Application of Local Lyapunov Exponents to Maneuver Design and Navigation

Dynamical systems theory has recently been employed for several missions to design trajectories within the three-body problem. This research applied a s tability t echnique, the c alculation o f 1 oca1 L yapunov exponents, to such trajectories. Local Lyapunov exponents give an indication of the effects that perturbations or maneuvers will have on trajectories over a specified time. Results from this technique present a possible explanation for the effectiveness of maneuvers at certain points on unstable orbits, and appear to have the potential to aid maneuver design. It also has applications to navigation and the planning of tracking for spacecraft missions. New methods have recently been developed using dynamical systems theory in an effort to aid in the design of trajectories within the three-body problem. These techniques have been applied to trajectory design for several different missions. These mission