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1	Transfer Trajectory Design Strategies Informed by Quasi-Periodic Orbits Dhruv Jain (17543799) 04 December 2023 (has links) <p dir="ltr">In the pursuit of establishing a sustainable space economy within the cislunar region, it is vital to formulate transfer design strategies that uncover economically viable highways between different regions of the space domain. The inherent complexity of spacecraft dynamics in the cislunar space poses challenges in determining feasible transfer options. However, the motion characterized by known dynamical structures modeled through the circular restricted three-body problem (CR3BP) aids in the identification of pathways with reasonable maneuver costs and flight times. A framework is proposed that incorporates a quasi-periodic orbit (QPOs) as an option to design transfer scenarios. This investigation focuses on the construction of transfers between periodic orbits. The framework is exemplified by the construction of pathways between an L2 9:2 synodic resonant Near-Rectilinear Halo Orbit (NRHO) and a planar Moon-centered Distant Retrograde Orbit (DRO). The innate difference in the geometries of the departure and arrival orbits of the sample case, along with the lack of natural flows towards and away from them, imply that links between these orbits may necessitate costly maneuvers. A strategy is formulated that leverages the stable and unstable manifolds associated with intermediate periodic orbits and quasi-periodic orbits to construct end-toend trajectories. As part of this strategy, a systematic methodology is outlined to streamline the determination of transfer options provided by the 5-dimensional manifolds associated with a QPO family. This approach reveals multiple local basins of solutions, both interior and exterior-types, characterized by selected intermediate orbits. The construction of transfers informed by the manifolds associated with QPOs is more intricate than those based on periodic orbits. However, QPO-derived solutions allow for the recognition of alternative local basins of solutions and often offer more cost-effective transfer options when compared to trajectories designed using periodic orbits that underlie the QPOs.</p> Flight dynamics CR3BP quasi-periodic orbits QPO transfer design invariant manifolds 9:2 NRHO DRO
2	Cislunar Trajectory Design Methodologies Incorporating Quasi-Periodic Structures With Applications Brian P. McCarthy (5930747) 29 April 2022 (has links) <p> </p> <p>In the coming decades, numerous missions plan to exploit multi-body orbits for operations. Given the complex nature of multi-body systems, trajectory designers must possess effective tools that leverage aspects of the dynamical environment to streamline the design process and enable these missions. In this investigation, a particular class of dynamical structures, quasi-periodic orbits, are examined. This work summarizes a computational framework to construct quasi-periodic orbits and a design framework to leverage quasi-periodic motion within the path planning process. First, quasi-periodic orbit computation in the Circular Restricted Three-Body Problem (CR3BP) and the Bicircular Restricted Four-Body Problem (BCR4BP) is summarized. The CR3BP and BCR4BP serve as preliminary models to capture fundamental motion that is leveraged for end-to-end designs. Additionally, the relationship between the Earth-Moon CR3BP and the BCR4BP is explored to provide insight into the effect of solar acceleration on multi-body structures in the lunar vicinity. Characterization of families of quasi-periodic orbits in the CR3BP and BCR4BP is also summarized. Families of quasi-periodic orbits prove to be particularly insightful in the BCR4BP, where periodic orbits only exist as isolated solutions. Computation of three-dimensional quasi-periodic tori is also summarized to demonstrate the extensibility of the computational framework to higher-dimensional quasi-periodic orbits. Lastly, a design framework to incorporate quasi-periodic orbits into the trajectory design process is demonstrated through a series of applications. First, several applications were examined for transfer design in the vicinity of the Moon. The first application leverages a single quasi-periodic trajectory arc as an initial guess to transfer between two periodic orbits. Next, several quasi-periodic arcs are leveraged to construct transfer between a planar periodic orbit and a spatial periodic orbit. Lastly, transfers between two quasi-periodic orbits are demonstrated by leveraging heteroclinic connections between orbits at the same energy. These transfer applications are all constructed in the CR3BP and validated in a higher-fidelity ephemeris model to ensure the geometry persists. Applications to ballistic lunar transfers are also constructed by leveraging quasi-periodic motion in the BCR4BP. Stable manifold trajectories of four-body quasi-periodic orbits supply an initial guess to generate families of ballistic lunar transfers to a single quasi-periodic orbit. Poincare mapping techniques are used to isolate transfer solutions that possess a low time of flight or an outbound lunar flyby. Additionally, impulsive maneuvers are introduced to expand the solution space. This strategy is extended to additional orbits in a single family to demonstrate "corridors" of transfers exist to reach a type of destination motion. To ensure these transfers exist in a higher fidelity model, several solutions are transitioned to a Sun-Earth-Moon ephemeris model using a differential corrections process to show that the geometries persist.</p> Aerospace Engineering trajectory design quasi-periodic orbits cislunar Multi-Body Dynamics astrodynamics Three-body problem four-body problem ballistic lunar transfers Dynamical Systems Theory Poincare Map orbit mechanics spacecraft path planning invariant curves
3	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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