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Dellnitz, M.; Junge, O.:
Set oriented numerical methods in space mission design,
Gurfil, P. (ed.): Modern Astrodynamics, Vol. I, pp. 127-153, Elsevier, 2006.

New techniques for the design of energy efficient trajectories for space missions have been proposed which are based on the circular restricted three body problem as the underlying mathematical model. These techniques exploit the structure and geometry of certain invariant sets and associated invariant manifolds in phase space in order to systematically construct efficient flight paths. In this chapter we present numerical methods that enable an implementation of this approach. Using a set oriented framework we show how to compute approximations to invariant sets and invariant manifolds and how to detect connecting orbits that might serve as initial guesses for the solution of a more detailed model. We also show how to extend the approach in order to account for a continuously applied control force on the spacecraft as realized by certain low thrust propulsion systems.

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