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21	Low-Energy Lunar Transfers in the Bicircular Restricted Four-body Problem Stephen Scheuerle Jr. (10676634) 26 April 2024 (has links) <p dir="ltr"> With NASA's Artemis program and international collaborations focused on building a sustainable infrastructure for human exploration of the Moon, there is a growing demand for lunar exploration and complex spaceflight operations in cislunar space. However, designing efficient transfer trajectories between the Earth and the Moon remains complex and challenging. This investigation focuses on developing a dynamically informed framework for constructing low-energy transfers in the Earth-Moon-Sun Bicircular Restricted Four-body Problem (BCR4BP). Techniques within dynamical systems theory and numerical methods are exploited to construct transfers to various cislunar orbits. The analysis aims to contribute to a deeper understanding of the dynamical structures governing spacecraft motion. It addresses the characteristics of dynamical structures that facilitate the construction of propellant-efficient pathways between the Earth and the Moon, exploring periodic structures and energy properties from the Circular Restricted Three-body Problem (CR3BP) and BCR4BP. The investigation also focuses on constructing families of low-energy transfers by incorporating electric propulsion, i.e., low thrust, in an effort to reduce the time of flight and offer alternative transfer geometries. Additionally, the investigation introduces a process to transition solutions to the higher fidelity ephemeris force model to accurately model spacecraft motion through the Earth-Moon-Sun system. This research provides insights into constructing families of ballistic lunar transfers (BLTs) and cislunar low-energy flight paths (CLEFs), offering a foundation for future mission design and exploration of the Earth-Moon system.</p> Trajectory Design cislunar space multi-body dynamics astrodynamics ballistic lunar transfers electric propulsion Low-thrust trajectory design Dynamical Systems Theory Orbital Mechanics Four-body Problem bicircular restricted four-body problem
22	Characterization of Quasi-Periodic Orbits for Applications in the Sun-Earth and Earth-Moon Systems Brian P. McCarthy (5930747) 17 January 2019 (has links) <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> Aerospace Engineering 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

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Low-Energy Lunar Transfers in the Bicircular Restricted Four-body Problem

Characterization of Quasi-Periodic Orbits for Applications in the Sun-Earth and Earth-Moon Systems