Singular subarcs arise in quite a few problems of flight dynamics. The present study is devoted to the specific problem of ascent and acceleration of a vehicle in atmospheric flight in which a variable-thrust arc forms a part of the optimal trajectory. A two-parameter family of singular arcs was generated for time-range-fuel problems of an ascending rocket, using the modelling of Zlatskiy and Kiforenko. The short-term optimality of the singular subarcs has been checked in terms of certain necessary conditions: the classical Clebsch condition, the Kelley condition or the Generalized Legendre-Clebsch condition and the Goh condition. All these are found to be satisfied computationally for all the candidates. The calculations were repeated for simplified thrust-along-the-path modelling and similar results on optimality obtained. / Master of Science

In aircraft research, there is keen interest in the procedure of determining the set of controls required to perform a maneuver from a definition of the trajectory. This is called the inverse problem. It has been proposed that if a complete set of states and state time derivatives can be derived from a trajectory then a model-following solution can allocate the controls necessary for the maneuver. This paper explores the problem of finding the complete state definition and provides a solution that requires numerical differentiation, fixed point iteration and a Newton's method solution to nonlinear equations. It considers trajectories that are smooth, piecewise smooth, and noise ridden. The resulting formulation was coded into a FORTRAN program. When tested against simple smooth maneuvers, the program output was very successful but demonstrated the limitations imposed by the assumptions and approximations in the development. / Master of Science

This thesis presents two studies related to head injury. The study presented in Chapter 1 reviewed findings of cranial movement in animal and human specimens and evaluate the validity of cranial movement due to manual manipulation in humans through engineering analysis. The study had two parts. In Part I, the literature was reviewed to determine the cranial motion in animals and humans. Engineering analysis was done in Part II to determine the amount of force necessary to cause cranial motion in the studies from Part I using skull stiffness values from published studies. Chapter 2 explored data collection methodologies used in frontal sled tests. Several data collection methodologies exist for collecting kinematic data, such as Vicon motion analysis, video analysis, and sensors. Head trajectories from motion data and accelerometer data were plotted up to maximum forward excursion of the head for eight frontal sled tests, four conducted at Virginia Tech and four at the University of Virginia. In addition, the percent difference between maximum forward excursion values from sensor and motion data were calculated. Finally, Chapter 3 discusses the literary contributions of each study and to which journals they will be submitted. / Master of Science

The capability to perform rendezvous and proximity operations about space objects is central to the next generation of space situational awareness. The ability to diagnose and respond to spacecraft anomalies is often hampered by the lack of capability to perform inspection or testing on the target vehicle in flight. While some limited ability to perform inspection can be provided by an extensible boom, such as the robotic arms deployed on the space shuttle and space station, a free-flying companion vehicle provides maximum flexibility of movement about the target. Safe and efficient utilization of a companion vehicle requires trajectories capable of minimizing spacecraft resources, e.g., time or fuel, while adhering to complex path and state constraints. This paper develops an efficient solution method capable of handling complex constraints based on a grid search A* algorithm and compares solution results against a state-of-the-art nonlinear optimization method. Trajectories are investigated that include nonlinear constraints, such as complex keep-out-regions and thruster plume impingement, that may be required for inspection of a specific target area in a complex environment. This work is widely applicable and can be expanded to apply to a variety of satellite relative motion trajectory planning problems. / The capability to perform rendezvous and proximity operations about space objects is central to the next generation of space situational awareness. The ability to diagnose and respond to spacecraft anomalies is often hampered by the lack of capability to perform inspection or testing on the target vehicle in flight. While some limited ability to perform inspection can be provided by an extensible boom, such as the robotic arms deployed on the space shuttle and space station, a free-flying companion vehicle provides maximum flexibility of movement about the target. Safe and efficient utilization of a companion vehicle requires trajectories capable of minimizing spacecraft resources, e.g., time or fuel, while adhering to complex path and state constraints. This paper develops an efficient solution method capable of handling complex constraints based on a grid search A* algorithm and compares solution results against a state-of-the-art nonlinear optimization method. Trajectories are investigated that include complex nonlinear constraints, such as complex keep-out-regions and thruster plume impingement, that may be required for inspection of a specific target area in a complex environment. This work is widely applicable and can be expanded to apply to a variety of satellite relative motion trajectory planning problems. / Master of Science / The ability of one satellite to perform actions near a second space satellite or other space object is important for understanding the space environment and accomplishing space mission goals. The development of a method to plan the path that one satellite takes near a second satellite such that fuel usage is minimized and other constraints satisfied is important for accomplishing mission goals. This thesis focuses on developing a fast solution method capable of handling complex constraints that can be applied to plan paths satellite relative motion operations. The solution method developed in this thesis is then compared to an existing solution method to determine the efficiency and accuracy of the method.

