We consider Sundman and Poincaré transformations for the long-time numerical
integration of Hamiltonian systems whose evolution occurs at different time scales. The transformed
systems are numerically integrated using ...
Using a Newtonian model of the Solar System with all 8 planets, we perform extensive tests on various symplectic integrators of high orders, searching for the best splitting scheme for long term studies in the Solar System. ...
[EN] New numerical integrators specifically designed for solving the two-body gravitational problem with a time-varying mass are presented. They can be seen as a generalization of commutator-free quasi-Magnus exponential ...