Two fast integrators for the Galactic tide effects in the Oort Cloud

Two fast and reliable numerical integrators for the motion of the Oort Cloud comets in the Galactic tidal potential are presented. Both integrators are constructed as Hamiltonian splitting methods. The first integrator is based upon the canonical Hamiltonian equations split into the Keplerian part and a time-dependent perturbation. The system is regularized by the application of the Kuustanheimo-Stiefel variables. The composition rule of Laskar and Robutel with a symplectic corrector is applied. The second integrator is based on the approximate, averaged Hamiltonian. Non-canonical Lie-Poisson bracket is applied allowing the use of non-singular vectorial elements. Both methods prove superior when compared to their previously published counterparts.