Ship motions are influenced by the sea state. Conventionally the responses are calculated in the frequency domain. This method, however, is valid only for narrow band spectra. As the seaway becomes more nonlinear, the ship motions cannot be readily predicted using the spectral method. Experiments conducted by Dalzell, have shown that the Response Amplitude Operator (RAO) decreased with increasing sea state or non linearity. Conventionally in the shipbuilding industry, the ship motions are studied by the linear RAOs and the energy density spectrum of the seaway. This method does not take into consideration any non linearities in the system. These are ignored and the ship seaway system is modeled linearly. The following work analyzes ship motions in the conventional linear approach and compares it to time domain simulations using the technique outlined in the work, viz. UNIOM (Universal Nonlinear Input Output Method). Time domain simulation of the SL-7 container ship hull is carried out. A comparison of the most probable peak value of the different modes of motion indicates that the linear theory tends to overpredict.

The extreme motion and load of ships have been assessed using a linear frequency domain method or a linear energy spectral method and RAOs, which may be too approximate to be used for estimation of ship motion in severest seas. The new technology uses simulation in the time domain to deal with the non-linear responses to the random seas. However, the current simulation technique has been successful only up to the sea state of 7 (“high seas”), defined by the significant wave height of 9 meters. The above cannot provide the extreme wave loads and motions for seas higher than the sea state 7. The ultimate goal of this work would be to develop a new technique that can simulate responses to the seas of states 8 and 9. The objective of the present study is to simulate the vertical relative motion and wave topping of a moored ship in the time domain by varying the significant wave heights. The analysis was able to predict with a fair accuracy the relative motion characteristics of a freely floating body in the head and beam sea conditions. The resonance aspects and its significance in the overall response are also analyzed.

Formation flying is a new satellite mission concept that is concerned with clusters of satellites in neighboring orbits cooperating to perform a specific task. The tasks may be Earth observation or space-based interferometry where a cluster of small satellites is able to fulfill the same requirements as that of a larger, monolithic satellite. There exist a variety of models for the study of relative motion between two satellites. These include models based upon differential orbital elements, and relative position and velocity coordinates. Extensive work has been done on such models, both in the absence and presence of the J2 perturbation arising from the aspherical nature of the Earth, which causes variations in the orbital elements that describe the orbit. The approximate relative motion can be obtained analytically by using mean elements. However, the true orbit can only be described by the instantaneous osculating elements. An analytical method to propagate the relative motion between two satellites in highly elliptic orbits is the main focus of this thesis. The method is kinematically exact and it maintains a high degree of accuracy even in the presence of J2 perturbations. Mean orbital elements are used for orbit propagation, and expansions involving the powers of eccentricity are not utilized. The true anomaly of the reference satellite is treated as the independent variable, instead of time. The relative orbit kinematics are obtained by using a projection onto a unit sphere. This procedure allows the relative position variables to be treated as angles depending on the orbital element differences. The effect of adding short-period corrections due to J2 to the mean elements is also studied. Finally, the problem of formation reconfiguration is studied. The reconfiguration of a formation may be achieved by using impulsive thrust (velocity increments) or continuous control. This thesis presents a method to obtain the optimal velocity increments through numerical optimization, utilizing the analytical technique developed for relative orbit propagation. A continuous control law is also developed using a candidate Lyapunov function, and the asymptotic stability of the closed-loop system is ascertained.

The extreme motion and load of ships have been assessed using a linear frequency domain method or a linear energy spectral method and RAOs, which may be too approximate to be used for estimation of ship motion in severest seas. The new technology uses simulation in the time domain to deal with the non-linear responses to the random seas. However, the current simulation technique has been successful only up to the sea state of 7 (“high seas”), defined by the significant wave height of 9 meters. The above cannot provide the extreme wave loads and motions for seas higher than the sea state 7. The ultimate goal of this work would be to develop a new technique that can simulate responses to the seas of states 8 and 9. The objective of the present study is to simulate the vertical relative motion and wave topping of a moored ship in the time domain by varying the significant wave heights. The analysis was able to predict with a fair accuracy the relative motion characteristics of a freely floating body in the head and beam sea conditions. The resonance aspects and its significance in the overall response are also analyzed.

