# Browsing by Subject "Aerospace engineering"

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Item On the role of invariant objects in applications of dynamical systems(2012-05) Blazevski, Daniel, 1984-; Llave, Rafael de la; Chen, Thomas (Ph. D. in mechanical engineering and Ph. D. in mathematical physics); Koch, Hans; Morrison, Phil; Ocampo, Cesar; Pavlovic, Natasa; Vasseur, AlexisShow more In this dissertation, we demonstrate the importance of invariant objects in many areas of applied research. The areas of application we consider are chemistry, celestial mechanics and aerospace engineering, plasma physics, and coupled map lattices. In the context of chemical reactions, stable and unstable manifolds of fixed points separate regions of phase space that lead to a certain outcome of the reaction. We study how these regions change under the influence of exposing the molecules to a laser. In celestial mechanics and aerospace engineering, we compute periodic orbits and their stable and unstable manifolds for a object of negligible mass (e.g. a satellite or spacecraft) under the presence of Jupiter and two of its moons, Europa and Ganymede. The periodic orbits serve as convenient spot to place a satellite for observation purposes, and computing their stable and unstable manifolds have been used in constructing low-energy transfers between the two moons. In plasma physics, an important and practical problem is to study barriers for heat transport in magnetically confined plasma undergoing fusion. We compute barriers for which heat cannot pass through. However, such barriers break down and lead to robust partial barriers. In this latter case, heat can flow across the barrier, but at a very slow rate. Finally, infinite dimensional coupled map lattice systems are considered in a wide variety of areas, most notably in statistical mechanics, neuroscience, and in the discretization of PDEs. We assume that the interaction amont the lattice sites decays with the distance of the sites, and assume the existence of an invariant whiskered torus that is localized near a collection of lattice sites. We prove that the torus has invariant stable and unstable manifolds that are also localized near the torus. This is an important step in understanding the global dynamics of such systems and opens the door to new possible results, most notably studying the problem of energy transfer between the sites.Show more Item Transportation-Related Constructs of Activity Spaces of Small Town Residents(Council for Advanced Transportation Studies, 1974-12) Burnett, Pat; Betak, John; Chang, David; Enders, Wayne T.; Montemayor, JoseShow more This paper first discusses the nature of the space which people in small urban areas use for recurrent activities. It is postulated that most work on the individual's activity space is founded on a classical geometric conception of place. An alternative cognitive definition is proposed. Places which are used for such purposes as shopping or recreation are described by learned bundles of meanings (constructs), given a transportation system permitting movement within space. Recent modifications of Kelly's Personal Construct Theory and elicitation procedures are used to demonstrate the richness of the cognitive definition of place, with data from a small sample of 31 University students. In conclusion, it is suggested how elicited transportation-related constructs of places can be utilized to develop improved models of behavior within urban activity spaces.Show more