The goals of this thesis are to modify a full-scale personal hovercraft to perform autonomous maneuvers on flat ground, develop a first principles of the craft, and present data on the vehicle behavior in field trials. The hovercraft, initially designed for manual control by a rider, was modified both physically and with software to allow for remote and autonomous operation. The design leverages the actuator control solutions that are already implemented on the hovercraft for ease of installation and control. A key modification made in the design is the addition of auxiliary fans to increase overall thrust. Controller designs are presented to manage the rotation rate of the added fans. The purpose of the dynamic model is to assist in the design and evaluation of model-based controllers for the vehicle speed and heading. A first principles model was developed to give an approximate understanding of the vehicle's behavior. Data collected during field trials was used to challenge the assumptions made in the first principles model. Based on the field data, the model was updated to provide a better basis to evaluate model based controllers. Additionally, several key observations about the hovercraft performance were noted during the field trials. Controlling the vehicle heading is a nontrivial task and will require a responsive and authoritative controller / Master of Science / Hovercraft are useful vehicles because they can travel over many terrains, including water and land, without being impacted severely by friction. However, they also have several drawbacks including being difficult to steer and having insufficient thrust to scale a steep incline. To address these concerns, we present a design for a modified hovercraft that is capable of being steered with a remote control or with autonomy software. Additionally, eight fans were added to increase the overall thrust of the vehicle to allow it to drive uphill. A model of the hovercraft dynamics was made to allow us to study its behavior. Field trials were conducted to collect data on the hovercraft's performance from the onboard sensors. This data was used to improve the dynamic model so that it can be used in the future to decide the best control design for the hovercraft steering.

An analytical study of the dynamics of manned rotating space stations under various steady-state and transient excitation, such as docking impacts, attitude system torques, and crew motions, has been conducted. The basic equations of motion for the spinning station are developed and expressions simulating the applied disturbances are introduced. Two stability systems, a gyroscopic wobble damper and a proportional jet damper are represented mathematically, and the motion of the station under the external disturbances has been determined with and without the effects of these stability systems. Computer results for a toroidal example station are presented, and the effects of a variation in the moment of inertia distribution are discussed. A description of an experimental facility capable of simulating the excitation considered in the theoretical analysis and of determining and recording the resultant station lotion is also included. / M.S.

Nondestructive methods of detecting cracks in structural components and machinery are important, both in preventing failures and in establishing maintenance procedures. This thesis considers how the vibration behavior of cracked members can be modelled mathematically and how these mathematical models may lead to advancements in crack detection procedures. Two separate cases are considered: the longitudinal vibration of a cracked bar and the coupled vibrations of a cracked rotating shaft. In the longitudinal vibration study, the equation of motion is developed for a cantilevered bar with a symmetric surface crack. Next, Galerkin's Method is used to obtain one- and two-term approximate solutions. Both forced and free vibrations of the bar are analyzed. Graphical results showing the relationships between displacement and crack size, crack position, and forcing frequency are presented and discussed. Spectral analysis is used to compare uncracked and cracked bar behavior. Finally, a sensitivity analysis of the forced vibration case is conducted to observe how the forcing frequency affects the rate of change of steady-state response at the onset of cracking. In the second part of the thesis, a similar analysis is conducted for a cracked, simply-supported Timoshenko shaft rotating at a constant angular speed. The equations of motion derived by Wauer (b) are used as the basis of the study. Again, Galerkin's Method is applied to obtain approximate solutions. Time histories and spectra are used to observe how changes in various parameters influence the vibration behavior. The effects of mass eccentricity and gravity are studied. Finally, the effect of a periodic axial impact load is considered. / Master of Science

