Lie-series for orbital elements: II. The spatial case

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

If one has to attain high accuracy over long timescales during the numerical computation of the N-body problem, the method called Lie-integration is one of the most effective algorithms. In this paper, we present a set of recurrence relations with which the coefficients needed by the Lie-integration of the orbital elements related to the spatial N-body problem can be derived up to arbitrary order. Similarly to the planar case, these formulae yield identically zero series in the case of no perturbations. In addition, the derivation of the formulae has two stages, analogously to the planar problem. Namely, the formulae are obtained to the first order, and then, higher-order relations are expanded by involving directly the multilinear and fractional properties of the Lie-operator.

Original languageEnglish
Pages (from-to)97-107
Number of pages11
JournalCelestial Mechanics and Dynamical Astronomy
Volume124
Issue number1
DOIs
Publication statusPublished - Jan 1 2016

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orbital elements
many body problem
perturbation
timescale
derivation
operators
coefficients
method

Keywords

  • Lie-integration
  • N-body problem
  • Numerical methods
  • Planetary systems

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

Lie-series for orbital elements : II. The spatial case. / Pál, A.

In: Celestial Mechanics and Dynamical Astronomy, Vol. 124, No. 1, 01.01.2016, p. 97-107.

Research output: Contribution to journalArticle

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