Demonstramos o seguinte teorema: Seja M uma variedade Riemanniana compacta, conexa e sem bordo. Dados um endomorismo f : M ightarrow M, uma função contínua \\phi: M ightarrow R e \\epsilon > 0, então existe um endomorísmo \\tilde f : M ightarrow M tal que d(f; \\tide f) = \\max_{x \\in M} d(f(x); \\tilde f(x)) < \\epsilon, e existe uma medida \\phi-maximizante para \\tilde f que está suportada em uma orbita periodica. Este teorema e uma generalização dos resultados obtidos por S. Addas-Zanatta e F. Tal. / We prove the following theorem: Let M be a bondaryless, compact and connected Riemannian Manifold. Given an endomorphism f on M, a continuous function \\phi : M ightarrow R and \\epsilon > 0, then there exist an endomorphism \\tilde f on M with d(f; \\tilde f) < \\epsilon such that, some \\phi-maximizing measure for \\tilde f is supported on a periodic orbit. This theorem is a generalization of the results obtained by S. Addas-Zanatta and F. Tal.

O propósito deste trabalho é estudar a existência de solução periódica para problemas de oscilação não linear de barras submetidas a forças periódicas. Estudaremos concretamente dois problemas, que serão interpretados como equações diferenciais abstratas de segunda ordem cuja classe foi considerada em Ceron e Lopes [1]. Para garantir a existência de solução periódica dos problemas considerados, mostraremos que a aplicação de Poincaré S é limitada dissipativa e alfa-contração. Isso garante a existência de um atrator invariante compacto e a existência de um ponto fixo de S, o que é equivalente a existência da solução periódica. / Our aim in this work is to study the existence of periodic solution to oscillation in nonlinear problems of beams submitted to periodic forcing. We will study concretely two problems, which can be interpreted as an abstract second order diferential equation studied by Ceron and Lopes [1]. Our intention is to prove the existence of periodic solution to these problems. To this end, we will show that the Poincaré map S is uniform ultimately bounded and alpha-contraction. Thus we have the existence of invariant compact attractor, therefore S have a fixed point, which is equivalent the existence of a periodic solution.

Resumo: Uma abordagem analítica para o movimento rotacional de satélites artificiais estabilizados por rotação é apresentada, considerando os satélites em órbita elíptica e a influência do torque magnético residual. O torque magnético residual resulta da interação entre o campo magnético residual do satélite e o campo geomagnético, sendo este representado pelo modelo de quadripolo. As equações do movimento são descritas em termos do módulo da velocidade de rotação do satélite, da declinação e da ascensão reta do eixo de rotação do satélite. As componentes médias do torque residual em um sistema fixo no satélite são determinadas para um período orbital. Uma solução analítica para as equações do movimento é determinada, sendo válida para um período orbital. Por esta solução observa-se que o torque residual não afeta o módulo da velocidade de rotação, contribuindo apenas para as variações temporais da ascensão reta e declinação do eixo de rotação, associadas com a precessão e deriva do eixo de rotação do satélite. Aplicações são realizadas para os Satélites de Coleta de Dados Brasileiros SCD1 e SCD2, mostrando uma concordância entre os resultados obtidos pela teoria e os dados fornecidos pelo Centro de Controle de Satélites do INPE. O comportamento do erro gerado na direção do eixo de rotação do satélite é também apresentado, sendo que os desvios obtidos se mostram de acordo com as precisões requeridas para as missões destes satélites. / Abstract: An analytical approach is show for attitude motion of the spin stabilized artificial satellite in an elliptic orbit. Residual magnetic torque is considered and the geomagnetic torque is defined by the quadripole model. The equations of motion are described by the magnitude of the spin velocity, right ascension and declination of the spin axis. The components of the averaged residual torque are computed for one orbital period in a satellite reference system. An analytical solution is presented and it is valid for one orbit period. By this solution it is possible to observe that the residual torque causes the precession and the drift of the spin axis, but it does not affect the magnitude of spin velocity. Some applications are done for Brazilian Satellite SCD1 and SCD2, and they show the agreement of the theory results and the data provide by INPE Satellite Control Center. The behavior of the error in the spin axis direction is also presented and this error agrees with the required precision of these satellite missions. / Orientador: Maria Cecília F. de Paula Santos Zanardi / Coorientador: Hélio Koiti Kuga / Banca: Rodolpho Vilhena de Moraes / Banca: Valcir Orlando / Mestre

Demonstramos o seguinte teorema: Seja M uma variedade Riemanniana compacta, conexa e sem bordo. Dados um endomorismo f : M ightarrow M, uma função contínua \\phi: M ightarrow R e \\epsilon > 0, então existe um endomorísmo \\tilde f : M ightarrow M tal que d(f; \\tide f) = \\max_{x \\in M} d(f(x); \\tilde f(x)) < \\epsilon, e existe uma medida \\phi-maximizante para \\tilde f que está suportada em uma orbita periodica. Este teorema e uma generalização dos resultados obtidos por S. Addas-Zanatta e F. Tal. / We prove the following theorem: Let M be a bondaryless, compact and connected Riemannian Manifold. Given an endomorphism f on M, a continuous function \\phi : M ightarrow R and \\epsilon > 0, then there exist an endomorphism \\tilde f on M with d(f; \\tilde f) < \\epsilon such that, some \\phi-maximizing measure for \\tilde f is supported on a periodic orbit. This theorem is a generalization of the results obtained by S. Addas-Zanatta and F. Tal.

