Explicit Symplectic Integrators with Force Gradient Extend to the Perturbed Two-body Problem

This paper extends explicit symplectic integrators with force gradients corresponding Hamiltonian system which has decomposed form as T+V to decomposed form as H0+H1(where T and V is kinetic and potential energy.Both H0 and H1 are integrable,and the former is the main part of the Hamiltonian function).Then use them to solve the perturbed two-body problem and find that explicit symplectic integrators with gradients decomposed as H0+H1 are better than corresponding decomposed as T+V by analyzing the relative energy error of the perturbed two-body problem.