Thesis advisor: Solomon Friedberg / We study the generalized theta lifting between the double covers of split special orthogonal groups, which uses the non-minimal theta representations constructed by Bump, Friedberg and Ginzburg. We focus on the theta liftings of non-generic representations and make a conjecture that gives an upper bound of the first non-zero occurrence of the liftings, depending only on the unipotent orbit. We prove both global and local results that support the conjecture. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18766号 / 理博第4024号 / 新制||理||1580(附属図書館) / 31717 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 伊藤 哲史, 教授 上田 哲生, 教授 雪江 明彦 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Ongoing changes in spaceflight – continuing miniaturization, declining costs of rocket launches and satellite components, and improved satellite computing and control capabilities – are advancing Satellite Formation Flying (SFF) as a research and application area. SFF enables new applications that cannot be realized (or cannot be realized at a reasonable cost) with conventional single-satellite missions. In particular, distributed Earth observation applications such as photogrammetry and tomography or distributed space telescopes require precisely placed and controlled satellites in orbit. Several enabling technologies are required for SFF, such as inter-satellite communication, precise attitude control, and in-orbit maneuverability. However, one of the most important requirements is a reliable distributed Guidance, Navigation and Control (GNC) strategy. This work addresses the issue of distributed GNC for SFF in 3D with a focus on Continuous Low-Thrust (CLT) propulsion satellites (e.g., with electric thrusters) and concentrates on circular low Earth orbits. However, the focus of this work is not only on control theory, but control is considered as part of the system engineering process of typical small satellite missions. Thus, common sensor and actuator systems are analyzed to derive their characteristics and their impacts on formation control. This serves as the basis for the design, implementation, and evaluation of the following control approaches: First, a Model Predictive Control (MPC) method with specific adaptations to SFF and its requirements and constraints; second, a distributed robust controller that combines consensus methods for distributed system control and $H_{\infty}$ robust control; and finally, a controller that uses plant inversion for control and combines it with a reference governor to steer the controller to the target on an optimal trajectory considering several constraints. The developed controllers are validated and compared based on extensive software simulations. Realistic 3D formation flight scenarios were taken from the Networked Pico-Satellite Distributed System Control (NetSat) cubesat formation flight mission. The three compared methods show different advantages and disadvantages in the different application scenarios. The distributed robust consensus-based controller for example lacks the ability to limit the maximum thrust, so it is not suitable for satellites with CLT. But both the MPC-based approach and the plant inversionbased controller are suitable for CLT SFF applications, while showing again distinct advantages and disadvantages in different scenarios. The scientific contribution of this work may be summarized as the creation of novel and specific control approaches for the class of CLT SFF applications, which is still lacking methods withstanding the application in real space missions, as well as the scientific evaluation and comparison of the developed methods. / Die anhaltenden Veränderungen in der Raumfahrt – die fortschreitende Miniaturisierung, die sinkenden Kosten für Raketenstarts und Satellitenkomponenten sowie die verbesserten Rechen- und Steuerungsmöglichkeiten von Satelliten – fördern den Satelliten-Formationsflug (SFF) als Forschungs- und Anwendungsgebiet. SFF ermöglicht neue Anwendungen, die mit herkömmlichen Einzelsatellitenmissionen nicht (oder nicht mit vertretbarem Aufwand) realisiert werden können. Insbesondere verteilte Erdbeobachtungsanwendungen wie Photogrammetrie und Tomographie oder verteilte Weltraumteleskope erfordern präzise positionierte und kontrollierte Satelliten in der Umlaufbahn. Für den SFF sind verschiedene Basistechnologien erforderlich, z. B. Kommunikation zwischen den Satelliten, präzise Lageregelung und Manövrierfähigkeit. Eine der wichtigsten Anforderungen sind jedoch zuverlässige verteilte Leit- und Regelungsverfahren (Guidance, Navigation and Control, GNC). Diese Arbeit befasst sich mit dem Thema der verteilten GNC für SFF in 3D mit dem Schwerpunkt auf Satelliten mit kontinuierlichem, niedrigen Schub (Continuous Low-Thrust, CLT) z.B. mit elektrischen Triebwerken und legt den Fokus hier zusätzlich auf niedrige kreisförmige Erdumlaufbahnen. Der Schwerpunkt dieser Arbeit liegt jedoch nicht nur auf der Regelungstheorie, vielmehr wird Regelung als Teil des Systementwicklungsprozesses typischer Kleinsatellitenmissionen betrachtet. So werden gängige Sensor- und Aktuatorsysteme analysiert, um ihre Eigenschaften und ihre Auswirkungen auf die Formationskontrolle abzuleiten. Dies dient als Grundlage für den Entwurf, die Implementierung und die Bewertung der folgenden Regelungsansätze: Erstens eine Modellprädiktive Regelung (Model-Predictive Control, MPC) mit spezifischen Anpassungen an die Anforderungen und Beschränkungen des SFFs, zweitens ein robuster Regler, der Konsensmethoden für die Steuerung verteilter Systeme mit robuster $H_{\infty}$-Regelung kombiniert, und schließlich ein kaskadierter Regler, der zur Steuerung die Regelstrecke invertiert und dessen Referenz von einem Referenzregler auf einer optimalen Trajektorie unter Berücksichtigung verschiedener Beschränkungen zum Ziel gesteuert wird. Die entwickelten Regler werden auf der Grundlage umfangreicher Softwaresimulationen validiert und miteinander verglichen. Realistische 3D-Formationsflug-Szenarien wurden der NetSat-Formationsflug-Mission entnommen. Die drei verglichenen Methoden zeigen unterschiedliche Vor- und Nachteile in den verschiedenen Anwendungsszenarien. Der verteilten robusten konsensbasierten Regelung fehlt bspw. die Fähigkeit, den maximalen Schub zu begrenzen, sodass sie nicht für Satelliten mit CLT geeignet ist. Aber sowohl der MPC-basierte Ansatz als auch der auf der Invertierung der Regelstrecke basierende Ansatz sind für CLT SFF-Anwendungen geeignet und weisen wiederum ander Vor- und Nachteile in unterschiedlichen Szenarien auf. Der wissenschaftliche Beitrag dieser Arbeit besteht in der Entwicklung neuartiger und spezifischer Regelungsansätze für die Klasse der CLT-SFF-Anwendungen, für die es noch keine Methoden gibt, die der Anwendung in realen Weltraummissionen standhalten, sowie in der wissenschaftlichen Bewertung und dem Vergleich der entwickelten Methoden.

