A Massively Parallel Method for Fast Computation of Invariant Manifolds

The computation of invariant manifolds in the Circu-lar Restricted 3-Body Problem (CR3BP) is essential for space mission design as they provide low energy trajectories for var-ious mission applications. These include the design of gravity assist flybys, low energy capture and escape around bodies in the Solar System. The conventional way of computing these manifolds is by determining the stable and unstable directions across the entire orbit through an eigen decomposition of the monodromy matrix of the periodic orbit. These directions are then propagated along the entire orbit with the state transi-tion matrix. This paper presents a simpler novel method for computing invariant manifolds directly without the monodromy matrix so it can be extended to compute the invariant manifolds of unstable objects besides periodic orbits. We also parallelize our algorithm on a GPU and achieve a speed-up by 3 orders of magnitude compared to the conventional method ran on a CPU. Moreover, since invariant manifolds are ubiquitous for differential equations governing all sorts of disciplines, this ultra-simple new method for computing invariant manifolds will have applications in many fields besides astrodynamics.