Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Includes bibliographical references. / by Sean Kevin Collins. / Ph.D.

Thesis. 1976. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / Microfiche copy available in Archives and Aero. / Bibliography: leaf 90. / by Thomas J. Fill. / M.S.

Orientador: Ernesto Vieira Neto / Coorientador: Antônio Delson Conceição de Jesus / Banca: Othon Cabo Winter / Banca: Cristiano Fiorilo de Melo / Resumo: Neste trabalho, estudamos o problema da viabilidade de missões espaciais em ambiente de detritos espaciais. Geralmente, um veículo espacial em curso de colisão com um detrito espacial é destruído ou danificado e tem sua missão prejudicada. A preservação destas missões depende da capacidade do satélite de evitar a colisão, como por exemplo, através de uma manobra orbital conhecida como manobra evasiva. Neste estudo, estabelecemos estratégias de manobras evasivas realizadas por um satélite através de um sistema de propulsão, cuja eficiência é medida por parâmetros tecnológicos. Os parâmetros tecnológicos são configurados no planejamento da missão, e descrevem a quantidade de combustível a bordo e a capacidade de expelir propelente do sistema de propulsor. As manobras evasivas foram estudadas para serem aplicadas de tal forma que o satélite escape do detrito espacial sem a evasão da sua órbita nominal de missão, e para este objetivo, incluímos uma propulsão de controle e tratamos o sistema de propulsão como uma perturbação na órbita do satélite. Também foi estabelecido, para realizar manobras evasivas econômicas, uma propulsão que é ligada em uma fração do tempo total disponível para a manobra. Esta fração de tempo é definida como um tempo de pulso de propulsão. As manobras evasivas são estudadas por simulações numéricas da dinâmica de um detrito e um veículo espacial sob a ação da força gravitacional da Terra e de perturbações orbitais oriundas de um sistema de propulsão e da atmosfera da Terra. Nestas simulações calculamos as condições de colisão do detrito e do satélite, que ocorrem ao redor da Terra, e utilizamos para criar catálogos de parâmetros tecnológicos acessíveis ao satélite para escapar destas colisões / Abstract: We studied the problem of the viability of space missions in debris environment space. Generally, a space vehicle in collision course with a space debris is destroyed or damaged and has impaired their mission. The preservation of these missions depends on the satellite capacity to avoid the collision, for example by an orbital maneuver known as evasive maneuver. In this study, we established strategies evasive maneuvers performed by a satellite via a propulsion system, whose efficiency is measured by technological parameters. Technological parameters are set in the planning of the mission, and describe the amount of fuel on board and the ability to expel propellant propulsion system. The evasive maneuvers were studied to be applied in such a way that the satellite escape the space debris without evasion of its nominal orbit mission, and for this purpose, include a propulsion control and treat the propulsion system as a disturbance in the orbit of satellite. It has also been established, to perform evasive maneuvers driven, propulsion which is connected at a fraction of the total time available for the maneuver. This fraction of time is defined as a propulsion pulse time. The evasive maneuvers are studied by numerical simulations of the dynamics of a debris and a vehicle space under the action of the Earth's gravitational and orbital perturbations arising from a propulsion system and the Earth's atmosphere. In these simulations calculate the debris of the collision conditions and the satellite, which occur around the Earth, and used to create technological parameters catalogs accessible to the satellite to escape these collisions / Mestre

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Stephen Paul Taylor. / M.S.

No description available.

Let G be a compact Lie group and let π be an irreducible representation of G of highest weight λ. We study the operator-valued Fourier transform of the product of the j-function and the pull-back of ?? by the exponential mapping. We show that the set of extremal points of the convex hull of the support of this distribution is the coadjoint orbit through ?? + ??. The singular support is furthermore the union of the coadjoint orbits through ?? + w??, as w runs through the Weyl group. Our methods involve the Weyl functional calculus for noncommuting operators, the Nelson algebra of operants and the geometry of the moment set for a Lie group representation. In particular, we re-obtain the Kirillov-Duflo correspondence for compact Lie groups, independently of character formulae. We also develop a "noncommutative" version of the Kirillov character formula, valid for noncentral trigonometric polynomials. This generalises work of Cazzaniga, 1992.