With the miniaturization of satellites a fundamental change took place in the space industry. Instead of single big monolithic satellites nowadays more and more systems are envisaged consisting of a number of small satellites to form cooperating systems in space. The lower costs for development and launch as well as the spatial distribution of these systems enable the implementation of new scientific missions and commercial services. With this paradigm shift new challenges constantly emerge for satellite developers, particularly in the area of wireless communication systems and network protocols. Satellites in low Earth orbits and ground stations form dynamic space-terrestrial networks. The characteristics of these networks differ fundamentally from those of other networks. The resulting challenges with regard to communication system design, system analysis, packet forwarding, routing and medium access control as well as challenges concerning the reliability and efficiency of wireless communication links are addressed in this thesis. The physical modeling of space-terrestrial networks is addressed by analyzing existing satellite systems and communication devices, by evaluating measurements and by implementing a simulator for space-terrestrial networks. The resulting system and channel models were used as a basis for the prediction of the dynamic network topologies, link properties and channel interference. These predictions allowed for the implementation of efficient routing and medium access control schemes for space-terrestrial networks. Further, the implementation and utilization of software-defined ground stations is addressed, and a data upload scheme for the operation of small satellite formations is presented. / Mit der Miniaturisierung von Satelliten hat eine fundamentale Änderung in der Raumfahrtindustrie stattgefunden. Anstelle von einzelnen, großen, monolithischen Satelliten werden heutzutage immer mehr Systeme entworfen die aus mehreren Kleinstsatelliten bestehen die kooperativ zusammenarbeiten. Die geringeren Kosten für Entwicklung und Start sowie die räumliche Verteilung dieser Satellitensysteme ermöglichen die Realisierung neuer wissenschaftlicher Missionen und kommerzieller Dienstleistungen. Durch diesen Paradigmenwechsel entstehen neue Herausforderungen für Ingenieure, insbesondere in den Bereichen Funkkommunikation und Netzwerkprotokolle. Satelliten in erdnahen Umlaufbahnen und Bodenstationen bilden sogenannte Satelliten-terrestrische Netzwerke. Die Eigenschaften dieser Netzwerke unterscheiden sich wesentlich von denen anderer Netzwerke. Die resultierenden Herausforderungen in den Bereichen Systemdesign, Systemanalyse, Paketvermittlung, Routing und Medienzugriffskontrolle, sowie Herausforderungen in Bezug auf die Zuverlässigkeit und Effizienz der Funkkommunikation werden in dieser Dissertation behandelt. Die physikalische Modellierung von Satelliten-terrestrischen Netzwerken wird behandelt durch die Analyse von existierenden Satelliten- und Funkkommunikationssystemen, durch die Nutzung von Messungen an einer Bodenstation und einem Satelliten und durch die Implementierung eines Simulators für Satelliten-terrestrische Netzwerke. Die resultierenden System- und Kanalmodelle wurden als Basis für die Prädiktion der dynamischen Netzwerktopologien, Verbindungseigenschaften und Kanalinterferenzen genutzt. Diese Prädiktionen haben die Implementierung effizienter Verfahren für Routing und Medienzugriffskontrolle in Satelliten-terrestrischen Netzwerken ermöglicht. Darüber hinaus wird die Implementierung und Nutzung von Bodenstationen auf Basis von digitaler Signalverarbeitung behandelt und ein Datenübertragungsverfahren für den Betrieb von Kleinstsatellitenformationen beschrieben und evaluiert.

