Role of Invariant Manifolds in Low-Thrust Trajectory Design

Abstract

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