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

Commonwealth of Independent States aerospace science and technology, 1992: A bibliography with indexes

This bibliography contains 1237 annotated references to reports and journal articles of Commonwealth of Independent States (CIS) intellectual origin entered into the NASA Scientific and Technical Information System during 1992. Representative subject areas include the following: aeronautics, astronautics, chemistry and materials, engineering, geosciences, life sciences, mathematical and computer sciences, physics, social sciences, and space sciences

Pjezorobotų trajektorijų valdymas nanopalydovų stabilizavimui

Rapid industrial advancement requires novel ideas, new scientific approaches and effective technologies that would ensure quality and precision. Application of piezoelectric actuators in robotics opens many possibilities to create systems with extreme precision and control. A very important step in the development of autonomous robots is the formation of motion trajectories. Classical interpolation methods used for formation of the trajectories are suitable only when robots have wheels, legs or other parts for motion transmission. Piezorobots that are analyzed in this dissertation have no additional components that create motion, only contact points with the static plane. Therefore, traditional motion formation methods are not suitable and a problem arises how to define motion trajectory of such device. The aim of this work is to create a trajectory control algorithm of multi-degrees-of-freedom piezorobot used for nanosatellite stabilization. In order to achieve the objective, the following tasks had to be solved: to analyze constructions of precise piezorobots, their operating principles and motion formation methods; to analyze stabilization problems of satellites and application of multi-degrees-of-freedom piezorobots for nanosatellite stabilization; to create piezorobots’ motion formation algorithms according to electrode excitation schemes, to perform an experimental research; to determine quantitative characteristics of the constructed piezorobots and their motion trajectories. The introduction describes the importance and novelty of this thesis, goals of this work, its practical value and defended statements. The first chapter analyses the principals of ultrasonic devices, gives a thorough review of constructions of ultrasonic devices with multi-degrees-of-freedom. The second chapter provides a review of satellite stabilization principles and how multi-degrees-of-freedom piezorobots can be applied for nanosatellite stabilization. Motion formation methods for ultrasonic devices with multi-degrees-of-freedom are presented. The third chapter presents the detailed analysis of different piezorobots. In the fourth chapter experimental results are provided. Trajectory planning of piezorobot is shown, results are compared to numerical calculations performed in the third chapter. The conclusions about applicability of piezorobots’ motion formation algorithms according to electrode excitation schemes are given. Seven articles focusing on the subject of the dissertation have been published, two presentations on the subject have been presented in conferences at international level. The research for the dissertation has been funded by the Lithuanian State Science and Studies Foundation: European Regional Development Fund, Project No. DOTSUT-234 and Research Council of Lithuania, Project No. MIP-084/2015.Dissertatio

An information geometric perspective on the complexity of macroscopic predictions arising from incomplete information

Motivated by the presence of deep connections among dynamical equations, experimental data, physical systems, and statistical modeling, we report on a series of findings uncovered by the Authors and collaborators during the last decade within the framework of the so-called Information Geometric Approach to Chaos (IGAC). The IGAC is a theoretical modeling scheme that combines methods of information geometry with inductive inference techniques to furnish probabilistic descriptions of complex systems in presence of limited information. In addition to relying on curvature and Jacobi field computations, a suitable indicator of complexity within the IGAC framework is given by the so-called Information Geometric Entropy (IGE). The IGE is an information geometric measure of complexity of geodesic paths on curved statistical manifolds underlying the entropic dynamics of systems specified in terms of probability distributions. In this manuscript, we discuss several illustrative examples wherein our modeling scheme is employed to infer macroscopic predictions when only partial knowledge of the microscopic nature of a given system is available. Finally, we include comments on the strengths and weaknesses of the current version of our proposed theoretical scheme in our concluding remarks.Comment: 26 pages, invited review articl

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

Proceedings of the Workshop on Identification and Control of Flexible Space Structures, Volume 2

The results of a workshop on identification and control of flexible space structures held in San Diego, CA, July 4 to 6, 1984 are discussed. The main objectives of the workshop were to provide a forum to exchange ideas in exploring the most advanced modeling, estimation, identification and control methodologies to flexible space structures. The workshop responded to the rapidly growing interest within NASA in large space systems (space station, platforms, antennas, flight experiments) currently under design. Dynamic structural analysis, control theory, structural vibration and stability, and distributed parameter systems are discussed

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