A method is developed for computing the minimum fuel trajectory for a satellite that moves between two different positions and orientations using a sequence of impulsive burns. The method makes use of the linear Clohessy-Wiltshire equations to describe translational motions, Euler's equations of rigid body motion for describing the attitude motions, and a sequential quadratic programming optimization code. Initial solutions are found assuming no coupling between the translational and rotational motions and with no imposed constraint on the time of the rendezvous. Further solutions are then found by varying the vehicle center of gravity location along one axis, thereby coupling the rotational motions into two axes of translation thrusters, and by imposing time limits on the rendezvous. A discussion of the impact that these parameters have on the optimal solutions for two different models of the satellite thruster systems is then presented. / Master of Science

Consider the problem of developing an algorithm that computes optimal preprogrammed evasive maneuvers for a Maneuvering Reentry Vehicle (MaRV) attacking a target defended with Anti-Ballistic Missiles (ABMs). The problem is large in terms of the number of optimization parameters, and perhaps in terms of the number of nonlinear constraints. Since both MaRV and ABM trajectories are expensive to compute, rapid convergence of the optimization algorithm is of prime concern. This paper examines a discontinuity in the cost function that degrades both the speed and the reliability of optimizer convergence. A solution is offered, proposing that the optimization algorithm be operated in a new parameter space, in which the discontinuity occurs at infinity. Effectively, the mapping prevents the optimization algorithm from crossing the discontinuity thereby improving optimizer convergence. Results comparing convergence with and without the parameter mapping demonstrate the effectiveness of the procedure. / Master of Science

In the complex landscape of healthcare, patients navigate through various institutions from hospitals to long-term care facilities, and each step of their journey plays a crucial role in their disease progression and treatment plan. Traditional analyses often focus on individual transitions, offering limited insight into the broader picture of patient care and disease progression. This thesis aims to explore the entire sequence of patient transitions within the Canadian healthcare system to uncover meaningful patterns and commonalities. This research employs an innovative approach to leveraging the Canadian Institute for Health Information (CIHI) dataset, consisting of around 250,000 patient records after data cleaning and including approximately 10-11 variables. Extracting a diverse category of features, such as temporal, semantic, and clinical information, constructs a detailed profile for each patient journey. These profiles then undergo an parallel mini-batch average agglomerative hierarchical clustering process, grouping together patients with similar healthcare trajectories to identify prevailing pathways and transitions within the system. By understanding these patterns, healthcare providers and policymakers can gain insights into the patient experience, potentially revealing areas for improvement, optimization, and personalization of care. Key findings include uncovering transitions in the healthcare environment, identifying the most common pathways, and studying the alternate level of care length of stay for each scenario. Looking ahead, the research anticipates incorporating additional layers of data, such as specific interventions and medications, to enrich the analysis. This expansion aims to offer a more comprehensive view of patient journeys, further enhancing the ability to tailor healthcare services to meet individual needs effectively. / Thesis / Master of Computer Science (MCS)

We present a new trajectory generation algorithm for autonomous guidance and control of unmanned vehicles from a given starting point to a given target location. We build and update incomplete a priori maps of the operating environment in real time using onboard sensors and compute level sets on the map reflecting the minimal cost of traversal from the current vehicle location to the goal. We convert the trajectory generation problem into a finite-time-horizon optimal control problem using the computed level sets as terminal costs in a receding horizon framework and transform it into a simpler nonlinear programming problem by discretization of the candidate control and state histories. We ensure feasibility of the generated trajectories by constraining the solution of the optimization problem using a simplified vehicle model. We provide strong performance guarantees by checking for stability of the algorithm through the test of matching conditions at the end of each iteration. The algorithm thus explicitly incorporates the vehicle dynamics and constraints and generates trajectories realizable by the vehicle in the field. Successful preliminary field demonstrations and complete simulation results for a marine unmanned surface vehicle demonstrate the efficacy of the proposed approach for fast operations in poorly characterized riverine environments. / Master of Science

Yes / A significant proportion of healthcare that is delivered is wasteful, harmful and not evidence based. There are many wound care related guidelines, but their implementation in practice is variable. The Society of Tissue Viability (SoTV) published updated seating guidelines in 2017, but there is a lack of theoretical and conceptual clarity about how these guidelines are being utilised to inform clinical practice. Therefore, the aim of this paper is to generate a theory that can be used to incorporate the SoTV seating guidelines into policy and clinical practice. Methods: We critically reflected on data from an evaluation study utilising systems-thinking approach, informed by implementation and safety science using wider literature as well as our expertise to generate a guideline implementation theory. Discussion: Factors that facilitate or hinder the incorporation of the SoTV guidelines into policy and practice were characterised. We conceptualised the implementation of these guidelines into policy and practice into a Translation or Implementation into Policy or Practice (TIPP) theory with distinct stages, that we called liminal spaces. Knowledge of the guidelines, and the agency or authority to effect change, are key factors in the translation of these guidelines into clinical practice. Conclusion: Our theory is that there are liminal spaces in the implementation trajectory of these guidelines into practice, which have their own characteristics. This theory provides a framework that can be used to underpin guidelines strategies to embed skin and wound care guidelines into policy and clinical practice in order to improve patient care.

Public transportation ticketing has evolved from traditional paper tickets to advanced digital systems. This study combines GPS data from users’ smartphones with General Transit Feed Specification (GTFS) data from the bus network in Hamilton, Ontario, to analyze trajectory similarities using Dynamic Time Warping (DTW) and Longest Common Subsequence (LCSS) algorithms. By matching user trajectories with GTFS data, the system accurately identifies the bus services used, enabling frictionless fare calculation and integration of payment systems. Our results show that DTW is more effective than LCSS, particularly for longer trips due to the large quantity of data points. This research demonstrates the practicality of this approach, providing a promising solution for improving fare collection and the efficiency of public transportation. These findings make a significant contribution to the development of smart, user-friendly transportation infrastructure. / Thesis / Master of Applied Science (MASc)