Coadjoint orbits of Lie algebras come naturally imbued with a symplectic two-form allowing for the construction of dynamical actions. Consideration of the coadjoint orbit action for the Kac-Moody algebra leads to the Wess-Zumino-Witten model with a gauge-field coupling. Likewise, the same type of coadjoint orbit construction for the Virasoro algebra gives Polyakov’s 2D quantum gravity action with a coupling to a coadjoint element, D, interpreted as a component of a field named the diffeomorphism field. Gauge fields are commonly given dynamics through the Yang-Mills action and, since the diffeomorphism field appears analogously through the coadjoint orbit construction, it is interesting to pursue a dynamical action for D. This thesis reviews the motivation for the diffeomorphism field as a dynamical field and presents results on its dynamics obtained through projective connections. Through the use of the projective connection of Thomas and Whitehead, it will be shown that the diffeomorphism field naturally gains dynamics. Results on the analysis of this dynamical theory in two-dimensional Minkowski background will be presented.

This thesis demonstrates that any individual can provide relevant observational data to further research efforts within the Aerospace community, through the use of amateur telescopes. A Meade LX200 12 in. telescope and Lumenera Skynyx 2.0 camera were utilized to observe small LEO satellites, using a well-documented point-and-wait staring method. Over a period of three months, a total of 186 observation attempts were made resulting in 97 successful captures. From the gathered data, three possible aerospace applications were analyzed: validation of a satellite brightness prediction model, angles-only orbit determination including extended Kalman filtering, and temporal error growth in TLE-based orbit propagation. Further investigations include a preliminary optimization using MATLAB's fmincon function (informed by the previous analyses) to determine an optimal telescope size for performing LEO observations.

Geosynchronous Equatorial Orbit (GEO) is critical to Earth communications, weather monitoring, and national defense. Orbit estimation of GEO objects is difficult due to physical constraints placed on ground-based tracking devices such as weather, object range, and tracking frequency restrictions. These constraints are commonly mitigated through the use of two-way signaling devices for cooperative GEO satellites. However, determining the position and velocity of uncooperative GEO satellites and/or objects is more challenging. The objective of this dissertation is to quantify the increased orbital accuracy of objects in the GEO catalog when the Air Force Space Command Space Surveillance Network (AFSPC SSN) is augmented with space-based angles-only measurements from a sensor in a unique near-GEO orbit. Linear covariance theory and analysis provides an efficient method to determine the covariance of the position and velocity of an uncooperative GEO object, while incorporating uncertainties in the dynamics and sensor errors. Once this covariance is determined, an error budget analysis is performed to determine the major sources of uncertainty contributing to position errors of objects in the GEO catalog. As a result, it is shown through linear covariance analysis that incorporating measurements from a space-based sensor in a near-GEO orbit increases the orbital accuracy of GEO objects when compared to the orbital accuracy achieved with AFSPC SSN measurements alone.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 174-186).

No description available.

The stabilization of electron beam in the Storage Ring (SR) is an important task in the 3rd generation synchrotron facility worldwide. Deviations in the position and angle of electron beam with respect to a desired orbit must be below 10% of the beam size. This requirement corresponds to about 3 μm deviations at the Canadian Light Source (CLS). Further, the higher the correction bandwidth, the better in the stabilization process. The correction bandwidth at CLS was expected to increase to be 45 Hz or higher from the current operating rate at 18 Hz. In addition, there is requirement to control the beam deviation at specific positions on the orbit. To meet these requirements, a comparative study of the existing methods for the stabilization of electron beam in the SR is thus necessary, which is the main motivation of this thesis study. The overall objective of this thesis study was to find the most suitable method for CLS so that the correction bandwidth can be 45 Hz or higher. The study was primarily conducted by simulation due to the restriction in performing experiments on the whole beamline. The transfer functions of three important devices at the storage ring, which are Beam Position Monitor (BPM), Orbit Correction Magnets (OCM) and Vacuum Chamber (VC), were identified. Noises on the storage ring were also identified to improve the reliability of the simulation study. The existing methods for beam orbit correction, such as (1) Singular Value Decomposition (SVD), (2) Eigen Vector method with Constraints (EVC) and (3) SVD plus Proportional integral derivative (PID), were compared based on the simulation technique. Several conclusions can be drawn from this study: (1) there is no significant difference between the EVC method and SVD method in terms of overall orbit correction performance, and they both can meet the correction bandwidth of 45 Hz. The EVC method is however much better than the SVD method in terms of the beam orbit correction performance at specific positions; (2) the SVD plus PID method is much better than the SVD method as well as EVC method in terms of the overall orbit correction performance, and its performance for specific position orbit correction is comparable with the performance of EVC. Therefore, the SVD plus PID method is recommended for CLS. This study has made the following contributions on the problem of beam stabilization the storage ring in the synchrotron technology: (1) provision of the models of BPM and OCM and the PID controller tailored to specific BPM and OCM devices, which is useful to other synchrotron facilities in the world; (2) generation of the knowledge regarding the performances of SVD, EVC and SVD plus PID methods on one synchrotron facility is valuable, and this knowledge is useful to other synchrotron facilities in selection of the best methods for electron orbit correction.