Tall fescue (Festuca arundinacea Schreb.) and alfalfa (Medicago sativa L.) have many desirable forage attributes, are grown extensively throughout the USA, and combined form a productive pasture mixture. The objective of this research was to develop recommended management practices for alfalfa-tall fescue mixtures and compare livestock performance, forage quality, and productivity of this mixture to N-fertilized endophyte-free tall fescue. Forty-eight Angus or Angus crossbred steers were rotationally stocked on a four-replicate alfalfa-tall fescue and N-fertilized tall fescue pasture system during 2002 and 2003. Livestock gain, forage quality, and forage production were monitored throughout the seasons. Management treatments conducted within wire exclosures included defoliation height, rest period, exclosure movement, and month and were evaluated using detailed botanical composition and persistence measurements. Defoliation height, rest period, and month all affected alfalfa-tall fescue competition. Alfalfa was generally more competitive with longer rest periods and shorter heights, although results were not consistent. Alfalfa composition and persistence declined dramatically over the 2003 season due to climate, grazing management, and cultivar. Cool, high moisture conditions stimulated tall fescue growth and reduced alfalfa vigor and survival. Livestock gains were higher for pure tall fescue at one date in 2002, but higher overall for alfalfa-tall fescue during 2003. Forage quality (CP, NDF and ADF) was consistently higher for alfalfa-tall fescue during both seasons. In conclusion, both alfalfa-tall fescue and N-fertilized endophyte-free tall fescue produce productive pastures and high ADG in beef steers in Virginia, but continued management research is required to maintain the alfalfa component of this mixture. / Master of Science

Agricultural conservation practices can have a vast number of environmental benefits but adoption of these practices may not be widespread. If farm operators are able to reap financial returns for environmental services, adoption of these conservation practices could increase. One source of potential financial returns is in greenhouse gas (GHG) emission reductions or increased GHG sequestration. An example of a conservation management strategy for beef and dairy operations which has the potential to decrease GHG emissions or increase GHG sequestration is an intensively managed rotational grazing system. The objective of this study is to estimate potential financial returns from conversion to rotational grazing and the sale of GHG credits by Virginia beef and dairy farms. The three GHGs examined in the study are carbon dioxide, nitrous oxide, and methane. Primary and secondary data are used to simulate financial performance and GHG emissions for three case study farms under different levels of production and pasture utilization. Each case study farm is simulated under three reference conditions to calculate financial performance and three baseline scenarios and a regional performance standard to calculate GHG emissions on both a per farm and a per metric ton of product sold metric. The change in emissions between the scenarios is found and potential returns from the sale of GHG emissions credits are calculated. Results of the analysis demonstrate that conversion to rotational grazing has the potential to increase overall revenues for the farm operation from $4,197.72 to $50,007.46. GHG emission changes for the farm operation do not show a clear trend towards reduction. The amount of financial return from the sale of GHG reduction credits varies from $37.15 to $76.26 for the three case study farms for the initial calculations, and varies from $24.10 to $755.36 once the study performs sensitivity analysis for methane emissions. Therefore, results indicate that rotational grazing can increase net revenues for farm operations but additional net revenue from the sale of GHG reduction credits is small and dependent on the chosen baseline scenario and metric. Follow up research should address the following areas: changes in the cost of on-farm labor, risk of conversion to rotational grazing, increased accuracy of the measurement of GHG emissions and soil carbon, the effects of rotational grazing on forage TDN, and the water quality impacts of rotational grazing. / Master of Science

A theoretical technique to extract drilling-angular velocities from a nodal-spatial array of in-plane translational velocities is developed. The technique utilizes numerical methods for simulation of solutions. A finite element method using I-DEAS 4.1 is used for calculation of in-plane translational velocities and a MATLAB code is written for extraction of the drilling-angular velocities. The case of data with noise content is also considered. All numerical results are compared to a closed-form theoretical solution which is used as a reference for accuracy. Recommendations are made for future testing and experimental applications of this technique. / Master of Science

Optimal control theory analysis is applied to a rotating cylinder partially filled with an inviscid, incompressible fluid. Two models of the system are investigated: (1) a two discrete mass system with fluid inside one mass and the control force applied to the other, and (2) a continuously distributed cylindrical mass system with control force applied to a discrete lower suspension mass. For (2) the method of assumed modes is used to discretize the system and obtain a set of n linear algebraic equations. In both cases the treatment is two dimensional and axial motion of the fluid is considered negligible. In both models, the uncontrolled system, shown by earlier researchers to be inherently unstable, is found to be controllable. The appropriate optimal feedback control is derived and system responses investigated. In addition, both models are shown to be observable. Direct measurement of only a portion of the components of the state vector are sufficient, using a Luenberger Observer, to estimate the entire state vector. / Ph. D.