No description available.

This thesis outlines an orbit determination and 3-axis attitude determination system for use on orbit as applicable to 1U CubeSats and other picosatellites. The constraints imposed by the CubeSat form factor led to the need for a simple configuration and relaxed accuracy requirements. To design a system within the tight mass, volume, and power constraints inherent to CubeSats, a balance between hardware complexity, software complexity and accuracy is sought. The proposed solution consists of a simple orbit propagator, magnetometers with a magnetic field look-up table, Sun sensors with an analytic Sun direction model, and the TRIAD method to combine vector observations into attitude information. The orbit propagator is a simple model of a circular trajectory with several frequently updated parameters and can provide orbital position data with average and maximum errors—when compared to SGP4—of less than 3.7km and 10.7km for 14 days. The magnetic field look up table provides useful information from a small memory footprint; only 480 data points provide a mean error of approximately 0.2° and a maximum error of approximately 2°—when compared to the IGRF model. The Sun’s direction is modeled, and as expected, can be modeled simply and accurately. Combining the magnetic field and Sun direction models with inaccurate sensors and the TRIAD method results in useful attitude information from a very simple system. A system with Sun sensor error standard deviation of 1° and magnetometer error standard deviation of 5° yields results with average error of only 2.74°, and 99% of the errors in this case are less than approximately 13°. The system outlined provides crude attitude determination with software and hardware requirements that are well within the capabilities of current 1U CubeSats—something that many other systems, such as Kalman filters or star trackers, cannot do. It also provides an excellent starting point for future ADCS systems, which will significantly increase the ability of CubeSats.

In this dissertation, regularization of simultaneous binary collision, existence of a Schubart-like periodic orbit, existence of a planar symmetric periodic orbit with multiple simultaneous binary collisions, and their linear stabilities are studied. The detailed background of those problems is introduced in chapter 1. The singularities of simultaneous binary collision in the collinear four-body problem is regularized in chapter 2. We use canonical transformations to collectively analytically continue the singularities of the simultaneous binary collision solutions in both the decoupled case and the coupled case. All the solutions are found and more importantly, we find a crucial first integral which describes the relationship between the decoupled solutions and the coupled solutions. In chapter 3, we show the existence of a Schubart-like orbit, a periodic orbit with singularities in the symmetric collinear four-body problem. In each period of the orbit, there is a binary collision (BC) between the inner two bodies and a simultaneous binary collision (SBC) of the two clusters on both sides of the origin. The system is regularized and the existence is proven by using a "turning point" technique and a continuity argument on differential equations of the regularized Hamiltonian. Analytical methods are used in chapter 4 to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method can be extended to any even number of bodies. Multiple simultaneous binary collisions are a key feature of the orbits generated. In chapter 5, we apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four body problem with masses 1, m, m , 1, and also in a symmetric planar four-body problem with equal masses. For the collinear problem, this verifies the earlier numerical results of Sweatman for linear stability.

