Global ETD Search

91	Multi-Body Trajectory Design in the Earth-Moon Region Utilizing Poincare Maps Paige Alana Whittington (12455871) 25 April 2022 (has links) <p>The 9:2 lunar synodic resonant near rectilinear halo orbit (NRHO) is the chosen orbit for the Gateway, a future lunar space station constructed by the National Aeronautics and Space Administration (NASA) as well as several commercial and international partners. Designing trajectories in this sensitive lunar region combined with the absence of a singular systematic methodology to approach mission design poses challenges as researchers attempt to design transfers to and from this nearly stable orbit. This investigation builds on previous research in Poincar\'e mapping strategies to design transfers from the 9:2 NRHO using higher-dimensional maps and maps with non-state variables. First, Poincar\'e maps are applied to planar transfers to demonstrate the utility of hyperplanes and establish that maps with only two or three dimensions are required in the planar problem. However, with the addition of two state variables, the spatial problem presents challenges in visualizing the full state. Higher-dimensional maps utilizing glyphs and color are employed for spatial transfer design involving the 9:2 NRHO. The visualization of all required dimensions on one plot accurately reveals low cost transfers into both a 3:2 planar resonant orbit and an L2 vertical orbit. Next, the application of higher-dimensional maps is extended beyond state variables. Visualizing time-of-flight on a map axis enables the selection of faster transfers. Additionally, glyphs and color depicting angular momentum rather than velocity lead to transfers with nearly tangential maneuvers. Theoretical minimum maneuvers occur at tangential intersections, so these transfers are low cost. Finally, a map displaying several initial and final orbit options, discerned through the inclusion of Jacobi constant on an axis, eliminates the need to recompute a map for each initial and final orbit pair. Thus, computation time is greatly reduced in addition to visualizing more of the design space in one plot. The higher-dimensional mapping strategies investigated are relevant for transfer design or other applications requiring the visualization of several dimensions simultaneously. Overall, this investigation outlines Poincar\'e mapping strategies for transfer scenarios of different design space dimensions and represents initial research into non-state variable mapping methods.</p> Aerospace Engineering astrodynamics Poincare map trajectory design transfer CR3BP Circular Restricted Three-Body Problem Invariant Manifolds higher-dimensional maps Jacobi constant
92	There and Back Again: Generating Repeating Transfers Using Resonant Structures Noah Isaac Sadaka (15354313) 25 April 2023 (has links) <p>Many future satellite applications in cislunar space require repeating, periodic transfers that shift away from some operational orbit and eventually return. Resonant orbits are investigated in the Earth-Moon Circular Restricted Three Body Problem (CR3BP) as a mechanism to enable these transfers. Numerous resonant orbit families possess a ratio of orbital period to lunar period that is sufficiently close to an integer ratio and can be exploited to uncover period-commensurate transfers due to their predictable periods. Resonant orbits also collectively explore large swaths of space, making it possible to select specific orbits that reach a region of interest. A framework for defining period-commensurate transfers is introduced that leverages the homoclinic connections associated with an unstable operating orbit to permit ballistic transfers that shuttle the spacecraft to a certain region. Resonant orbits are incorporated by locating homoclinic connections that possess resonant structures, and the applicability of these transfers is extended by optionally linking them to resonant orbits. In doing so, transfers are available for in-orbit refueling/maintenance as well as surveillance/communications applications that depart and return to the same phase in the operating orbit.</p> Astrodynamics Orbital mechanics Mission design Circular Restricted Three-Body Problem Resonant orbits Homoclinic connections Space infrastructure Numerical modeling
93	Dynamical Flow Characteristics in Response to a Maneuver in the L1 or L2 Earth-Moon Region Colton D Mitchell (15347518) 25 April 2023 (has links) <p>National security concerns regarding cislunar space have become more prominent due to</p> <p>the anticipated increase in cislunar activity. Predictability is one of these concerns. Cislunar</p> <p>motion is difficult to predict because it is chaotic. The chaotic nature of cislunar motion is</p> <p>pronounced near the L1 and L2 Lagrange points. For this reason, among others, it is likely</p> <p>that a red actor (an antagonist) would have its cislunar spacecraft perform a maneuver in</p> <p>one of the aforementioned vicinities to reach some cislunar point of interest. This realization</p> <p>unveils the need to ascertain some degree of predictability in the motion resulting from a</p> <p>maneuver performed in the L1 or L2 region. To investigate said motion, impulsive maneuvers</p> <p>are employed on the L1 and L2 Lagrange points and on L1 and L2 Lyapunov orbits in the</p> <p>model that is the circular restricted three-body problem. The behavior of the resultant</p> <p>trajectories is analyzed to understand how the magnitude and direction of a maneuver in</p> <p>said regions affect the behavior of the resultant trajectory. It is found that the direction</p> <p>of such maneuvers is particularly influential with respect to said behavior. Regarding both</p> <p>the L1 and L2 regions, certain maneuver directions yield certain behaviors in the resultant</p> <p>trajectory over a wide range of maneuver magnitudes. This understanding is informative to</p> <p>cislunar mission design.</p> astronautics astronautical engineering orbital mechanics astrodynamics multi-body dynamics circular restricted three-body problem cislunar space