The study of satellite relative motion has been of great historic interest, primarily due to its application to rendezvous, intercept, and docking maneuvers, between spacecraft in orbit about gravitational bodies, such as the Earth. Recent interest in the problem of satellite formation flight has also led to renewed effort in understanding the dynamics of relative motion. Satellite formations have been proposed for various tasks, such as deep-space interferometry, and terrestrial observation, among others. Oftentimes, the rich natural dynamics of the relative motion problem near a gravitational body are exploited to design formations of a specific geometry. Traditional analysis models relative motion under the assumptions of a circular reference orbit, linearized differential gravity field (small relative distance), and without environmental perturbations such as oblateness effects of the attracting body, and atmospheric drag. In this dissertation, the dynamics of the relative motion problem are studied when these assumptions are relaxed collectively. Consequently, the combined effects of nonlinearity, eccentricity, and Earth oblateness effects on relative motion, are studied. To this end, coupling effects between the various environmental perturbations are also accounted for. Five key problems are addressed - the development of a state transition matrix that accounts for eccentricity, nonlinearity, and oblateness effects; oblateness effects on averaged relative motion; eccentricity effects on formation design and planning; new analytical expressions for periodic relative motion that account for nonlinearity and eccentricity effects; and a solution to the optimal rendezvous problem near an eccentric orbit. The most notable feature of this dissertation, is that the solutions to the stated problems are completely analytical, and closed-form in nature. Use has been made of a generalized reversion of vector series, and several integral forms of Kepler’s equations, without any assumptions on the magnitude of the eccentricity of the reference orbit.

Raw material accounts for a large proportion (approximately 75 percent) of a sawmill’s operating costs. However, about 15 percent of raw material ends up as low valued sawdust and planer shavings due to inaccurate cutting. Sizable financial benefits can be realized through maximizing conversion of raw material into valuable solid wood. Advanced process control in a sawmill can help achieve straighter cuts closer to final product dimensions and reduce loss of valuable raw material. A novel and practical method for enhanced process control in a sawmill is presented. A laser arrangement consisting of industrial point and line scanners is used to obtain a surface profile of the entire (two-dimensional) top and bottom surfaces of a lumber board. Each surface profile is independent of the other and free of data contamination caused by relative motions between the measured surface and sensors. Point scanners and line scanners simultaneously record 1-D and 2-D height data, respectively, along the length of the board. One-dimensional height data are used to identify relative motions through a mathematical technique based on linear inverse theory. Subtracting relative motion information from raw line scanner data provides an accurate 2-D surface profile. A second line scanner placed below the board can be used to obtain a separate 2-D profile of the bottom lumber surface. Separate-sided profiling is advantageous because typically a different saw or machine mills each side of a board. Thus, knowing the surface profile of each side of a board is crucial not only in diagnosing a deficiency in the milling process but also in determining the location of this deficiency. Results demonstrate that two-dimensional surface profiling can identify common surface defects such as step, washboard and knot tear-out with an accuracy of 0.3mm. Reproduction of each surface is rapid (approximately 0.2 seconds) and stable.

Raw material accounts for a large proportion (approximately 75 percent) of a sawmill’s operating costs. However, about 15 percent of raw material ends up as low valued sawdust and planer shavings due to inaccurate cutting. Sizable financial benefits can be realized through maximizing conversion of raw material into valuable solid wood. Advanced process control in a sawmill can help achieve straighter cuts closer to final product dimensions and reduce loss of valuable raw material. A novel and practical method for enhanced process control in a sawmill is presented. A laser arrangement consisting of industrial point and line scanners is used to obtain a surface profile of the entire (two-dimensional) top and bottom surfaces of a lumber board. Each surface profile is independent of the other and free of data contamination caused by relative motions between the measured surface and sensors. Point scanners and line scanners simultaneously record 1-D and 2-D height data, respectively, along the length of the board. One-dimensional height data are used to identify relative motions through a mathematical technique based on linear inverse theory. Subtracting relative motion information from raw line scanner data provides an accurate 2-D surface profile. A second line scanner placed below the board can be used to obtain a separate 2-D profile of the bottom lumber surface. Separate-sided profiling is advantageous because typically a different saw or machine mills each side of a board. Thus, knowing the surface profile of each side of a board is crucial not only in diagnosing a deficiency in the milling process but also in determining the location of this deficiency. Results demonstrate that two-dimensional surface profiling can identify common surface defects such as step, washboard and knot tear-out with an accuracy of 0.3mm. Reproduction of each surface is rapid (approximately 0.2 seconds) and stable.

