Celestial Mechanics and Dynamical Astronomy

, Volume 117, Issue 2, pp 169–185 | Cite as

A symplectic integrator for the symmetry reduced and regularised planar 3-body problem with vanishing angular momentum

  • Danya Rose
  • Holger R. Dullin
Original Article


We construct an explicit reversible symplectic integrator for the planar 3-body problem with zero angular momentum. We start with a Hamiltonian of the planar 3-body problem that is globally regularised and fully symmetry reduced. This Hamiltonian is a sum of 10 polynomials each of which can be integrated exactly, and hence a symplectic integrator is constructed. The performance of the integrator is examined with three numerical examples: The figure eight, the Pythagorean orbit, and a periodic collision orbit.


Geometric integration Explicit symplectic integration Numerical integration 3-Body problem Symmetry reduction Hamiltonian system Regularisation 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia

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