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We present a non-canonically symplectic integration scheme tailored tonumerically computing the post-Newtonian motion of a spinning black-holebinary. Using a splitting approach we combine the flows of orbital and spincontributions. In the context of the splitting, it is possible to integrate theindividual terms of the spin-orbit and spin-spin Hamiltonians analytically,exploiting the special structure of the underlying equations of motion. Theoutcome is a symplectic, time-reversible integrator, which can be raised toarbitrary order by composition. A fourth-order version is shown to giveexcellent behavior concerning error growth and conservation of energy andangular momentum in long-term simulations. Favorable properties of theintegrator are retained in the presence of weak dissipative forces due toradiation damping in the full post-Newtonian equations.

Symplectic Integration of Post-Newtonian Equations of Motion with Spin