The mathematical formulation that represents the motion of a particle under the simultaneous influence of two gravitational fields is identified as the Circular Restricted Three-Body Problem (CR3BP). This model of an autonomous dynamical system displays both ordered and chaotic behavior. For some behaviors, simple linear analysis relative to a numerically determined point solution in the problem is sufficient to reveal interesting aspects of the motion, while other scenarios require more extensive procedures to capture the unique features comprising the dynamical behavior. This balance between predictability and complexity that is exhibited in the CR3BP, along with the typical approaches for its analysis, supplies excellent justification for the application of relatively straightforward techniques typically applied in more complicated problems. Among these, a number of versatile analysis tools are based on the concepts of the Finite-Time Lyapunov Exponent (FTLE) and Lagrangian Coherent Structures (LCS).

Lagrangian coherent structures appear as height ridges, or curves of constrained maxima, in a field of FTLE values. Application of interactive visualization, numerical methods, and parallel computation is employed to obtain FTLE data and the associated LCS. These results are compared with known structures to further establish LCS as a useful tool for application in the CR3BP and to demonstrate LCS as a seed for a variety of additional research questions. Results associated with potential applications to mission design are supplied, and comparisons between LCS methods and concurrent research efforts involving other, more familiar, approaches are generated with particular focus on the advantages of FTLE and LCS methods. Ultimately, this analysis serves to validate the concepts of FTLE and LCS as an effective means to further understand the complex behavior in the CR3BP.