%0 Thesis %A McCarthy, Brian P. %D 2019 %T Characterization of Quasi-Periodic Orbits for Applications in the Sun-Earth and Earth-Moon Systems %U https://hammer.purdue.edu/articles/thesis/Characterization_of_Quasi-Periodic_Orbits_for_Applications_in_the_Sun-Earth_and_Earth-Moon_Systems/7423658 %R 10.25394/PGS.7423658.v1 %2 https://hammer.purdue.edu/ndownloader/files/13747673 %K aerospace %K engineering %K trajectory %K trajectory design %K astrodynamics %K three body %K three body mechanics %K circular restricted three body problem %K CR3BP %K quasi-periodic orbits %K periodic orbits %K orbit mechanics %K celestial mechanics %K dynamical systems %K dynamical systems theory %K dynamics %K applications %K orbits %K astronautics %K differential corrections %K invariance %K invariant circle %K invariant torus %K torus %K invariant tori %K stroboscopic mapping %K manifolds %K Sun-Earth system %K Earth-Moon system %K stability %K multiple shooting %K stroboscopic map %K eclipse avoidance %K vertical orbit %K halo orbit %K distant retrograde orbit %K quasi-halo %K quasi-vertical %K lissajous %K quasi-DRO %K DRO %K NRHO %K quasi-NRHO %K synodic resonance %K trajectory arcs %K mission design %K astromechanics %K spaceflight mechanics %K dynamical structures %K Aerospace Engineering %X
As destinations of missions in both human and robotic spaceflight become more exotic, a foundational understanding the dynamical structures in the gravitational environments enable more informed mission trajectory designs. One particular type of structure, quasi-periodic orbits, are examined in this investigation. Specifically, efficient computation of quasi-periodic orbits and leveraging quasi-periodic orbits as trajectory design alternatives in the Earth-Moon and Sun-Earth systems. First, periodic orbits and their associated center manifold are discussed to provide the background for the existence of quasi-periodic motion on n-dimensional invariant tori, where n corresponds to the number of fundamental frequencies that define the motion. Single and multiple shooting differential corrections strategies are summarized to compute families 2-dimensional tori in the Circular Restricted Three-Body Problem (CR3BP) using a stroboscopic mapping technique, originally developed by Howell and Olikara. Three types of quasi-periodic orbit families are presented: constant energy, constant frequency ratio, and constant mapping time families. Stability of quasi-periodic orbits is summarized and characterized with a single stability index quantity. For unstable quasi-periodic orbits, hyperbolic manifolds are computed from the differential of a discretized invariant curve. The use of quasi-periodic orbits is also demonstrated for destination orbits and transfer trajectories. Quasi-DROs are examined in the CR3BP and the Sun-Earth-Moon ephemeris model to achieve constant line of sight with Earth and avoid lunar eclipsing by exploiting orbital resonance. Arcs from quasi-periodic orbits are leveraged to provide an initial guess for transfer trajectory design between a planar Lyapunov orbit and an unstable halo orbit in the Earth-Moon system. Additionally, quasi-periodic trajectory arcs are exploited for transfer trajectory initial guesses between nearly stable periodic orbits in the Earth-Moon system. Lastly, stable hyperbolic manifolds from a Sun-Earth L1 quasi-vertical orbit are employed to design maneuver-free transfer from the LEO vicinity to a quasi-vertical orbit.
%I Purdue University Graduate School