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

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

Jun 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010cemda.107..157s&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 107, Issue 1-2, pp. 157-168

Astronomy and Astrophysics

Astronomy

3

Regularisation, Close Encounters, Restricted Four-Body Problem, Caledonian Symmetrical Four-Body Problem

Scientific paper

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.

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