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

  • Anoop Sivasankaran
  • Bonnie A. Steves
  • Winston L. Sweatman
Original Article


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.


Regularisation Close encounters Restricted four-body problem Caledonian symmetrical four-body problem 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Anoop Sivasankaran
    • 1
  • Bonnie A. Steves
    • 1
  • Winston L. Sweatman
    • 2
  1. 1.School of Engineering and Computing, Glasgow Caledonian UniversityGlasgowUK
  2. 2.Institute of Information and Mathematical SciencesMassey University at AlbanyAucklandNew Zealand

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