A method of symplectic integrations with adaptive time-steps for individual Hamiltonians in the planetary N-body problem

Abstract

A new algorithm is developed for long-term integrations of the N-body problem. The method uses symplectic integrations of the Hamiltonian equations of motion for each body. This allows one to employ individual adaptive time-steps in computations. The efficiency of this technique is demonstrated by several tests performed for typical problems of Solar System dynamics. © 2007 Springer Science+Business Media B.V.