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.

Fit is often pointed to as the most important factor to consider when selecting a helmet. However, there is no published biomechanical evidence suggesting that of helmet fit effects concussion risk. The objectives of this study were to quantify helmet fit on a headform and to determine the effect fit has on helmet performance. An impact pendulum was used to strike a helmeted NOCSAE headform mounted on a Hybrid III neck. Helmets were impacted at 4 locations at 3 energies representing a range of concussive to sub-concussive impacts. The fit conditions evaluated in this study represent fitting scenarios in which an athlete is provided a helmet that is properly or improperly sized and cases in which a properly sized helmet is too loose, too tight, or properly adjusted. A custom pressure sensor was developed and used to characterize helmet fit in each condition with a quantitative fit metric representative of a variation from zero pressure on the headform. All helmets produced significant differences in both peak linear and peak angular acceleration due to fit. Differences were generally small with some exceptions. Furthermore, air bladder inflation generated significant differences in both peak linear and peak angular acceleration, but these were generally small in magnitude. While fit associated with size and air bladder inflation significantly affected linear and rotational head acceleration for most impact conditions, the best fit condition did not always generate the lowest accelerations. Differences can be attributed to varying helmet characteristics between and within helmet models. / Master of Science / Fit is often pointed to as the most important factor to consider when selecting a helmet. However, there is no published biomechanical evidence suggesting that of helmet fit effects concussion risk. The objectives of this study were to quantify helmet fit on a headform and to determine the effect fit has on helmet performance. An impact pendulum was used to strike a helmeted biofidelic headneck assembly in a multitude of impact velocities and locations in order to simulate a range of onfield head impacts in a laboratory setting. The fit conditions evaluated in this study represent fitting scenarios in which an athlete is provided a helmet that is properly or improperly sized and cases in which a properly sized helmet is too loose, too tight, or properly adjusted. A custom pressure sensor was developed and used to characterize helmet fit in each condition with a quantitative fit metric representative of a variation from zero pressure on the headform. Linear and rotational acceleration were evaluated to characterize concussion risk as they have been found to be the best correlate for concussion risk in previous work. In this study, the effects of helmet fit and helmet air bladder inflation on peak linear and rotational head acceleration were evaluated. In general, the effects of both fit and air bladder inflation were small, but there were cases of substantial differences. However, the best fit condition did not always result in the lowest head acceleration. Differences can be attributed to varying helmet characteristics between and within helmet models. This data can be used to progress helmet safety through improving helmet performance evaluation, which will increase consumer awareness.

Locked-in planar rotational motion for satellites moving in a gravity gradient field is examined using both analytical and numerical techniques. It is shown that rotational locks at spin rates of n/2 (where n is an integer) satellite rotations per orbit revolution exist for specific combinations of satellite inertia properties and orbital eccentricity. For nearly axial symmetric satellites, the maximum and minimum instantaneous rates which permit the satellite to remain in a particular rotational lock are found analytically by applying the averaging techniques of Kryloff and Bogolinboff and that of Symon. For these cases, it is found that the strength of the higher rotational locks (n > 3) are greater than the strength of the n = 2 or 1/1 rotational lock for proper combinations of lock number, n, and orbital eccentricity. Comparison of the results for the case of the planet Mercury are shown to be in good agreement with both observations of the planet and the 2 numerical calculations of Liu. Numerical results were obtained for representative values throughout the range of satellite inertia properties. Periodic solutions of periods 2π and 4 π are found and their variational stability investigated by Floquet analysis. The results which are presented on stability charts show that for satellites that deviate appreciably from axial symmetry, the stable periodic solutions occur at eccentricities which tend to increase as the absolute value of the lock number |n| increases. Estimates of the strength of these rotational locks are found by applying the phase space technique of Brereton and Modi. For nearly axially symmetric satellites, the results of this technique agreed favorably with the analytical results. Rotational locks for satellites that are not nearly axial symmetric were found in general to be considerably weaker than the more frequently investigated 1/1 lock. / Ph. D.