Benchmark Test for Parallel Computation of Resonant Periodic Orbit Families in the Planar Circular Restricted Three-Body Problem

A benchmark test is presented for the computation of families of resonant periodic orbits in the planar circular restricted three-body problem using sequential and nonsequential methods. As sequential representatives, the natural parameter and the pseudo-arclength continuation techniques are employed. The nonsequential implementation is followed using a hybrid method, which is based on a numerical unification of the theory of generating orbits and an analytical asymptotic approximation of resonant orbits close to periodic second-species solutions. This paper explores the extent to which the hybrid method can benefit from parallel computing on multicore processors to build families orbit-by-orbit simultaneously. With eight cores, the results show better performance than the pseudo-arclength in family portions approaching the small primary and comparable to that of the natural parameter continuation in regular areas. The main advantages of the hybrid method are also discussed, and the existence of a lower threshold in the minimum distances to the secondary that periodic orbits can reach is investigated, which is a consequence of using the nonregularized equations of motion.