Currently, there are few analytical tools within the ballistics community to aid in the design and performance evaluation of aerodynamically asymmetric projectiles. The scope of this thesis is to (1) create analytical tools that are capable of quantifying aerodynamically asymmetric projectile performance, (2) demonstrate the ability of these models to accurately account for aerodynamic asymmetries, and (3) gain insight into the flight mechanics of several aerodynamically asymmetric projectiles. First, a six-degree-of-freedom (6 DOF) flight dynamic model, which uses a point-force lifting-surface aerodynamic model, was developed to replicate flight characteristics observed from measured results of common projectiles. A quasi-linear flight dynamic model was then created using the machinery of Projectile Linear Theory (PLT). From this, flight dynamic stability models were developed for linear time-invariant (LTI) and linear time-periodic (LTP) systems. Dynamic simulation and stability trade studies were then conducted on asymmetric variants of 4-finned, 3-finned, 2-finned, and hybrid projectile configurations. First, stability of symmetric projectiles are validated and show that the classical and extended PLT model yielded identical results. Results show that aerodynamic asymmetries can sometimes cause instabilities and other times cause significant increase in dynamic mode damping and increase/decrease in mode frequency. Partially asymmetric (single plane) configurations were shown to cause epicyclic instabilities as the asymmetries became severe, while fully asymmetric (two plane) can grow unstable in either the epicyclic modes or the roll/yaw mode. Another significant result showed that the LTP stability model is able to capture aerodynamic lifting-surface periodic affects to evaluate dynamic stability requirements for asymmetric projectiles.

In this thesis, We study the driven Morse system in a strong time-periodic field. We are interested in the quasi-bound states, which live in the driven system with limit life-times, with an increasing field strength in a low frequency region. We found those states by using Floquet theory, and the exterior complex scaling method (ECCS), which widely use in the resonance system. Choosing the Morse potential with supports 3 bound states, we found that as we increase the time-periodic external field, the number of the quasi-bound states decrease to 2. The distributions of the quasi-bound states which represented by the Husimi distribution were also studied, and compared with the Poincaré surface of section plots of the system. / text

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On utilise la théorie de Floquet-Lin pour des systèmes différentiels linéaires quasi- périodiques pour établir des résultats d'existence et d'unicité et de dépendance continue des systèmes différentiels non linéaires quasi-périodiques. Et dans un second temps on établit un résultat de réductibilité d'un système différentiel linéaire presque-périodique en un système différentiel linéaire triangulaire supérieur avec conservation du nombre des solutions presque-périodiques indépendantes. Ensuite, un résultat d’existence et d’unicité et de dépendance continue des systèmes différentiels non linéaires presque-périodiques par rapport au terme du contrôle. / We use a Floquet theory for quasi-periodic linear ordinary differential equations due to Zhensheng Lin to obtain results, of existence, unicity, continuous and differentiable dependence, on the quasi-periodic solutions of quasi-periodic nonlinear ordinary differential equations. in a second time we establish the reducibility of linear systems of almost periodic differential equations into upper triangular systems of a. p. differential equations. This is done while the number of independent a. p. solutions is conserved. We prove existence and uniqueness of a. p. solutions of a nonlinear system with an a. p. linear part. Also we prove the continuous dependence of a. p. solutions of a nonlinear system with respect to an a. p. control term.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第22988号 / 理博第4665号 / 新制||理||1669(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 柳瀬 陽一, 教授 田中 耕一郎, 教授 石田 憲二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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Tethered satellite systems (TSS) can be utilized for a wide range of space-based applications, such as satellite formation control and propellantless orbital maneuvering by means of momentum transfer and electrodynamic thrusting. A TSS is a complicated physical system operating in a continuously varying physical environment, so most research on TSS dynamics and control makes use of simplified system models to make predictions about the behavior of the system. In spite of this fact, little effort is ever made to validate the predictions made by these simplified models. In an ideal situation, experimental data would be used to validate the predictions made by simplified TSS models. Unfortunately, adequate experimental data on TSS dynamics and control is not readily available at this time, so some other means of validation must be employed. In this work, we present a validation procedure based on the creation of a top-level computational model, the predictions of which are used in place of experimental data. The validity of all predictions made by lower-level computational models is assessed by comparing them to predictions made by the top-level computational model. In addition to the proposed validation procedure, a top-level TSS computational model is developed and rigorously verified. A lower-level TSS model is used to study the dynamics of the tether in a spinning TSS. Floquet theory is used to show that the lower-level model predicts that the pendular motion and transverse elastic vibrations of the tether are unstable for certain in-plane spin rates and system mass properties. Approximate solutions for the out-of-plane pendular motion are also derived for the case of high in-plane spin rates. The lower-level system model is also used to derive control laws for the pendular motion of the tether. Several different nonlinear control design techniques are used to derive the control laws, including methods that can account for the effects of dynamics not accounted for by the lower-level model. All of the results obtained using the lower-level system model are compared to predictions made by the top-level computational model to assess their validity and applicability to an actual TSS. / Ph. D.

