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The solution to the problem of a satellite with a small constant thrust and under the influence of a central force field presents difficulties due to equations non-linearity. An investigation was made to determine what range of values of the thrust parameter could be utilized to obtain a valid approximate solution for the case of tangential thrusting. The investigation was accomplished by developing programs for the 1620 High Speed Digital Computer, since the solution to the exact and approximate equations would otherwise be exceedingly laborious. Under the assumption of no atmosphere, and neglecting the earth's oblateness, the study showed that the validity of the Kryloff and Bogoliuboff method was dependent on both the specific thrust aud the vehicle speed. For a Speed corresponding to an orbit of smaller eccentricity it was determined that the method of Kryloff and Bogoliuboff remained valid for larger values of W than when V was a velocity corresponding to an orbit with a greater eccentricity. The method of Kryloff and Bogoliuboff represents a practical approach to the solution of satellite motion both from the aspect of ease of application and reasonable calculation times. / Master of Science

There is an ever increasing need for low-cost communication systems in the world. One such system, low-earth-orbit satellites, can provide store-and-forward, as opposed to real time, communication for many earth stations. The advantages and disadvantages of such a system is presented. Material covering protocols and communications architectures is elaborated upon for the use of amateur radio communications. Doppler shift and its effect on satellites in low-earth-orbit is examined. Efficiency and throughput of the Amateur X.25 Protocol will be explored. The last chapter entails the analysis of the PACSAT experiment. / Master of Science

Range and,interferometric observations have been examined for their potential, application in a geometric approach to determination of satellite ephemeri. The approach differs from the normal (dynamic) approach in that each satellite position is treated as an independent state variable or benchmark. Programs have been developed that simulate and format the input, data for the least squares estimation routines, and perform statistical analyses of those results. Random error, tropospheric refraction errors, and atomic clock errors have been considered, and the range observation adjustment program directed to solve for clock errors. / Master of Science

Three methods for solving the orbital intercept problem in the presence of an oblate earth are presented. Both iterative and direct approaches for solving the problem were compared in the bases of computational time and relative accuracy of the results. The two iterative methods were found to agree to eight significant figures for all elliptic intercept orbits studied. The results obtained from the direct approach were found to agree with the iterative methods's results to eight significant figures for low intercept eccentricities ( e < 0.2), and to five significant figures for high intercept orbit eccentricities (e = 0.9). However, the direct method was found to be twice as fast, computationally, as either of the two iterative methods. The iterative methods each take essentially the same amount of computational time. Neither type of routine yields accurate results for half-revolution intercept and hyperbolic intercept orbits. The method for developing these procedures, the computer code implementing the methods, and selected results are included. / M.S.

The convective fluid dynamics and chaos between two parallel plates with temperature discrepancy has been investigated via classic and extended Lorenz system. Both the classic 3-dimensional and extended 5-dimensional Lorenz system are developed by truncating a double Fourier series, which is the solution of the streamline function. Boundary conditions are also considered. The implicit discrete mapping method has been employed to solve the classic and extended Lorenz system, and the motion stability is determined by the eigenvalue analysis. Bifurcation diagram varying with Rayleigh parameter and Prandtl parameter are obtained by solving the stable and unstable period-m motions (m=1,2,4). Symmetric period-1 to asymmetric period-4 motions have been illustrated in the phase space. Therefore, the route from period-1 to period-4 motions to chaos through the period-doubling bifurcation has been demonstrated in the classic and extended Lorenz system. For the extended 5-dimensional Lorenz system, the harmonic frequency-amplitude characteristics are also presented, which provides energy distribution in the parameter space. On bifurcation tree, the non-spiral and spiral homoclinic orbits have been seen and been illustrated in 2-D view and 3-D view. Such homoclinic orbits represent the asymptotic convection steady state that generates the chaos in the convective fluid dynamics. The rich dynamical behaviors of the convective fluid are discovered, and this investigation may help one understand the chaotic dynamics for other thermal convection problems.

