Computation of quasi-periodic tori in the circular restricted three-body problem

Quasi-periodic orbits lying on invariant tori in the circular restricted three-body problem offer a broad range of mission design possibilities, but their computation is more complex than that of periodic orbits. A preliminary framework for directly computing two-dimensional invariant tori is presented including a natural parameterization and a continuation scheme. The approach is based on a scheme designed for generic dynamical systems. Modifications are included to account for the special family structure in the circular restricted three-body problem. A discretized partial differential equation is solved along with constraint equations to compute members of the family and their associated frequencies. The continuation process is initialized from a linear estimate of a quasi-periodic torus. A regularization scheme is included for computing invariant tori that pass close to a primary body. A method to generate a quasi-periodic trajectory lying on the surface of the invariant torus is also presented. The numerical methodology is demonstrated by generating families of quasi-periodic tori with fixed Jacobi constant values that emanate from periodic orbits in the vicinity of the Earth-Moon libration points.