Numerical approximation of invariant manifolds in the restricted three-body problem

In this paper a two-step approach to approximate the invariant manifolds in the circular restricted three-body problem is presented. Given any combination of the two scalars used to parameterize the manifolds, a two-dimensional interpolation is computed, and a successive correction is performed. A two-dimensional cubic convolution interpolation is implemented to reduce the computational effort, and a nonlinear correction is made to enforce the energy level of the approximated state. Results show efficiency and moderate accuracy. The present method fits the needs of trajectory optimization algorithms, where a great number of manifold insertion points has to be evaluated for any combination of the design variables.