and Dynamical Astronomy, Vol. 119, No. 1, 2014, p. 45-54.

Research output: Contribution to journalArticle

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