Dynamics of a Gyrostat Satellite with the Vector of Gyrostatic Moment along the Principal Plane of Inertia

Artificial satellites are one of the most crucial components of modern life. The study of attitude control and stabilization of satellite is necessary to ensure a successful operation. There are two types of stabilization schemes: the passive methods and active methods. In this dissertation is investigated the dynamics of a gyrostat satellite, subjected to a semi-passive method of stabilization, namely the gravitational torque and the gyroscopic proprieties of rotating rotors, along a circular orbit. In a particular case, when the gyrostatic moment vector is along one of satellite’s principal central planes of inertia. To solve the problem is proposed a mathematical analytical-numerical method for determining all equilibrium positions of the gyrostat satellite in the orbital coordinate system in function of dimensionless gyrostatic moment vector components (???? ??=1,2,3) and the dimensionless inertial parameter ??. The conditions of existence of the equilibrium solutions are obtained. Sufficient conditions of stability for each group of equilibrium solutions are derived from the analysis of the generalized integral energy used as a Lyapunov’s function. The study of the evolution of equilibria bifurcation of the gyrostat is carried out in function of parameter ?? in detail. Also, the evolution of equilibrium solutions in function of spacecraft angles is analyzed and it is verified the existence of small regions of 12 and 16 equilibrium positions referred in [14] and [20]. This work shows that the number of equilibria of a gyrostat satellite, in this particular case, does not exceeds 24 and does not go below 8. The study of the equilibria bifurcation shows that there are small regions of 12 equilibrium positions that approach each other for infinite ??3 and never vanish, these regions seems to have a relation with the regions referred by Santos in [14] and Santos et. al. [20]. The study of the evolution of stability for every equilibrium solution in function ?? and ??3, shows that the number of stable equilibria varies between 2 and 6.Satélites artificias são uns dos componentes cruciais da vida moderna. O estudo do controlo da atitude e estabilização de um satélite é necessário para assegurar uma missão bem-sucedida. Existem dois tipos de métodos de estabilização: os métodos passivos e os métodos ativos. Nesta dissertação é investigado a dinâmica de um satélite tipo giróstato, sujeito a um método semi-passivo de estabilização, nomeadamente o momento gravítico e as propriedades giroscópicas de rotores, ao longo de uma órbita circular. No caso particular, quando o vetor de momento girostático está ao longo de um dos principais planos de inércia do satélite. Para resolver este problema é proposto um modelo matemático numérico-analítico para determinar todos as posições de equilíbrio de um satélite giróstato, em um sistema coordenado orbital em função das componentes adimensionais do vetor de momento girostático (???? ??=1,2,3) e do parâmetro inercial adimensional ??. As condições de existência das soluções de equilíbrio são obtidas. As condições suficientes de estabilidade para cada grupo de soluções de equilíbrio são derivadas, a partir da análise do integral de energia generalizado como uma função de Lyapunov. O estudo da evolução da bifurcação do equilíbrio foi realizado em detalhe em função do parâmetro ??. Também, a evolução das soluções de equilíbrio em função dos ângulos do satélite é analisada e é verificado a existência de pequenas regiões de 12 e 16 posições de equilíbrio referidas em [14] e [20]. Este trabalho mostra que o número de posições de equilíbrio de um satélite tipo giróstato, neste caso particular, não ultrapassa 24 e não é inferior a 8. O estudo da bifurcação do equilíbrio revela a existência de regiões de 12 posições de equilíbrio que se aproximam, para valores infinitos de ??3 e que nunca desaparecem, estas regiões sugerem ter uma relação com as regiões referidas por Santos [14] e Santos et al.[20]. O estudo da evolução da estabilidade para cada solução de equilíbrio em função de ?? e ??3 revela que o número de posições de equilíbrio estáveis varia entre 2 e 6

Dynamics of a gyrostat satellite with the vector of gyrostatic moment tangent to the orbital plane

In this paper, a gyrostat satellite in a circular orbit with its gyrostatic moment tangent to the orbital plane and collinear with the orbital speed is studied regarding its equilibria, bifurcation of equilibria, and asymptotic stability conditions. In the general case, where any gyrostat angular momentum is aligned with any of the orbital coordinate frames, interesting results arose regarding its equilibria bifurcation regarding conditions near to the ones presented in this paper, namely equilibria regions outside their main regions near to the orbital plane tangent. For equilibria and bifurcation of equilibria, a symbolic-numerical method is used to obtain the polynomial equations in function of non-dimensional parameters whose roots are equivalent to the number of equilibria positions. For the asymptotic stability, the results are tested using the Lyapunov stability theory scheme

Computer Science for Continuous Data:Survey, Vision, Theory, and Practice of a Computer Analysis System

