These include planets that orbit one of the binary stars, with the orbital motion of the planet being perturbed by the gravitational force of the other star, and can exist for either binary star. Planets can also orbit both binaries, either around the outside of the stars or a figure eight or racetrack pattern. They can also exist in orbits around a Lagrange point. Each possibility poses unique challenges. Before these dynamically possible systems can be examined, our preliminary analysis has been focusing on the issue of numerical integration techniques.
Further work is underway evaluating symplectic integrators.
While results are still very preliminary, this paper provides an overview of the technical problems being investigated, and demonstrates the process needed to solve this problem.