Optimal Low-Thrust Transfer from an Earth Parking orbit to a Lyapunov Orbit

Orbits around the equilibrium points in the Earth-Moon and Sun-Earth frames have been investigated in the past to aid with missions like deep space observatory and lunar missions. As the interest in these missions increase, there is now more focus on transfer trajectories to the orbits around the equilibrium points. This thesis studies the optimization of the transfer trajectory from an Earth parking orbit to a Lyapunov orbit about L2 in the Earth-Moon system by implementing the multiple-shooting method. This method, lowers the cost of the transfer by breaking the trajectory into multiple segments which makes it possible to apply smaller but more frequent impulses rather than having to apply bigger impulses at the start and end of the transfer. The result of this thesis shows that the cost of the transfer is lowered by implementing the multiple-shooting method on an initial Hohmann transfer trajectory. The multiple-shooting method was implemented with the use of MATLAB and the trajectories were plotted in a graph to help visualize new points. The new trajectory is also plotted with the initial trajectory to show the difference between the two after a number of iterations. With this method, the cost of the transfer was reduced from J=4.4 to J=3.1034.