A computational methodology for invariant manifold connections between quasi-periodic libration point orbits in non-autonomous problems

Semi-analytical and numerical techniques to systematically analyze and compute natural connections between quasi-periodic orbits associated to non-autonomous systems are considered. Focusing in the non-autonomous Sun–Earth+Moon coherent QBCP model, the center-unstable and center-stable invariant manifolds of Lyapunov quasi-periodic orbits are parameterized and a methodology to detect heteroclinic connections between manifolds is introduced. The methodology aims to decrease the dimensionality of the problem and to address the issue of searching good initial conditions inside the high dimensional state space. Then, connections are identified by searching for approximate patch points in a state-time Poincaré section. These points are subsequently refined to obtain smooth paths that are further continued inside their families.