Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (p. 285-289).

Thesis (doctoral)--Techn. Hochschule, Stuttgart, 1924. / Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 199-204).

Thesis (Ph.D.)--University of Delaware, 2005. / Principal faculty advisor: Dennis R. Mertz, Dept. of Civil & Environmental Engineering. Includes bibliographical references.

Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO. / Includes bibliographical references. / by Olivier Andre Bauchau. / Sc.D.

This thesis has been motivated by the idea of harvesting the energy from ambient vibrations via nonlinear dynamics of the parametric pendulum. It aims to cover those aspects of the pendulum dynamics, which are relevant for energy extraction purposes and have not been addressed in previous studies. A simple system like parametric pendulum can experience variety of responses. One of them is rotary motion, which is characterised by significantly higher kinetic energy than oscillations and thus has a potential of delivering more energy, when subjected to the parametric excitation. Initially, a preliminary study on the dynamics of parametric pendulum has been conducted. This involved comparison of oscillatory and rotary responses with a view to application in energy harvesting, numerical continuation of rotary solutions and developing a control method for initiating and maintaining the desired response. As a next step, different forcing configurations have been considered, including pendulum excited along a tilted axis and a combined excitation, where pendulum additionally performs rocking action. The influence of the forcing arrangement on the lower limit of stability of rotary motion has been examined. The vibrations which can be observed in the environment are rarely perfectly harmonic. To provide more realistic results, the response of the pendulum under noisy excitation has been studied. Different types of noise have been considered and their influence on the pendulum rotation examined. One of the major energy sources, which could be utilised are the oscillating ocean surfaces. Therefore, a stochastic model of the sea wave has been constructed and the response of the pendulum system studied under parametric excitation by a wave profile. Finally, taking into account the imbalanced forces which rotating pendulum exerts on the supporting base, the model has been extended to a system of two pendulums. Synchronization in such a system was studied. The influence of the synchronization mode on the rotation of the pendulums and on the stability of supporting structure was considered. All of the numerical results presented in this thesis have been verified experimentally to ensure good correspondence.

Dissertation (Ph. D.)--University of Akron, Dept. of Electrical and Computer Engineering, 2008. / "December, 2008." Title from electronic dissertation title page (viewed 12/29/2008) Advisor, Nathan Ida; Committee members, Robert J. Veillette, George C. Giakos, Jiang John Zhe, Gerald W. Young; Department Chair, Jose Alexis De Abreu-Garcia; Dean of the College, George K. Haritos; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.

Measurement of dynamic/transient torques is important in the dynamic analysis of rotating machinery as it provides insight into the internal state of the machine. Existing methods are difficult to implement, results are not obtained in real-time and are not very accurate. This thesis introduces a new method of determining real-time dynamic torque. An optical encoder is used to sense motion at a convenient point in the rotating system containing the rigid shaft of interest. The encoder's output is processed digitally to yield angular velocity, acceleration and dynamic torque. Two different experiments were conducted to demonstrate the advantages of this new method of determining dynamic torque over conventional methods. In one experiment, an extension spring was mounted on a crank arrangement coupled to a fractional horsepower motor to apply a periodic load to the system. A mathematical model of this dynamic system was developed to compare the results of this model with that of the instrumentation system. In another experiment, the instrumentation system was used on an existing motor-compressor system. The dynamic torque thus determined was again compared with the results of a simulation program. In both the above experiments the evaluated dynamic torque and computed dynamic torque were within 5% of each other, demonstrating accuracy and reliability of this personal computer based dynamic torque determining system. / Master of Science

Optimal rigid-body angular maneuvers are investigated, using restricted control moments—a problem inspired in the context of rotational maneuvers for <i>super-maneuverable</i> aircraft. Most of the analysis is based on the formulation with no direct control over the roll component of angular velocity. The present research effort is conducted in two phases. In the first phase, optimal control of angular <i>rates</i> is closely examined. The second phase deals with the problem of optimal <i>attitude</i> control. Optimal rigid-body angular <i>rate</i> control is first examined via an <i>approximate</i> dynamic model. The proposed model admits analytical solutions of the optimality conditions. The analysis reveals that over a large range of boundary conditions, there are, in general, <i>several</i> distinct extremal solutions. Second-order necessary conditions are investigated to establish local optimality of candidate minimizers. Global optimality of the extremal solutions is discussed. Next, the optimal angular <i>rate</i> problem is studied using the <i>exact</i> dynamic model. Numerical solutions of optimality conditions are obtained which corroborate and extend the findings of the <i>approximate</i> problem. The qualitative feature of <i>multiple extremal solutions</i> is retained. Several of these extremal solutions did not satisfy the Jacobi necessary condition. The choice of <i>minimizing</i> solution could be narrowed down to two sub-families of extremal solutions. A locus of Darboux Points is obtained which demarcates the domain over which these two sub-families are globally minimal. The above studies look at <i>minimum control effort</i> families of extremal solutions. As a next step, we examine the <i>minimum time</i> control of angular rates, with prescribed hard bounds on available control. Existence of singular subarcs in time-optimal trajectories is explored. Qualitative features exhibited by the <i>exact</i> problem are preserved. In addition, the control space is deformed to allow roll control and its effect on extremal solutions is investigated. In the next phase, we introduce the <i>kinematics</i> into the optimal control problem. Minimum time <i>attitude</i> control of a rigid-body is investigated with prescribed hard bounds on available control. The attitude of the rigid-body is defined using Euler parameters. Existence of singular subarcs in time-optimal trajectories is explored. A numerical survey of first-order necessary conditions reveals that there are <i>several</i> distinct extremal solutions. The character of extremal solutions depend whether <i>pitch</i> or <i>yaw</i> motion assumes the dominating role in controlling <i>roll</i> motion. Moreover, certain <i>spatial symmetries</i> are identified. Maneuvers such as a <i>Roll Around the Velocity Vector</i> and <i>Fuselage Pointing</i> are analyzed. / Ph. D.

The primary study of this thesis is the experimental realization of the non-equilibrium dynamics of a quantum inverted pendulum as examined in the collective spin dynamics of a spin-1 Bose-Einstein condensate. In order to compare experimental results with the simulation past the low depletion limit, current simulation techniques needed to be extended to model atomic loss. These extensions show that traditional measurements of the system evolution (e.g. measuring the mean and standard deviation of the evolving quantity) were insufficient in capturing the quantum nature of the evolution. It became necessary to look at higher order moments and cumulants of the distributions in order to capture the quantum fluctuations. Extending the implications of the loss model further, it is possible that the system evolves in a way previously unpredicted. Spin-mixing from a hyperbolic fixed point in the phase space and low noise atom counting form the core of the experiment to measure the evolution of the distributions of the spin populations. The evolution of the system is also compared to its classical analogue, the momentum-shortened inverted pendulum. The other experimental study in this thesis is mapping the mean-field phase space. The mean-field phase space consists of different energy contours that are divided into both phase-winding trajectories and closed orbits. These two regions are divided by a separatrix whose orbit has infinite period. Coherent states can be created fairly accurately within the phase space and allowed to evolve freely. The nature of their subsequent evolution provides the shape of the phase space orbit at that initial condition. From this analysis a prediction of the nature of the entire phase space is possible.