Optimal control methods for designing trajectories have been studied extensively by astro-dynamicists. Direct and indirect methods provide separate approaches to arrive at the optimal solution, each having their associated advantages and challenges. Among the realm of optimized transfer trajectories, fuel-optimal trajectories are typically most sought and characterized by se-quential thrust and coast arcs.
On the other hand, it is well known that a simplified dynamical model like the CR3BP analyzed in a rotating coordinate system, reveal fixed points known as Lagrange points. These spatial points can be orbited, with researchers categorizing periodic orbits around them starting from the simple planar Lyapunov orbits and continuing to the more enigmatic butterfly orbits. Studying linearized dynamics using eigenanalysis in the vicinity of a point on these periodic orbits lead to interesting departures spatially manifesting into the invariant manifolds.
This thesis delves into the novel idea of merging aspects of invariant manifold theory and indirect optimal control methods to provide efficient computation of feasible transfer trajectories. The marriage of these ideas provide the possibility of alleviating the challenges of an end-to end optimization using indirect methods for a long mission by utilizing the pre-computed and analyzed manifolds for insertion points of a long terminal coast arc. In addition to this, realistic and accurate mission scenarios require consideration of a high-fidelity dynamical model as well as shadow constraints. A methodology to use the “manifold analogues” in such cases has been discussed and utilized in this thesis along with modelling of eclipses during optimization, providing mission designers a basis for efficient and accurate/mission-ready trajectory design. This overcomes the shortcomings in state of the art software packages such as MYSTIC and COPERNICUS
