A global regularisation for integrating the Caledonian symmetric four-body problem

Anoop Sivasankaran*, Bonnie A. Steves, Winston L. Sweatman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Several papers in the last decade have studied the Caledonian symmetric four-body problem (CSFBP), a restricted four-body system with a symmetrically reduced phase space. During these studies, difficulties have arisen when the system approaches a close encounter. These are due to collision singularities causing numerical integration algorithms to fail. In this paper, we give the full details of a regularisation approach that now enables us to study these close encounters and collision events. The resulting equations of motion can be efficiently integrated by a high-order integrator. The results from numerical testing of the algorithm verify that the regularisation is advantageous in preserving numerical stability. The effectiveness of the approach is illustrated for a range of CSFBP orbits. Numerical experiments show that the newly developed regularisation algorithm has excellent energy conservation properties.

Original languageEnglish
Pages (from-to)157-168
Number of pages12
JournalCelestial Mechanics and Dynamical Astronomy
Issue number1
Early online date28 Apr 2010
Publication statusPublished - Jun 2010


  • Caledonian symmetrical four-body problem
  • close encounters
  • regularisation
  • restricted four-body problem

ASJC Scopus subject areas

  • Modelling and Simulation
  • Mathematical Physics
  • Astronomy and Astrophysics
  • Space and Planetary Science
  • Computational Mathematics
  • Applied Mathematics


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