Дисертації з теми "Satellites en Rotation"

Cette thèse a pour sujet l'étude des mouvements de rotation des corps dits triaxiaux, qui ne sont pas seulement aplatis comme la Terre, mais qui s'écartent aussi de la symétrie axiale. Nous commençons par construire une théorie analytique fondée sur un formalisme Hamiltonien, que nous appliquons ensuite à deux corps triaxiaux : la planète Vénus et le neuvième satellite de Saturne, Phoebe. Ceci nous permet de déterminer pour la première fois leurs coefficients de précession-nutation en longitude et en obliquité. On présente aussi les caractéristiques du mouvement libre de Vénus. Puis nous réévaluons par une approche numérique incluant les éphémérides planétaires ces mouvements de précession-nutation. Pour Vénus, tout en confirmant nos résultats analytiques à une précision relative de 10(-5), ceci nous donne accès aux effets indirects des planètes qui agissent sur son orbite, ainsi qu'a l'évolution de l'obliquité sur une longue période (500\,000 ans). Pour Phoebe, l'étude approfondie des éphémérides montre que le mouvement orbital de ce satellite est loin d'être Keplerien, et qu'il faut développer un modèle analytique plus complexe pour atteindre la même précision que l'intégration numérique dans le cas des corps très perturbés. De manière générale, nous montrerons que l'effet de la triaxialité sur le mouvement de rotation devient plus important à mesure que la vitesse de rotation de l'objet considéré décroît. Pour finir, nous étudions les effets de l'atmosphère, du noyau et des marées gravitationnelles du Soleil sur la durée du jour de Vénus, et comment l'observation de ces effets pourrait contraindre les propriétés géophysiques de la planète

Command generation is a process by which input commands are constructed or modified such that the system's response adheres to a set of desired performance specifications. Previously, a variety of command generation techniques such as input shaping have been used to reduce residual vibration, limit transient deflection, conserve fuel or adhere to numerous other performance specifications or performance measures. This dissertation addresses key issues regarding the application of command generation techniques to tethered satellite systems. The three primary objectives of this research are as follows: 1) create analytically commands that will limit the deflection of flexible systems 2) combine command generation and feedback control to reduce the retrieval time of tethered satellites, and 3) develop command generation techniques for spinning tether systems. More specifically, the proposed research addresses six specific aspects of command generation for tethered satellites systems: 1) create command shapers that can limit the trajectory tracking for a mass under PD control to a pre-specified limit in real time 2) create commands analytically that can limit the transient deflection of a model with one rigid-body and one flexible mode during rest-to-rest maneuvers 3) command generation for a 2-D model of earth-pointing tethered satellites without tether flexibility, 4) command generation for a 2-D model of earth-pointing tethered satellites to reduce tether retrieval time and reduce swing angle, 5) command generation for a 3-D model of earth-pointing tethered satellites without tether flexibility, and 6) command generation for improved spin-up of spinning tethered satellite systems. The proposed research is anticipated to advance the state-of-the-art in the field of command generation for tethered satellite systems and will potentially yield improvements in a number of practical satellite and tether applications.

Attitude control remains one of the top engineering challenges faced by small satellite mission planning and design. Conventional methods for attitude control include propulsion, reaction wheels, magnetic torque coils, and passive stabilization mechanisms, such as permanent magnets that align with planetary magnetic fields. Drawbacks of these conventional attitude control methods for small satellites include size, power consumption, dependence on external magnetic fields, and lack of full control authority. This research investigates an alternative, novel approach to attitude-control method for small satellites, utilizing the noncommutative property of rigid body rotation sequences. Piezoelectric bimorph actuators are used to induce sinusoidal small-amplitude satellite oscillations on two of the satellites axes. While zero net change occurs on these signaled axes, the third axis can develop an average angular rate. This noncommutative attitude control methodology has several advantages over conventional methods, including scalability, power consumption, and operation outside of Earth's magnetic field. This research looks into the feasibility of such a system, and lays the foundation for a simple control system architecture.

We have obtained new images of the protoplanetary disk orbiting TW Hya in visible, total intensity light with the Space Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope (HST), using the newly commissioned BAR5 occulter. These HST/STIS observations achieved an inner working angle of similar to 0."2, or 11.7 au, probing the system at angular radii coincident with recent images of the disk obtained by ALMA and in polarized intensity near-infrared light. By comparing our new STIS images to those taken with STIS in 2000 and with NICMOS in 1998, 2004, and 2005, we demonstrate that TW Hya's azimuthal surface brightness asymmetry moves coherently in position angle. Between 50 au and 141 au we measure a constant angular velocity in the azimuthal brightness asymmetry of 22 degrees.7. 7 yr(-1) in a counterclockwise direction, equivalent to a period of 15.9. yr assuming circular motion. Both the (short) inferred period and lack of radial dependence of the moving shadow pattern are inconsistent with Keplerian rotation at these disk radii. We hypothesize that the asymmetry arises from the fact that the disk interior to 1 au is inclined and precessing owing to a planetary companion, thus partially shadowing the outer disk. Further monitoring of this and other shadows on protoplanetary disks potentially opens a new avenue for indirectly observing the sites of planet formation.

