Role of Invariant Manifolds in Low-Thrust Trajectory Design

摘要

This paper demonstrates the significant role that invariant manifolds play in the dynamics of low-thrustntrajectories moving through unstable regions in the three-body problem. It shows that an optimization algorithmnincorporating no knowledge of invariant manifolds converges on low-thrust trajectories that use the invariantnmanifolds of unstable resonant orbits to traverse resonances. It is determined that the algorithm could both changenthe energy through thrusting to a level where the invariant manifolds could more easily be used, as well as usenthrusting to move the trajectory along the invariant manifolds. Knowledge of this relationship has the potential to benvery useful in developing initial guesses and new control laws for these optimization algorithms. In particular, thisnapproach can speed up the convergence of the optimization process, retain the essential geometric and topologicalncharacteristics of the initial design, and provide a more accurate estimate of theu0001V and fuel usage based on the initialntrajectory.