94	DESIGN OF LUNAR TRANSFER TRAJECTORIES FOR SECONDARY PAYLOAD MISSIONS Alexander Estes Hoffman (15354589) 27 April 2023 (has links) <p>Secondary payloads have a rich and successful history of utilizing cheap rides to orbit to perform outstanding missions in Earth orbit, and more recently, in cislunar space and beyond. New launch vehicles, namely the Space Launch System (SLS), are increasing the science opportunity for rideshare class missions by providing regular service to the lunar vicinity. However, trajectory design in a multi-body regime brings a host of novel challenges, further exacerbated by constraints generated from the primary payload’s mission. Often, secondary payloads do not possess the fuel required to directly insert into lunar orbit and must instead perform a lunar flyby, traverse the Earth-Moon-Sun system, and later return to the lunar vicinity. This investigation develops a novel framework to construct low-cost, end-to-end lunar transfer trajectories for secondary payload missions. The proposed threephase approach provides unique insights into potential lunar transfer geometries. The phases consist of an arc from launch to initial perilune, an exterior transfer arc, and a lunar approach arc. The space of feasible transfers within each phase is determined through low-dimension grid searches and informed filtering techniques, while the problem of recombining the phases through differential corrections is kept tractable by reducing the dimensionality at each phase transition boundary. A sample mission demonstrates the trajectory design approach and example solutions are generated and discussed. Finally, alternate strategies are developed to both augment the analysis and for scenarios where the proposed three-phase technique does not deliver adequate solutions. The trajectory design methods described in this document are applicable to many upcoming secondary payload missions headed to lunar orbit, including spacecraft with only low-thrust, only high-thrust, or a combination of both. </p> Astrodynamics Trajectory design Secondary payload Multi-body dynamics Circular Restricted Three-Body Problem bicircular restricted four-body problem Lunar transfer CubeSats
95	ZERO-MOMENTUM POINT ANALYSIS AND EPHEMERIS TRANSITION FOR INTERIOR EARTH TO LIBRATION POINT ORBIT TRANSFERS Juan-Pablo Almanza-Soto (15341785) 24 April 2023 (has links) <p>The last decade has seen a significant increase in activity within cislunar space. The quantity of missions to the Lunar vicinity will only continue to rise following the collab- orative effort between NASA, ESA, JAXA and the CSA to construct the Gateway space station. One significant engineering challenge is the design of trajectories that deliver space- craft to orbits in the Lunar vicinity. In response, this study employs multi-body dynamics to investigate the geometry of two-maneuver transfers to Earth-Moon libration point or- bits. Zero-Momentum Points are employed to investigate transfer behavior in the circular- restricted 3-body problem. It is found that these points along stable invariant manifolds indicate changes in transfer geometry and represent locations where transfers exhibit limit- ing behaviors. The analysis in the lower-fidelity model is utilized to formulate initial guesses that are transitioned to higher-fidelity, ephemeris models. Retaining the solution geometry of these guesses is prioritized, and adaptations to the transition strategy are presented to circumvent numerical issues. The presented methodologies enable the procurement of desir- able trajectories in higher-fidelity models that reflect the characteristics of the initial guess generated in the circular restricted 3-body problem.</p> Astrodynamics Mission Design Dynamical Systems Theory numerical modeling simulations N-body problems Circular Restricted Three-Body Problem Ephemeris Multi-Body Dynamics