Raw material accounts for a large proportion (approximately 75 percent) of a sawmill’s operating costs. However, about 15 percent of raw material ends up as low valued sawdust and planer shavings due to inaccurate cutting. Sizable financial benefits can be realized through maximizing conversion of raw material into valuable solid wood. Advanced process control in a sawmill can help achieve straighter cuts closer to final product dimensions and reduce loss of valuable raw material. A novel and practical method for enhanced process control in a sawmill is presented. A laser arrangement consisting of industrial point and line scanners is used to obtain a surface profile of the entire (two-dimensional) top and bottom surfaces of a lumber board. Each surface profile is independent of the other and free of data contamination caused by relative motions between the measured surface and sensors. Point scanners and line scanners simultaneously record 1-D and 2-D height data, respectively, along the length of the board. One-dimensional height data are used to identify relative motions through a mathematical technique based on linear inverse theory. Subtracting relative motion information from raw line scanner data provides an accurate 2-D surface profile. A second line scanner placed below the board can be used to obtain a separate 2-D profile of the bottom lumber surface. Separate-sided profiling is advantageous because typically a different saw or machine mills each side of a board. Thus, knowing the surface profile of each side of a board is crucial not only in diagnosing a deficiency in the milling process but also in determining the location of this deficiency. Results demonstrate that two-dimensional surface profiling can identify common surface defects such as step, washboard and knot tear-out with an accuracy of 0.3mm. Reproduction of each surface is rapid (approximately 0.2 seconds) and stable. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

<div>To meet the challenges posed by future space exploration activities, relative satellite motion techniques and capabilities require development to incorporate dynamically complex regimes. ?Specific relative motion applications including orbital rendezvous and spacecraft loitering will play a significant role in NASA's Gateway and Artemis missions which aim to land the ?first woman and next man on the Moon by 2024. In this investigation, relative motion in the restricted 3-body problem is formulated, validated, and tested in a rotating local-vertical-local-horizontal (LVLH)</div><div>frame situated at a target spacecraft and followed by a chaser. Two formulations of the restricted 3-body problem are considered, namely the Circular Restricted 3-Body</div><div>Problem (CR3BP) and the Elliptical Restricted 3-Body Problem (ER3BP). Comparisons between the relative dynamical models in the CR3BP and ER3BP, respectively,</div><div>and other standard relative motion sets of equations such as the Euler-Hill (HCW) model and the Linear Equations of Relative Motion (LERM) are accomplished to identify limitations and inaccuracies pertaining to the in orbits that exist in the CR3BP and ER3BP, respectively. Additionally, the relative motion equations are linearized to develop computational tools for solutions to the rendezvous and space loitering problems in the Earth-Moon system.</div>

The number of dynamics needed to model the motion between a Chief and Deputy satellites has grown greatly since the introduction of the Hill, Clohessy-Wilshire (HCW) equations of motion were introduced. The models have grown to include various things like perturbations, specifically drag, J2, and solar radiation pressure. Dynamics models have also been developed that use True Anomaly as the independent variable instead of time. A lot of work has been put forth to also include cases where the Chief is in an eccentric orbit. While these models have increased the fidelity of relative dynamics these models become very complicated to implement. That is why the HCW equations remain extremely popular after all these developments. However, their simplicity causes issues when there is In-Track separation between the Chief and Deputy satellites. The error in the dynamics increases as this separation increases which leads to a typical constraint that the separation between the Chief and Deputy needs to be much smaller than the radius of the Chief's orbit. That is where this works starts, by examining into ways to increase the accuracy in the HCW equations as the In-Track separation between the Chief and Deputy grows. In which, this will be done by using a curvilinear coordinate system. Furthermore, a technique of using a Virtual Chief satellite will by employed to allow for the HCW equations to be valid for cases where the Chief is in an eccentric orbit. / Master of Science / There are many different models that are used to model the relative motion between two satellites. These models vary from low to high fidelity in the different types of perturbation and ranges that they can model. These higher fidelity models because very complex to implement and while useful the low fidelity models are still popular, specifically the HCW equations. This thesis works on making the HCW equations valid for a larger range of cases.