Finding Order in Chaos: Resonant Orbits and Poincaré Sections

Resonant orbits in a multi-body environment have been investigated in the past to aid the understanding of perceived chaotic behavior in the solar system. The invariant manifolds associated with resonant orbits have also been recently incorporated into the design of trajectories requiring reduced maneuver costs. Poincaré sections are now also extensively utilized in the search for novel, maneuver-free trajectories in various systems. This investigation employs dynamical systems techniques in the computation and characterization of resonant orbits in the higher-fidelity Circular Restricted Three-Body model. Differential corrections and numerical methods are widely leveraged in this analysis in the determination of orbits corresponding to different resonance ratios. The versatility of resonant orbits in the design of low cost trajectories to support exploration for several planet-moon systems is demonstrated. The efficacy of the resonant orbits is illustrated via transfer trajectory design in the Earth-Moon, Saturn-Titan, and the Mars-Deimos systems. Lastly, Poincaré sections associated with different resonance ratios are incorporated into the search for natural, maneuver-free trajectories in the Saturn-Titan system. To that end, homoclinic and heteroclinic trajectories are constructed. Additionally, chains of periodic orbits that mimic the geometries for two different resonant ratios are examined, i.e., periodic orbits that cycle between different resonances are determined. The tools and techniques demonstrated in this investigation are useful for the design of trajectories in several different systems within the CR3BP