A symplectic integrator for the symmetry reduced and regularised planar 3-body problem with vanishing angular momentum. (English) Zbl 1293.37031
Summary: 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.
MSC:
| 37M15 | Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems |
| 70F07 | Three-body problems |
| 37N05 | Dynamical systems in classical and celestial mechanics |
| 37J15 | Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010) |
Keywords:
geometric integration; explicit symplectic integration; numerical integration; 3-body problem; symmetry reduction; Hamiltonian system; regularisationReferences:
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