Libration point orbits and its invariant manifolds structure

The invariant manifold structures of the libration points for restricted three-body problem will provide the framework for understanding complex dynamical phenomena. These stable and unstable invariant manifold tubes associated to libration point orbits can be used to construct new low-energy spacecraft trajectories. So, in this paper, we will introduce the libration point and its invariant manifolds structure. First, we introduce the restricted three-body problem, libration point and Halo orbit. Then, we discuss and provide the stable and unstable invariant manifold tubes associated to libration point orbits based on manifolds and dynamical system theory. Finally, we apply these dynamical properties to design the capture trajectory in planetary exploration.