Recent advances in experimental condensed matter physics suggest a powerful new paradigm for the realization of exotic phases of quantum matter in the laboratory. Rather than conducting an exhaustive search for materials that realize these phases at low temperatures, it may be possible to design quantum systems that exhibit the desired properties. With the numerous advances made recently in the fields of cold atomic gases, superconducting qubits, trapped ions, and nitrogen-vacancy centers in diamond, it appears that we will soon have a host of platforms that can be used to put exotic theoretical predictions to the test. In this dissertation, I will highlight two ways in which theorists can interact productively with this fast-emerging field. First, there is a growing interest in driving quantum systems out of equilibrium in order to induce novel topological phases where they would otherwise never appear. In particular, systems driven by time-periodic perturbations—known as “Floquet systems”—offer fertile ground for theoretical investigation. This approach to designer quantum matter brings its own unique set of challenges. In particular, Floquet systems explicitly violate conservation of energy, providing no notion of a ground state. In the first part of my dissertation, I will present research that addresses this problem in two ways. First, I will present studies of open Floquet systems, where coupling to an external reservoir drives the system into a steady state at long times. Second, I will discuss examples of isolated quantum systems that exhibit signatures of topological properties in their finite-time dynamics. The second part of this dissertation presents another way in which theorists can benefit from the designer approach to quantum matter; in particular, one can design analytically tractable theories of exotic phases. I will present an exemplar of this philosophy in the form of coupled-wire constructions. In this approach, one builds a topological state of matter from the ground up by coupling together an array of one-dimensional quantum wires with local interactions. I will demonstrate the power of this technique by showing how to build both Abelian and non-Abelian topological phases in three dimensions by coupling together an array of quantum wires.

Mobile communication has become an essential part of our daily life. We love the flexibility of wireless cell phones and even accept their lower quality of service when compared to wired links. Similarly, we are looking forward to the day that we can continue watching our favorite TV programs while travelling anywhere and everywhere. Mobility, flexibility, and portability are the themes of the next generation communication. Motivated and fascinated by such technology breakthroughs, this effort is geared towards enhancing the quality of wireless services and bringing mobile satellite reception one step closer to the market. Meanwhile, phased array antennas are vital components for RADAR applications where the antenna is required to have certain scan capabilities. One of the main concerns in that perspective is how to avoid the potential of scan blindness in the required scan range. Targeting to achieve wide-band wide-scan angle phased arrays free from any scan blindness our efforts is also geared. Conventionally, the key to lower the profile of the antenna is to use planar structures. In that perspective microstrip patch antennas have drawn the attention of antenna engineers since the 1970s due to their attractive features of being low profile, compact size, light weight, and amenable to low-cost PCB fabrication processes. However, patch elements are basically resonating at a single frequency, typically have <2% bandwidth, which is a major deficit that impedes their usage in relatively wide-band applications. There are various approaches to enhance the patch antennas bandwidth including suspended substrates, multi-stack patches, and metalized cavities backing these patches. Metalized cavity-backed patch structures have been demonstrated to give the best performance, however, they are very expensive to manufacture. In this dissertation, we develop an alternative low-cost bandwidth enhancement topology. The proposed topology is based on substrate-integrated waveguides. The great potential of the proposed structure lies in being amenable to the conventional PCB fabrication. Moreover, substrate-integrated cavity-backed structures facilitate the design of sophisticated arrays that are very expensive to develop using the conventional metalized cavity-backed topology, which includes the common broadside arrays used in fixed-beam applications and the scanned phased arrays used in RADAR applications.

abstract: In this work, we focused on the stability and reducibility of quasi-periodic systems. We examined the quasi-periodic linear Mathieu equation of the form x &#776;+(ä+&#1013;[cost+cosùt])x=0 The stability of solutions of Mathieu's equation as a function of parameter values (ä,&#1013;) had been analyzed in this work. We used the Floquet type theory to generate stability diagrams which were used to determine the bounded regions of stability in the ä-ù plane for fixed &#1013;. In the case of reducibility, we first applied the Lyapunov- Floquet (LF) transformation and modal transformation, which converted the linear part of the system into the Jordan form. Very importantly, quasi-periodic near-identity transformation was applied to reduce the system equations to a constant coefficient system by solving homological equations via harmonic balance. In this process we obtained the reducibility/resonance conditions that needed to be satisfied to convert a quasi-periodic system to a constant one. / Dissertation/Thesis / M.S.Tech Engineering 2012