I derive and apply quantum propagator techniques to atomic and condensed matter systems. I observe many interesting features by following the evolution of a wavepacket. In atomic systems, I revisit the Stern-Gerlach effect and study the spin dynamics inside an inhomogeneous magnetic field. The results I obtained are not exactly the same as the textbook description of the effect which is usually a manifestation of a perfect space and spin entanglement. This discovery can provide insight on more reliable quantum computation device designs. In condensed matter systems, the doping concentration inhomogeneity leads to the Rashba spin-orbit interaction. This makes it possible to control the spin without the external magnetic field. By propagating the wave packet in systems exhibiting Rashba spin-orbit interactions, I discover several features such as spin separation, spin accumulation, persistent spin-helix, and ripple formation.

Solar sails have the potential to benefit many future space exploration missions, but they lack the heritage required for present-day use. To grow confidence in solar sail technology, they could be deployed on LEO satellites higher than 600 km to help de-orbit the satellite within 25 years upon mission termination. To determine how atomic oxygen would affect the solar sail, material from Lightsail-2 was tested in a thermal-energy, isotropic, atomic oxygen vacuum chamber based in the space environments laboratory in California Polytechnic State University. The sail material, aluminized Mylar, was tested for its survivability on both the coated and uncoated side, as well as tested for the optical degradation of the coated side. The uncoated side was found to be completely eroded after a fluence of 2.27 x1020 atoms/cm2, or ~40 days in International Space Station orbit. The coated side experienced no mass loss, but signs of significant undercutting were found with a fluence of 1.19 x1021 atoms/cm2, or ~200 days at station orbit. The stitches present on the coated side, meant to prevent tear propagation, eroded before the sample experienced a fluence of 4.13 x1020 atoms/cm2, or ~70 days at station orbit. The average total reflectivity of the material dropped by ~5% after atomic oxygen exposure, however no correlation with fluence was found. Average specular reflectivity remained unchanged after atomic oxygen exposure. The reflectivity results were impacted by wrinkling in the material, which was found to have a much larger impact than atomic oxygen exposure. These results were paired with an optimal de-orbit trajectory algorithm, developed in this thesis, to determine how atomic oxygen would affect a solar sail deployed to de-orbit an 800 km LEO satellite with a ballistic coefficient of 0.1. Using a simplified 2D orbit case, it was found that the satellite would de-orbit within 12-18 years, depending primarily on the solar activity level. The measured worst-case for optical degradation increased de-orbit time by ~6 months. Additionally, assuming that the sail material was perfectly reflecting decreased de-orbit time by 2-4 years. The amount of fluence required to erode the uncoated Mylar, and the amount required to erode the stitches, were both reached long before the satellite re-entered. It is therefore recommended that the solar sail minimize uncoated side exposure to atomic oxygen, and a more atomic oxygen-resistant stitch material be found. The fluence required to produce significant material undercutting was reached only once the satellite’s orbit had degraded to below 400 km. But the undercutting was observed to structurally compromise the material; thus, future LEO solar sail mission designers must take care when balancing added performance with higher failure risk when considering the tension in the deployed sail.

The following thesis regards the use of small aperture telescopes for space domain awareness efforts. The rapidly populating space domain was motivation for the development of a new operation scheme to conduct space domain awareness feasibility studies using small telescopes. Two 14-inch Schmidt-Cassegrain Telescopes at the California Polytechnic State University and the Air Force Research Lab in Kirtland AFB, NM, in conjunction with a dedicated CCD camera and a commercial DSLR camera, were utilized to conduct optical observations on satellites in Earth orbit. Satellites were imaged during August 2019, and from January 2020 to March 2020, resulting in the collection of 77 valid images of 16 unique satellites. These images were used to obtain celestial spherical coordinates, which were used in Gauss and Double-R angles-only initial orbit determination methods. Initial orbit determination methods successfully produced valid results, reaffirming the feasibility of using small aperture telescopes for such methods. These orbit determinations were used to propagate orbit states forward in time to determine the feasibility of future imaging of the targets with the same apparatus. Propagation results demonstrated that initial orbit determinations rapidly decayed in accuracy over distant times and are most accurate for immediate satellite passes. In addition, an attempt to combine multiple initial orbit determinations using Lambert’s problem solutions was made. Combination of these multiple initial orbit determinations resulted in either no orbit state accuracy improvement compared to individual initial orbit determinations, or a decrease in accuracy compared to these methods. Ultimately, efforts demonstrated that small telescope usage is feasible for orbit determination operations, however there may be a need for hardware and operational revisions to improve the ability of the apparatus.