10.25394/PGS.7423658.v1
Brian P. McCarthy
Characterization of Quasi-Periodic Orbits for Applications in the Sun-Earth and Earth-Moon Systems
2019
Purdue University Graduate School
aerospace
engineering
trajectory
trajectory design
astrodynamics
three body
three body mechanics
circular restricted three body problem
CR3BP
quasi-periodic orbits
periodic orbits
orbit mechanics
celestial mechanics
dynamical systems
dynamical systems theory
dynamics
applications
orbits
astronautics
differential corrections
invariance
invariant circle
invariant torus
torus
invariant tori
stroboscopic mapping
manifolds
Sun-Earth system
Earth-Moon system
stability
multiple shooting
stroboscopic map
eclipse avoidance
vertical orbit
halo orbit
distant retrograde orbit
quasi-halo
quasi-vertical
lissajous
quasi-DRO
DRO
NRHO
quasi-NRHO
synodic resonance
trajectory arcs
mission design
astromechanics
spaceflight mechanics
dynamical structures
2019-01-17 01:51:50
article
https://hammer.figshare.com/articles/thesis/Characterization_of_Quasi-Periodic_Orbits_for_Applications_in_the_Sun-Earth_and_Earth-Moon_Systems/7423658
<div>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 L<sub>1</sub> quasi-vertical orbit are employed to design maneuver-free transfer from the LEO vicinity to a quasi-vertical orbit.</div>