Numerical continuation and stationkeeping of quasi-periodic quasi-satellite orbits

Quasi-satellite orbits (QSOs) have been under the research spotlight due to their linear stability and potential to remain in close proximity to the secondary body in a restricted three-body system. In this research, the numerical continuation and stationkeeping method of quasi-periodic QSOs is investigated based on the Poincaré section. By means of Differential Algebra (DA) techniques, a DA-enhanced numerical method for computing quasi-periodic orbits is proposed. This method is formulated to solve for the invariant curve of a quasi-periodic torus on a Poincaré section. An enhanced Poincaré map, which is established with DA techniques, effectively reduce the problem dimensionality and promote computational efficiency. A family of quasi-periodic QSOs around Phobos are continued to validate the proposed method. A subsequent stationkeeping approach adapted from the Target Phase Approach (TPhA) is tailored for the maintenance of generated quasi-periodic QSOs. A stochastic optimisation scheme for the adapted TPhA method is formulated in search for fuel-optimal and error-robust stationkeeping parameters. Stationkeeping simulations for the achieved quasi-periodic QSO family are provided to showcase the effectiveness of the adapted TPhA method.