Three-dimensional gravity-capillary steady waves on water of finite-depth, which are uniformly translating in a horizontal propagation direction and periodic in a transverse direction, are considered. The exact Euler equations are formulated as a spatial dynamic system in which the variable used for the propagating direction is the time-like variable. The existence of the solutions of the system is determined by two non-dimensional constants: the Bond number b and λ (the inverse of the square of the Froude number). The property of Sobolev spaces and the spectral analysis show that the spectrum of the linear part consists of isolated eigenvalues of finite algebraic multiplicity and the number of purely imaginary eigenvalues are finite. The distribution of eigenvalues is described by b and λ. Assume that C₁ is the curve in (b,λ)-plane on which the first two eigenvalues for three-dimensional waves collide at the imaginary axis, and that the intersection point of the curve C₁ with the line λ=1 is (b₀,1) where b₀>0. Two cases (b₀,1) and (b,λ) â C₁ where 0< b< b₀ are investigated. A center-manifold reduction technique and a normal form analysis are applied to show that for each case the dynamical system can be reduced to a system of ordinary differential equations with finite dimensions. The dominant system for the case (b₀,1) is coupled Schrödinger-KdV equations while it is a Schrödinger equation for another case (b,λ) â C₁. Then, from the existence of the homoclinic orbit connecting to the two-dimensional periodic solution (called generalized solitary wave) for the dominant system, it is obtained that such generalized solitary wave solution persists for the original system by using the perturbation method and adjusting some appropriate constants. / Ph. D.

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Approved for public release, distribution is unlimited / A Halo orbit about a libration point of a restricted three-body system provides additional opportunities for surveillance, communication, and exploratory missions in lieu of the classical spacecraft orbit. Historically libration point missions have focused on Halo orbits and trajectories about the Sun-Earth System. This thesis will focus on libration point orbit solutions in the Earth-Moon system using the restricted three body equations of motion with three low-thrust control functions. These classical dynamics are used to design and optimize orbital trajectories about stable and unstable libration points of the Earth-Moon system using DIDO, a dynamic optimization software. The solutions for the optimized performance are based on a quadratic cost function. Specific constraints and bounds were placed on the potential solution set in order to ensure correct target trajectories. This approach revealed locally optimal solutions for orbits about a stable and unstable libration point. / Lieutenant, United States Navy

Orientador: Othon Cabo Winter / Banca: Rafael Sfair de Oliveira / Banca: Felipe Bragda Ribas / Resumo: Ocultações estelares de Chariklo em 2013 revelaram algo que era desconhecido até o momento: anéis de partículas em torno de um corpo celeste do Sistema Solar diferente de um planeta. Este fato despertou o interesse da comunidade científica a respeito de assuntos como, por exemplo, o processo de formação desses anéis, por quanto tempo eles existirão, qual a probabilidade de corpos como o de Chariklo possuírem anéis ou ainda como eles se mantêm estáveis ao redor de um pequeno objeto, se comparado aos planetas. Neste trabalho estamos interessados em determinar o modelo físico de Chariklo através da manutenção da estrutura atual dos anéis. Acreditamos que este centauro é um corpo semelhante a um elipsoide, entretanto não sabemos com exatidão as dimensões de seus semieixos físicos a, b e c. As razões entre os valores destes semieixos resultam em diferentes valores para os termos de achatamento e elipticidade de Chariklo, que podem ser representados pelos termos J 2 e C 22 em seu potencial gravitacional. Além de determinar os limites para a forma de Chariklo, queremos também estudar quais são os efeitos que o achatamento e elipticidade do corpo central provocam na dinâmica das partículas dos anéis. Para isso, fizemos simulações numéricas usando um integrador que leva em conta os termos relacionados aos coeficientes J 2 e C 22 . O sistema que integramos é composto por Chariklo sendo orbitado por uma partícula com aproximadamente a mesma distância em que estão os anéis, fazendo uso d... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Chariklo's stellar occultations in 2013 revealed something that was unknown to date: particle rings around a celestial body of the Solar system other than a planet. This fact has aroused the interest of the scientific community on issues such as the process of forming these rings, how long they will exist, how likely Chariklo bodies are to have rings or how stable they are around of a small object, compared to the planets. In this work we are interested in determining Chariklo's physical model by maintaining the current structure of the rings. We believe that this centaur is a body similar to an ellipsoid, but we do not know exactly the dimensions of its physical axes a, b, and c. The ratios between the values of these semi axes result in different values for the Chariklo flattening and ellipticity terms which can be represented by the terms J2 and C22 in its gravitational potential. In addition to determining the limits for the Chariklo form, we also want to study the effects of flattening and ellipticity on the dynamics of ring particles. For this, we did numerical simulations using an integrator that takes into account the terms related to the coefficients J2 and C22. The system we integrate is composed of Chariklo being orbited by a particle approximately the same distance as the rings, making use of the orbital osculating elements. The objective of these simulations was to reproduce the physical characteristics of the rings obtained through stellar occultations, however ... (Complete abstract click electronic access below) / Mestre