Abstract
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 language | English |
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Pages (from-to) | 157-168 |
Number of pages | 12 |
Journal | Celestial Mechanics and Dynamical Astronomy |
Volume | 107 |
Issue number | 1 |
Early online date | 28 Apr 2010 |
DOIs | |
Publication status | Published - Jun 2010 |
Keywords
- 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