Solving linearized equations of the N-body problem using the Lie-integration method

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Several integration schemes exist to solve the equations of motion of the N-body problem. The Lie-integration method is based on the idea to solve ordinary differential equations with Lie-series. In the 1980s, this method was applied to solve the equations of motion of the N-body problem by giving the recurrence formulae for the calculation of the Lie-terms. The aim of this work is to present the recurrence formulae for the linearized equations of motion of N-body systems. We prove a lemma which greatly simplifies the derivation of the recurrence formulae for the linearized equations if the recurrence formulae for the equations of motions are known. The Lie-integrator is compared with other well-known methods. The optimal step-size and order of the Lie-integrator are calculated. It is shown that a fine-tuned Lie-integrator can be 30-40 per cent faster than other integration methods.

Original languageEnglish
Pages (from-to)1515-1526
Number of pages12
JournalMonthly Notices of the Royal Astronomical Society
Volume381
Issue number4
DOIs
Publication statusPublished - Nov 1 2007

Keywords

  • Celestial mechanics
  • Methods: N-body simulations
  • Methods: numerical

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Fingerprint Dive into the research topics of 'Solving linearized equations of the N-body problem using the Lie-integration method'. Together they form a unique fingerprint.

  • Cite this