Titolo della tesi: Detection of Interconnections between Unstable Resonant Orbits Triggering Resonant Flybys
In resonant flyby trajectories, a transition from one unstable resonant orbit to another occurs in the course of closest approach to a planet or minor body. They have historically been exploited as part of tour trajectory design in complex gravitational environments to leverage large-scale natural and low-energy transport across phase space, thereby reducing the propellant required for spacecraft. From conceptual trajectories with multiple gravity assists based on two-body models, through the gradual incorporation of three-body effects in early design phases, to the consolidation of Dynamical Systems Theory (DST) to study the transition mechanism, the implication of resonant flybys in deep space exploration is still evident today in missions such as the recently launched (2024) Europa Clipper. As this trend is expected to continue for future interplanetary missions, this research work conducts an in-depth analysis to uncover where unstable resonant orbits of different families are related along phase space in such a way that they act as precursors to resonant transitions, which is a phenomenon previously coined as interconnection. It only occurs at certain energies where the manifold structures of the orbits involved are almost coincident, leading to the appearance of homoclinic and heteroclinic connections in the vicinity of both orbits. Related research has chained such type of connections to construct sequences of resonant flybys. However, either this was done outside the framework of interconnections, resulting in resonant flybys that evolve through intermediate resonances and do not occur in the most direct way possible, or interconnections were sought between a few families without checking all possible combinations at multiple energies. Therefore, the aim is to pick up the baton from the predecessors and fill the gap left behind. More specifically, a systematic multi-energy analysis is carried out in the Circular Restricted Three-Body Problem (CR3BP). The goal is to search for the most relevant interconnections between fifteen families of resonant periodic orbits, covering the spectrum of resonances between Europa and Ganymede, in a range of energies where high instability grants transfer opportunities. To alleviate the high computational burden associated with the use of DST-based techniques, a series of machine learning models are designed and validated to build an independent tool capable of making predictions about the location of new interconnections in phase space. A database of detected interconnections is generated that can support space applications
based on the use of resonant flybys as transfer mechanisms. Two case study scenarios demonstrate the utility of developing predictive tools to provide assistance in preliminary resonant flyby designs that require rapid consideration of multiple solutions. The second of these has also been unveiled as a methodology for discovering new resonant cyclers that can be extended into families of resonant chains. For the sake of efficiency, the resonant families sampled for analysis are obtained using a hybrid method, developed from the theory of generating orbits and allowing calculations to be held in parallel. Benchmark tests show that the hybrid method is as valid a technique as the classical continuation methods for constructing families of resonant periodic orbits, and even outperforms them in some cases.