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

Anoop Sivasankaran (1) , Bonnie A. Steves (1) , Winston L. Sweatman (2)

1 GCU - Glasgow Caledonian University
2 Institute of Information and Mathematical Sciences

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.

Mots clés: Regularisation; Close encounters; Restricted four-body problem; Caledonian symmetrical four-body problem

Anoop Sivasankaran, Bonnie A. Steves, Winston L. Sweatman. A global regularisation for integrating the Caledonian symmetric four-body problem. Celestial Mechanics and Dynamical Astronomy, 2010, 107 (1-2), pp.157-168. ⟨10.1007/s10569-010-9270-x⟩. ⟨hal-00552511⟩