Abstract
Many problems in solar system dynamics are described by Hamiltonians of the form H = H(Kep) + eH(pert) , E 1, where H(Kep) is the usual Hamiltonian for the Kepler two-body problem and eH(pert) represents (for example) much weaker perturbations from the planets. We review symplectic integrators for Hamiltonians of this kind, focusing on methods that exploit the integrability of H(Kep). It is shown that the long-term errors in these integrators can be reduced by a factor of order e by suitable starting procedures, for example, by starting with a very small stepsize and gradually increasing the stepsize to its final value
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