An Analysis of Floquet Mode Control as a Station-Keeping Strategy for L2 Halo Orbits
Open Access
Author:
Thornton, Ian
Area of Honors:
Aerospace Engineering
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
Puneet Singla, Thesis Supervisor Robert G. Melton, Thesis Honors Advisor
Keywords:
orbit station-keeping astrodynamics
Abstract:
Halo orbits around the L1 and L2 Lagrange points in the Earth-Moon system are important for
various lunar missions. They are essential for communication relays and cislunar space surveil-
lance. These orbits are not fully periodic and thus require persistent corrective maneuvers to remain
closed over several revolutions. These orbits are also prone to small gravitational perturbations
from the Sun or Jupiter. For these reasons, various station-keeping algorithms have been studied to
design corrective maneuvers. In the simplified case of the Circular Restricted Three Body Problem
(CR3BP), Floquet theory can be used to extract valuable information regarding the unstable manifold of halo orbits. Leveraging this information, Floquet Mode Control (FMC) aims to eliminate
perturbations along the unstable manifold of the concerned halo orbit. As an under-constrained
problem, FMC allows for the addition of constraints to meet specific mission requirements, such
as minimizing ∆ V or restricting maneuver direction. Here, the CR3BP is examined in a series of
steps: use a single-shooting differential correction algorithm to find halo orbits based on an initial
guess, generate a family using parameter continuation, simulate several revolutions of a particular
orbit, and use FMC to identify and eliminate unstable motion.