into an elaborate functioning enterprise. It is for this reason that this dissertation seeks to contribute towards the search for simpler, efficacious and more reliable methodologies and tools that accurately model and analyze space systems dynamics. Inopportunely, despite the inimical physical hazards, space systems must endure a perturbing dynamical environment that persistently disorients spacecraft attitude, dislodges spacecraft from their designated orbital locations and compels spacecraft to follow undesired orbital trajectories. The ensuing dynamics’ analytical models are complexly structured, consisting of parametrically excited nonlinear systems with external periodic excitations–whose analysis and control is not a trivial task. Therefore, this dissertation’s objective is to overcome the limitations of traditional approaches (averaging and perturbation, linearization) commonly used to analyze and control such dynamics; and, further obtain more accurate closed-form analytical solutions in a lucid and broadly applicable manner. This dissertation hence implements a multi-faceted methodology that relies on Floquet theory, invariant center manifold reduction and normal forms simplification. At the heart of this approach is an intuitive system state augmentation technique that transforms non-autonomous nonlinear systems into autonomous ones. Two fitting representative types of space systems dynamics are investigated; i) attitude motion of a gravity gradient stabilized spacecraft in an eccentric orbit, ii) spacecraft motion in the vicinity of irregularly shaped small bodies. This investigation demonstrates how to analyze the motion stability, chaos, periodicity and resonance. Further, versal deformation of the normal forms scrutinizes the bifurcation behavior of the gravity gradient stabilized attitude motion. Control laws developed on transformed, more tractable analytical models show that; unlike linear control laws, nonlinear control strategies such as sliding mode control and bifurcation control stabilize the intricate, unwieldy astrodynamics. The pitch attitude dynamics are stabilized; and, a regular periodic orbit realized in the vicinity of small irregularly shaped bodies. Importantly, the outcomes obtained are unconventionally realized as closed-form analytical solutions obtained via the comprehensive approach introduced by this dissertation.
This research studies an alternative to the slider-crank mechanism for internal combustion engines, which was proposed by the Wiseman Technologies Inc. Their design involved replacing the crankshaft with a hypocycloid gear assembly. The unique hypocycloid gear arrangement allowed the piston and connecting rod to move in a straight line creating a perfect sinusoidal motion, without any side loads. In this work, the Wiseman hypocycloid engine was modeled in a commercial engine simulation software and compared to slider-crank engine of the same size. The engine’s performance was studied, while operating on diesel, ethanol, and gasoline fuel. Furthermore, a scaling analysis on the Wiseman engine prototypes was carried out to understand how the performance of the engine is affected by increasing the output power and cylinder displacement.
It was found that the existing 30cc Wiseman engine produced about 7% less power at peak speeds than the slider-crank engine of the same size. These results were concurrent with the dynamometer tests performed in the past. It also produced lower torque and was about 6% less fuel efficient than the slider-crank engine. The four-stroke diesel variant of the same Wiseman engine performed better than the two-stroke gasoline version. The Wiseman engine with a contra piston (that allowed to vary the compression ratio) showed poor fuel efficiency but produced higher torque when operating on E85 fuel. It also produced about 1.4% more power than while running on gasoline. While analyzing effects of the engine size on the Wiseman hypocycloid engine prototypes, it was found that the engines performed better in terms of power, torque, fuel efficiency, and cylinder brake mean effective pressure as the displacement increased. The 30 horsepower (HP) conceptual Wiseman prototype, while operating on E85, produced the most optimum results in all aspects, and the diesel test for the same engine proved to be the most fuel efficient.