In deep space exploration missions involving lunar flybys, to ensure the successful execution of the lunar gravity assist (LGA), one or more trajectory correction maneuvers (TCMs) are typically required before the perilune. The concept of singularity suggests that targeting future states either requires a significant amount of maneuvering or cannot be calculated within a finite iteration time. To mitigate the high computational costs associated with TCMs determined via the differential correction method, it is essential to analyze the singularity of the Lambert problem in the lunar flyby. This study demonstrates that the singularity of the Lambert problem in Keplerian orbits exhibits transferability in lunar flybys under the three-body model by using the Lagrange coefficients and pseudostate theory. This transferability is validated through the determinant theory of the state transition matrix (STM), which is further extendable to other three-body systems. Furthermore, this study elucidates the applicability of singularity in lunar flybys under the three-body model through numerical simulations in both prograde and retrograde motions, considering different arguments of perilune. These derivations and simulations establish criteria for assessing singularity, facilitating the rapid identification of positions associated with high maneuver costs. The conclusions drawn from this study have been validated using the ephemeris model. It is shown that it is possible to preemptively circumvent singularities and enhance the robustness of the guidance algorithm in practical lunar flyby missions.
Singularity of Lambert Problem for Lunar Flyby
01.06.2025
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
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