Approximation of Invariant Manifolds by Cubic Convolution Interpolation

In this paper a two-step approach to approximate the invariant manifolds in the circular restricted three-body problem is presented. The method consists in a two-dimensional interpolation, followed by a nonlinear correction. A two-dimensional cubic convolution interpolation is implemented to reduce the computational effort. A nonlinear correction is applied to enforce the energy level of the approximated state. The manifolds are parameterized by using two scalars. 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.