96	Stretching Directions in Cislunar Space: Stationkeeping and an application to Transfer Trajectory Design Vivek Muralidharan (11014071) 23 July 2021 (has links) <div>The orbits of interest for potential missions are stable or nearly stable to maintain long term presence for conducting scientific studies and to reduce the possibility of rapid departure. Near Rectilinear Halo Orbits (NRHOs) offer such stable or nearly stable orbits that are defined as part of the L1 and L2 halo orbit families in the circular restricted three-body problem. Within the Earth-Moon regime, the L1 and L2 NRHOs are proposed as long horizon trajectories for cislunar exploration missions, including NASA's upcoming Gateway mission. These stable or nearly stable orbits do not possess well-distinguished unstable and stable manifold structures. As a consequence, existing tools for stationkeeping and transfer trajectory design that exploit such underlying manifold structures are not reliable for orbits that are linearly stable. The current investigation focuses on leveraging stretching direction as an alternative for visualizing the flow of perturbations in the neighborhood of a reference trajectory. The information supplemented by the stretching directions are utilized to investigate the impact of maneuvers for two contrasting applications; the stationkeeping problem, where the goal is to maintain a spacecraft near a reference trajectory for a long period of time, and the transfer trajectory design application, where rapid departure and/or insertion is of concern.</div><div><br></div><div>Particularly, for the stationkeeping problem, a spacecraft incurs continuous deviations due to unmodeled forces and orbit determination errors in the complex multi-body dynamical regime. The flow dynamics in the region, using stretching directions, are utilized to identify appropriate maneuver and target locations to support a long lasting presence for the spacecraft near the desired path. The investigation reflects the impact of various factors on maneuver cost and boundedness. For orbits that are particularly sensitive to epoch time and possess distinct characteristics in the higher-fidelity ephemeris model compared to their CR3BP counterpart, an additional feedback control is applied for appropriate phasing. The effect of constraining maneuvers in a particular direction is also investigated for the 9:2 synodic resonant southern L2 NRHO, the current baseline for the Gateway mission. The stationkeeping strategy is applied to a range of L1 and L2 NRHOs, and validated in the higher-fidelity ephemeris model.</div><div><br></div><div>For missions with potential human presence, a rapid transfer between orbits of interest is a priority. The magnitude of the state variations along the maximum stretching direction is expected to grow rapidly and, therefore, offers information to depart from the orbit. Similarly, the maximum stretching in reverse time, enables arrival with a minimal maneuver magnitude. The impact of maneuvers in such sensitive directions is investigated. Further, enabling transfer design options to connect between two stable orbits. The transfer design strategy developed in this investigation is not restricted to a particular orbit but applicable to a broad range of stable and nearly stable orbits in the cislunar space, including the Distant Retrograde Orbit (DROs) and the Low Lunar Orbits (LLO) that are considered for potential missions. Examples for transfers linking a southern and a northern NRHO, a southern NRHO to a planar DRO, and a southern NRHO to a planar LLO are demonstrated.</div> Aerospace Engineering Dynamical Systems in Applications Applied Statistics Stationkeeping Orbit Maintenance Orbital Mechanics Transfer Trajectory Design Astrodynamics Cauchy-Green Tensor Circular Restricted Three-Body Problem Three-Body Problem Gateway Mission Guidance Navigation and Control Nonlinear Model Applied Statistics Stretching Directions Cislunar
97	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
98	Bound states for A-body nuclear systems Mukeru, Bahati 03 1900 (has links) In this work we calculate the binding energies and root-mean-square radii for A−body nuclear bound state systems, where A ≥ 3. To study three−body systems, we employ the three−dimensional differential Faddeev equations with nucleon-nucleon semi-realistic potentials. The equations are solved numerically. For this purpose, the equations are transformed into an eigenvalue equation via the orthogonal collocation procedure using triquintic Hermite splines. The resulting eigenvalue equation is solved using the Restarted Arnoldi Algorithm. Ground state binding energies of the 3H nucleus are determined. For A > 3, the Potential Harmonic Expansion Method is employed. Using this method, the Schr¨odinger equation is transformed into coupled Faddeev-like equations. The Faddeevlike amplitudes are expanded on the potential harmonic basis. To transform the resulting coupled differential equations into an eigenvalue equation, we employ again the orthogonal collocation procedure followed by the Gauss-Jacobi quadrature. The corresponding eigenvalue equation is solved using the Renormalized Numerov Method to obtain ground state binding energies and root-mean-square radii of closed shell nuclei 4He, 8Be, 12C, 16O and 40Ca. / Physics / M. Sc. (Physics) Potential Harmonic basis Coupled differential equations Orthogonal collocation procedure Eigenvalue equation Restarted Arnoldi Algorithm Renormalized Numerov Method Closed shell nuclei 539.70151535 Bound states (Quantum mechanics) Three-body problem Nuclear physics Mathematical physics Differential equations