Building on George Boole's work, Logic provides a rigorous foundation for the powerful tools in Computer Science that underlie nowadays ubiquitous processing of discrete data, such as strings or graphs. Concerning continuous data, already Alan Turing had applied "his" machines to formalize and study the processing of real numbers: an aspect of his oeuvre that we transform from theory to practice.The present essay surveys the state of the art and envisions the future of Computer Science for continuous data: natively, beyond brute-force discretization, based on and guided by and extending classical discrete Computer Science, as bridge between Pure and Applied Mathematics

Technology for large space systems: A bibliography with indexes (supplement 19)

This bibliography lists 526 reports, articles, and other documents introduced into the NASA scientific and technical information system between January 1, 1988 and June 30, 1988. Its purpose is to provide helpful information to the researcher, manager, and designer in technology development and mission design according to system, interactive analysis and design, structural and thermal analysis and design, structural concepts and control systems, electronics, advanced materials, assembly concepts, propulsion, and solar power satellite systems

Large space structures and systems in the space station era: A bibliography with indexes

Bibliographies and abstracts are listed for 1372 reports, articles, and other documents introduced into the NASA scientific and technical information system between January 1, 1990 and June 30, 1990. Its purpose is to provide helpful information to the researcher, manager, and designer in technology development and mission design according to system, interactive analysis and design, structural and thermal analysis and design, structural concepts and control systems, electronics, advanced materials, assembly concepts, propulsion, and solar power satellite systems

Technology for large space systems: A bibliography with indexes (supplement 10)

The bibliography lists 408 reports, articles and other documents introduced into the NASA scientific and technical information system to provide helpful information to the researcher, manager, and designer in technology development and mission design in the area of large space system technology. Subject matter is grouped according to systems, interactive analysis and design, structural and thermal analysis and design, structural concepts and control systems, electronics, advanced materials, assembly concepts, propulsion, and solar power satellite systems

Space station systems: A bibliography with indexes (supplement 6)

This bibliography lists 1,133 reports, articles, and other documents introduced into the NASA scientific and technical information system between July 1, 1987 and December 31, 1987. Its purpose is to provide helpful information to the researcher, manager, and designer in technology development and mission design according to system, interactive analysis and design, structural and thermal analysis and design, structural concepts and control systems, electronics, advanced materials, assembly concepts, propulsion, and solar power satellite systems. The coverage includes documents that define major systems and subsystems, servicing and support requirements, procedures and operations, and missions for the current and future Space Station

Abstracts on Radio Direction Finding (1899 - 1995)

The files on this record represent the various databases that originally composed the CD-ROM issue of "Abstracts on Radio Direction Finding" database, which is now part of the Dudley Knox Library's Abstracts and Selected Full Text Documents on Radio Direction Finding (1899 - 1995) Collection. (See Calhoun record https://calhoun.nps.edu/handle/10945/57364 for further information on this collection and the bibliography). Due to issues of technological obsolescence preventing current and future audiences from accessing the bibliography, DKL exported and converted into the three files on this record the various databases contained in the CD-ROM. The contents of these files are: 1) RDFA_CompleteBibliography_xls.zip [RDFA_CompleteBibliography.xls: Metadata for the complete bibliography, in Excel 97-2003 Workbook format; RDFA_Glossary.xls: Glossary of terms, in Excel 97-2003 Workbookformat; RDFA_Biographies.xls: Biographies of leading figures, in Excel 97-2003 Workbook format]; 2) RDFA_CompleteBibliography_csv.zip [RDFA_CompleteBibliography.TXT: Metadata for the complete bibliography, in CSV format; RDFA_Glossary.TXT: Glossary of terms, in CSV format; RDFA_Biographies.TXT: Biographies of leading figures, in CSV format]; 3) RDFA_CompleteBibliography.pdf: A human readable display of the bibliographic data, as a means of double-checking any possible deviations due to conversion

Advances in Fundamental Physics

This Special Issue celebrates the opening of a new section of the journal Foundation: Physical Sciences. Theoretical and experimental studies related to various areas of fundamental physics are presented in this Special Issue. The published papers are related to the following topics: dark matter, electron impact excitation, second flavor of hydrogen atoms, quantum antenna, molecular hydrogen, molecular hydrogen ion, wave pulses, Brans-Dicke theory, hydrogen Rydberg atom, high-frequency laser field, relativistic mean field formalism, nonlocal continuum field theories, parallel universe, charge exchange, van der Waals broadening, greenhouse effect, strange and unipolar electromagnetic pulses, quasicrystals, Wilhelm-Weber’s electromagnetic force law, axions, photoluminescence, neutron stars, gravitational waves, diatomic molecular spectroscopy, information geometric measures of complexity. Among 21 papers published in this Special Issue, there are 5 reviews and 16 original research papers