%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