Browsing by Author "Ron Fulp, Committee Member"

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    L(Infinity) Structures on Spaces of Low Dimension
    (2004-04-14) Daily, Marilyn Elizabeth; Kailash Misra, Committee Member; Ron Fulp, Committee Member; Jim Stasheff, Committee Member; Tom Lada, Committee Chair
    L(Infinity) structures are natural generalizations of Lie algebras, which need satisfy the standard graded Jacobi identity only up to homotopy. They have also been a subject of recent interest in physics, where they occur in closed string theory and in gauge theory. This dissertation classifies all possible L(Infinity) structures which can be constructed on a Z-graded (characteristic 0) vector space of dimension three or less. It also includes necessary and sufficient conditions under which a space with an L(3) structure is a differential graded Lie algebra. Additionally, it is shown that some of these differential graded Lie algebras possess a nontrivial L(n) structure for higher n.
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    The Lageos Satellite: A Comprehensive Spin Model and Analysis
    (2002-12-19) Williams, Scott Everett; Arkady Kheyfets, Committee Chair; Ron Fulp, Committee Member; Larry Norris, Committee Member; Pierre Gremaud, Committee Member
    A thorough investigation into the theoretical modeling of the Laser-Ranged Geodynamics Satellite (Lageos I) spin state evolution is presented. Starting from an existing dynamical model, we analyze in detail each of the model's assumptions and explore possible enhancements. Additional concerns not considered by the original model are also scrutinized in a bottom-up approach. In particular, we re-evaluate the orbit propagation module, survey and investigate all possible space-environment effects, assess numerical implementation concerns, and perform a number of software feature modifications. In the process, a parameterized approach is adopted and corresponding non-linear optimization tools are integrated into the revamped model. The outcome is a comprehensive, open-source model of the Lageos I spin dynamics which exhibits a significant advance in predictive accuracy. A corollary of the effort is a broad survey of the important space environment effects on the attitude of passive satellites. In addition, a thorough analysis of the model results is presented along with an expanded discussion of the interesting discoveries we made. Particularly significant is the sensitivity of the spin state evolution to small changes in the principal moments of the satellite–an idea discounted by previous efforts that nevertheless can be analytically verified. A consequence of the effort is the immediate application to a number of ongoing research activities involving the Lageos I satellite. Of particular interest is the potential role of Lageos I in a proposed experiment to measure the general relativistic force known as gravitomagnetism. A precise understanding of the evolution of Lageos' spin dynamics is required so that correlated thermal effects may be properly accounted for in the evaluation of orbital motion. A related effort is the attempt to empirically measure the spin state based on optical glint data. This process must be seeded with a quality initial estimate of the spin axis orientation for proper evaluation of the data. The model we present has implications for both of these efforts.