99	Le problème mathématique des trois corps, abordé simultanément sous l'angle de la recherche théorique et celui de la diffusion auprès de publics variés / The mathematical three body problem, simultaneoulsy addressed through theoretical research, and through popularization toward various publics Lhuissier, Marie 21 November 2018 (has links) Cette thèse contient deux parties distinctes, reliées par le thème de l’étude géométrique du problème à trois corps. La première partie présente un point de vue sur les enjeux et les perspectives liés à la diffusion des mathématiques, et illustre ce point de vue à l’aide de deux projets de diffusion « grand public » : une exposition virtuelle autour de la mécanique céleste et du problème à trois corps, et un duo de contes mathématiques pour enfants, l’un sur la forme de la lune, et l’autre sur l’enlacement de courbes fermées. La présentation de ces projets est suivie d’une analyse a priori et d’une étude des observations recueillies lors de différentes expérimentations auprès de publics variés. La deuxième partie est consacrée à l’étude – théorique et numérique – de l’enlacement des trajectoires de quelques systèmes dynamiques sur la 3-sphère, et en particulier de certaines instances du problème à trois corps. On y présente d’abord le problème à trois corps restreint, plan, circulaire, en s’intéressant tout particulièrement au cas où une des deux primaires disparait. On se ramène ainsi à un flot sur la 3-shpère dont on connaît explicitement des sections de Birkhoff en disque ou en anneau, et on met en lumière des éléments qui tendent à montrer le caractère lévogyre de ce flot. On explore ensuite, à l’aide de simulations numériques, la possibilité que le système reste lévogyre sur un domaine assez éloigné de ce cas dégénéré. Enfin, on s’intéresse aux flots sur la 3-sphère qui admettent une section de Birkhoff en disque et on traduit la notion d’enlacement de mesures invariantes pour le flot en termes d’enroulement de mesures invariantes pour le difféomorphisme de premier retour. / This thesis contains two distinct parts, connected by the subject of the geometric study of the three body problem.The first part presents a point of view about the stakes and prospects of the popularization of mathematics, and it illustrates this point of view with two projects of popularization for a general public : a virtual exhibition about celestial mechanics and the three body problem, and a pair of mathematical tales for children, one about the shape of the moon, and the other about the linking number of two closed curves. The presentation of these projects is followed by an initial analysis and by a study of the observations collected during different experimentations towards various publics. The second part is devoted to the theoretical and computational study of the linking number of trajectories from a few dynamical systems on the 3-sphere, and in particular from some cases of the restricted three body problem. We first present the planar, circular, restricted three body problem, with a particular attention to the case where one of the two heavy bodies vanishes. We thus restrict ourselves to a flow on the 3-shpere for which disk-like or annular-like Birkhoff sections are explicitely known, and we bring to light evidences of the right-handedness of this flow. Then we investigate, with the help of computer simulations, the possibility for the system to stay right-handed over a domain rather distant from this degenerate case. Finally, we consider the flows on the 3-sphere which admit a disk-like Birkhoff section, and we translate the notion of linking for measures that are invariant by a flow into the notion of winding for measures that are invariant by the first return map on the disk. Problème à trois corps Flots lévogyres Enlacement Diffusion des mathématiques Contes mathématiques Exposition virtuelle Mécanique céleste Simulations numériques Three body problem Right-handed vector fields Linking Popularization of mathematics Mathematical tales Virtual exhibition Celestial mechanics Computer simulations
100	Ressonâncias de três corpos: estudo da dinâmica da zona habitável do sistema exoplanetário GJ581 / The Three Body Resonances: Study of dynamic the habitable zone of exoplanetary system GJ 581 Silva, Gleidson Gomes da 06 December 2012 (has links) Estudo das ressonâncias de três corpos na zona habitável (ZH), da estrela GJ 581 (Gliese 581), envolvendo dois planetas conhecidos e um terceiro planeta dentro da ZH. Séries de Lie são usadas para obter o Hamiltoniano médio (de segunda ordem nas massas) e teoria de Chirikov é usada para gerar um novo sistema de varáveis canônicas em que os momentos se orientam ao longo e através da ressonância. Um mapa de Hadjidemetriou é construido e permite o cálculo rápido da difusão das órbitas em uma extensa grade de condições iniciais. / Study of three-body resonances in the habitable zone (ZH), the star GJ 581 (Gliese 581), involving two known planets, and a third planet in the ZH. Lie series are used to obtain the average Hamiltonian (the second-order mass) and Chirikov theory is used to generate a new canonical variables system in which the moments are oriented along and across the resonance. A map of Hadjidemetriou is constructed and allows rapid calculation of the diffusion of orbits in an extensive grid of initial conditions. Astronomia Dinâmica Chirikov\'s Theory. Orbital Diffusion. Difusão Orbital. Dynamical Astronomy GJ (Gliese) 581 GJ (Gliese) 581 Habitable Zone Ressonâncias de Três Corpos Teoria de Chirikov Three-Body Resonances Zona Habitável

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