A Dynamical Systems Perspective for Preliminary Low-Thrust Trajectory Design in Multi-Body Regimes

A key challenge in low-thrust trajectory design is generating preliminary solutions that simultaneously detail the evolution of the spacecraft position and velocity vectors, as well as the thrust history. To address this difficulty, a dynamical model that incorporates a low-thrust force into the circular restricted 3-body problem (CR3BP), i.e., the CR3BP+LT, is constructed and analyzed. Control strategies that deliver specific energy changes (including zero energy change to deliver a conservative system) are derived and investigated, and dynamical structures within the CR3BP+LT are explored as candidate solutions to seed initial low-thrust trajectory designs. Furthermore, insights from dynamical systems theory are leveraged to inform the design process. In the combined model, the addition of a low-thrust force modifies the locations and stability of the equilibrium solutions, resulting in flow configurations that differ from the natural behavior in the CR3BP. The application of simplifying assumptions yields a conservative, autonomous system with properties that supply useful insights. For instance, "forbidden regions" at fixed energy levels bound low-thrust motion, and analytical equations are available to guide the navigation through energy space. Linearized dynamics about the equilibria supply hyperbolic and center manifold structures, similar to the ballistic CR3BP. Low-thrust periodic orbits in the vicinity of the equilibrium solutions also admit hyperbolic and center manifolds, providing an even greater number of dynamical structures to be employed in preliminary trajectory designs. Several applications of the structures and insights derived from the CR3BP+LT are presented, including several strategies for transit and capture near the smaller CR3BP primary body. Finally, an interactive trajectory design framework is presented to explore and utilize the structures and insights delivered by this investigation.