<p>The dynamical evolution of the spin axis direction due to gravitational and thermal factors is examined. It is found that the spin axis variations generally are regular and relatively small for the bodies in the asteroid main belt. There are also reasons to believe that this is the case for minor objects beyond the main belt. However, it is found that these regular variations are larger when the orbital inclination of the objects is increased. This effect may explain certain features in the spin vector distribution of the main belt asteroids, not possible to explain by collisional factors. The spin vector evolution of the asteroids in the inner solar system, including the Earth- and Mars-crossing objects, is often subjected to strong forces related to frequencies in the orbital evolution. The variations in the spin vector direction are then very large and often subjected to chaos. The larger frequency related obliquity zones of the Mars-crossers are usually regular while the zones of the Earth-Mars-crossers often are of a chaotic nature. The spin vector evolution of asteroids with comet-like orbits is often chaotic regardless of initial obliquity. For the inner solar system asteroids, it is often possible for an initial prograde spin to turn into a retrograde one, or vice versa, due to the frequency related phenomena. Though some spin vector directions seem to be more probable than other ones over time, there are no indications for an evolution towards a more prograde or a more retrograde spin vector distribution.</p><p>The effects on the spin vector evolution from the thermal Yarkovsky force are examined for objects with radii larger than 50 m. This force will affect the orbital evolution and thus indirectly affect the spin vector evolution. However, it is found that the studied effects are minor as compared to the gravitationally related ones. This is true both for the diurnal and the seasonal variants of the Yarkovsky force.</p>

This Ph.D. thesis is devoted to the development of a specific semi-analytical algorithm especially well-suited to derive the long-term evolution of near geosynchronous space debris and based on the concept of mean orbital motion. In a first approach, the semi-analytical theory is concerned with the singularity issues arising for circular and equatorial orbits as well as with the geostationary resonance modeling. In a second part, motivated by the discovery of high area-to-mass ratios space debris in high altitude Earth's orbit (mostly near the geosynchronous region), the direct radiation pressure models are revisited and completed. Within this context, the main effects of the direct solar radiation pressure for the mid- and long-term evolution of both the eccentricity and the inclination vectors are analyzed through a well-suited model. Moreover, by means of a smart extension, the passage in the Earth's shadow is taken into account in the computations of the orbits. Finally, a further insight into the intrinsic stability of such space debris is performed, by means of a recent numerical technique (MEGNO) which is based on the concept of ``variational chaos indicator'.

The dynamical evolution of the spin axis direction due to gravitational and thermal factors is examined. It is found that the spin axis variations generally are regular and relatively small for the bodies in the asteroid main belt. There are also reasons to believe that this is the case for minor objects beyond the main belt. However, it is found that these regular variations are larger when the orbital inclination of the objects is increased. This effect may explain certain features in the spin vector distribution of the main belt asteroids, not possible to explain by collisional factors. The spin vector evolution of the asteroids in the inner solar system, including the Earth- and Mars-crossing objects, is often subjected to strong forces related to frequencies in the orbital evolution. The variations in the spin vector direction are then very large and often subjected to chaos. The larger frequency related obliquity zones of the Mars-crossers are usually regular while the zones of the Earth-Mars-crossers often are of a chaotic nature. The spin vector evolution of asteroids with comet-like orbits is often chaotic regardless of initial obliquity. For the inner solar system asteroids, it is often possible for an initial prograde spin to turn into a retrograde one, or vice versa, due to the frequency related phenomena. Though some spin vector directions seem to be more probable than other ones over time, there are no indications for an evolution towards a more prograde or a more retrograde spin vector distribution. The effects on the spin vector evolution from the thermal Yarkovsky force are examined for objects with radii larger than 50 m. This force will affect the orbital evolution and thus indirectly affect the spin vector evolution. However, it is found that the studied effects are minor as compared to the gravitationally related ones. This is true both for the diurnal and the seasonal variants of the Yarkovsky force.

The scalar tensor theory of gravitation is constructed in D dimensions in all possible geometries of spacetime. In Riemannian geometry, theory of gravitation involves a spacetime metric g with a torsion-free, metric compatible connection structure. If the geometry is non-Riemannian, then the gauge theory of gravitation can be constructed with a spacetime metric g and a connection structure with torsion. In non-Riemannian theory, connections may be metric compatible or non-metric compatible. It is shown that theory of gravitation which involves non-metric compatible connection and torsion, can be rewritten in terms of torsion-free theory. It is also shown that scalar tensor theory can be reformulated in Einstein frame by applying a conformal transformation. By adding an antisymmetric axion field, the axi-dilaton theory is studied in Riemannian and non-Riemannian geometries. Motion of massive test particles is examined in all these geometries. The static, spherically symmetric and stationary, Kerr-type axially symmetric solutions of the scalar tensor and axi-dilaton theories are presented. As an application, the geodesic elliptical orbits based on a torsion-free connection and the autoparallel orbits based on a connection with a torsion, are examined in Kerr Brans-Dicke geometry. Perihelion shift of the elliptical orbit is calculated in both cases and the results are compared.