Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 279-281). Available also in a digital version from Dissertation Abstracts.

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Thesis (M.A.)--Lehigh University, 1910. / Current name of asteroid is "691 Lehigh." Manuscript. Also available online.

A relatively general formulation for the governing equations of motion, applicable to a large class of flexible multibody systems, is developed using a concise matrix format. The model considered consists of a number of arbitrarily connected flexible deployable members forming branched and closed loop configurations. Joints between bodies are permitted up to six degrees of freedom in translation and rotation. To be effective, the matrix-Lagrangian formulation necessitates development of the kinetic energy expression in a quadratic form in terms of the system velocities. The mass matrix associated with such a quadratic form is known for simple systems such as a collection of point masses, a group of connected rigid bodies, and a discretized flexible structure. However, for a multibody system, where the contributing forces arise from system's translation, rotation, elasticity, deployment, and their interactions, such an expression is not available. To fill this gap, multibody kinematics is developed in terms of the elements of the geometry matrix, which uniquely describes the configuration of branched systems. The characteristic dynamical quantities, i.e., elements of the mass matrix, are identified and the formulation is approached in an increasing order of complexity. The concept of specified and generalized coordinates together with established procedures of analytical dynamics lead to characteristic quantities ( Lagrangian, Hamiltonian, etc. ) and finally result in governing equations of motion which are new to the multibody dynamics. To account for flexibility in a consistent manner, a second-degree nonlinear displacement field is permitted. Alternatively, a linear displacement field can be used if the nonlinear terms up to the fourth-degree are preserved in the strain energy. An algorithm for calculating the stiffness matrix of a flexible element is developed, where terms up to the third-degree of nonlinearity in displacement are retained. Application of this versatile formulation is illustrated through a set of examples of contemporary interest. They pertain to a spacecraft comprising of a central rigid body with attached flexible appendages. The configuration corresponds to a large class of present and planned communication satellites. It can also represent the Space Shuttle based deployment of beam and plate type appendages aimed at scientific experiments or construction of the proposed Space Station. The system static equilibrium and stability are discussed. A computer code is developed and specialized to the specific cases in hand. Typical results of an extensive parametric study are presented for two particular situations : (i) the Space Shuttle based deployment of a beam or a plate type structural member; (ii) the configuration similar to the Waves In Space Plasma (WISP) experiment jointly proposed by Canada and the U.S.A. The problems are analyzed systematically, through progressive introduction of complexity, to help appreciate interactions between librational dynamics, flexibility, deployment, inertia parameters, orbit eccentricity, initial conditions, appendage orientation, etc. The information is fundamental to the missions concerned and essential to help develop appropriate control strategies. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

archives@tulane.edu / Let G be a connected reductive complex algebraic group. We study the inclusion posets of diagonal G-orbit closures in a product of two partial flag varieties. In this dissertation, we show some results for G=SL_n and G=SO_{2n}. If the diagonal action is of complexity zero, then the poset is a graded lattice. If the diagonal action is of complexity one, then the poset is isomorphic to one of a finite number of posets that we determine explicitly. / 1 / Tien Minh Le

The primary objective of the NASA sponsored ICESat mission is to study the short and long term changes in the ice mass in the Greenland and Antarctica regions. The satellite was therefore placed into a frozen near-polar near-circular repeat groundtrack to ensure an adequate coverage of the polar regions while keeping the groundtrack periodic and reducing the variations in the orbital elements, and more specifically the semi-major axis of the ICESat orbit. After launch, a contingency plan had to be devised to compensate for a laser that dangerously compromised the lifetime of the ICESat mission. This new plan makes an intensive use of the ICESat subcycles, a characteristic of the repeat groundtrack orbits often over-looked. The subcycle of a repeat groundtrack orbit provide global coverage within a time shorter than the groundtrack repetition period. For a satellite with an off-nadir pointing capacity, the subcycles provide near-repeat tracks which represents added opportunity for altimetry measurement over a specific track. The ICESat subcycles were also used in a very innovative fashion to reposition the satellite within its repeat cycle via orbital maneuvers called phasing maneuver. The necessary theoretical framework is provided for the subcycle analysis and the implementation of phasing maneuvers for any future repeat orbit mission. In the perspective of performing cross-validation of missions like CryoSat using the ICESat off-nadir capacity, a study was conducted to determine the geolocations of crossovers between two different repeat groundtrack Keplerian orbits. The general analytical solution was applied to ICESat vs. several other repeat groundtrack orbit mission, including the future ICESat-II mission. ICESat’s repeat groundtrack orbit was designed using a disturbing force model that includes only the Earth geopotential. Though the third body effect from the Sun and the Moon was neglected in the orbit design, it does in fact disrupt the repeatability condition of the groundtrack and consequently implies orbit correction maneuvers. The perturbations on ICESat orbit due to the third body effect are studied as a preliminary work towards including these forces in the design of the future ICESat-II repeat groundtrack orbit. / text

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