Symplectic integration for the collisional gravitational

We present a new symplectic integrator designed for collisional gravitational N-body problems which makes use of Kepler solvers. The integrator is also reversible and conserves nine integrals of motion of the N-body problem to machine precision. The integrator is second order, but the order can easily be increased by the method of Yoshida. We use fixed time step in all tests studied in this paper to ensure preservation of symplecticity. We study small N collisional problems and perform comparisons with typically used integrators. In particular, we find comparable or better performance when compared to the fourth-order Hermite method and much better performance than adaptive time step symplectic integrators introduced previously. We find better performance compared to SAKURA, a non-symplectic, non-time-reversible integrator based on a different two-body decomposition of the N-body problem. The integrator is a promising tool in collisional gravitational dynamics.National Science Foundation (U.S.). Graduate Research Fellowship Program (Grant 1122374