Plus de 4000 exoplanètes ont été découvertes au cours de ces 25 dernières années, pour la plupart en orbite autour d’étoiles de faible masse. Dans les systèmes planétaires à très courte période orbitale, les interactions de marée étoile-planète sont connues pour gouverner l’évolution tardive de l’architecture orbitale des systèmes et de la rotation de leur étoile hôte, comme c’est aussi le cas dans les systèmes serrés planète-satellite(s) de notre système solaire tels que les systèmes jovien et saturnien. Les temps caractéristiques de variation des paramètres orbitaux et de rotation des corps, sont dictés par l’amplitude de la dissipation des marées qui varie considérablement avec la masse, la rotation et la métallicité des étoiles ainsi qu’avec la structure et la dynamique internes des étoiles et des planètes. Pour modéliser et caractériser de manière réaliste la dissipation de marée dans les enveloppes convectives de ces objets astrophysiques, deux mécanismes physiques clés sont étudiés dans cette thèse: la rotation différentielle et le magnétisme, au travers de leur influence sur les flots de marées en milieu convectif. Ces deux aspects sont explorés à l’aide d’approches semi-analytiques et numériques, tout en appliquant nos résultats à l’intérieur des étoiles au cours de leur évolution, et des planètes géantes gazeuses telles que Jupiter et Saturne. Tout d’abord, nous nous sommes intéressés à l’impact du magnétisme sur l’excitation et la dissipation des ondes magnéto-inertielles de marée, le long de l’évolution des étoiles de faible masse, de type spectral M à F, en examinant les limites de leur enveloppe convective, à savoir l’interface entre la zone radiative et convective et les régions proches de leur surface. Pour ce faire, nous avons utilisé en synergie la physique des ondes de marée, les lois d’échelle issues de la théorie dynamo qui nous permettent d’estimer l’amplitude d’un champ magnétique à grande échelle, et les grilles de modèles numériques d’évolution stellaire prenant en compte la rotation. On montre ainsi que la contribution du magnétisme sur le forçage de marée, c’est-à-dire sur l’excitation des ondes, reste négligeable devant la contribution hydrodynamique classiquement utilisée, et ce quelle que soit la position dans l’enveloppe convective, la masse, ou l’âge de l’étoile de faible masse étudiée. A contrario, le mécanisme de dissipation Ohmique des ondes magnéto-inertielles est un mécanisme très efficace, voire prépondérant devant la dissipation visqueuse, pour des étoiles de type M à F, de la pré-séquence principale à la fin de la séquence principale, dans toute leur enveloppe convective. Ces résultats s’appliquent aussi dans le cas de Jupiter et de ses satellites galiléens. Parallèlement à ce travail, nous avons développé un modèle local de boîte cisaillée, incliné par rapport à l’axe de rotation du corps étudié, afin de comprendre l’interaction complexe entre les ondes inertielles de marée et les flots zonaux au voisinage des couches critiques, et en particulier à la résonance de corotation, qui sont des régions où la fréquence des ondes de marée est nulle ou commensurable avec la fréquence de rotation locale du corps considéré. Ce modèle nous a permis d’étudier l’impact de différents profils de rotation réalistes, comme ceux que l’on peut observer dans les étoiles de type solaire, ou dans les planètes géantes telles que Jupiter et Saturne. Grâce à ce travail, nous avons identifié différents régimes de transmission du flux d’énergie transporté par les ondes, pour lesquels l’onde peut, au voisinage d’une couche critique, soit déposer de l’énergie et être amortie, soit extraire de l’énergie du flot moyen et ainsi être amplifiée. Ces différents régimes de transmission existent pour chacun des profils de rotation examinés, coniques et cylindriques, et dépendent du niveau critique rencontré, des propriétés des ondes et du profil de l’écoulement moyen
More than 4000 exoplanets have been discovered in the last 25 years, most of them around low-massstars. In close planetary systems, star-planet tidal interactions are known to govern the late evolution of the systems’ orbital architecture and the rotation of their host star, as is also the case in the tight planet-satellite systems of our solar system such as the Jovian and Saturnian systems. The characteristic times of variation of orbital parameters and bodies’ rotation are dictated by the magnitude of tidal dissipation, which varies considerably with the mass, rotation and metallicity of stars and with the structure and internal dynamics of stars and planets.In order to model and realistically characterise the tidal dissipation in the convective envelopes of these astrophysical objects, two key physical mechanisms are studied in this thesis : differential rotation and magnetism, through their influence on tidal flows in convective regions. These two aspects are explored using semi-analytical and numerical approaches, while applying our results inside stars during their evolution, and gas giant planets such as Jupiter and Saturn.First of all, we have been interested in the impact of magnetism on the excitation and dissipation of tidal magneto-inertial waves along the evolution of low-mass stars of spectral type M to F, by examining the limits of their convective envelope, i.e. the interface between the radiative and convective zones and the regions close to their surface. To do so, we have used in synergy tidal wave physics, the scaling laws from dynamo theory that allow us to estimate the amplitude of a large-scale magnetic field, and the grids of numerical models of stellar evolution taking into account rotation. We thus show that the contribution of magnetism on tidal forcing, i.e. on wave excitation, remains negligible compared to the hydrodynamic contribution classically used, whatever the position in the convective envelope, the mass, or the age of the studied low mass star. On the other hand, the Ohmic dissipation mechanism of magneto-inertial waves is a very efficient mechanism, even preponderant in front of the viscous dissipation, for M to F type stars, from the pre-main sequence to the end of the main sequence, in all their convective envelope. These results also apply in the case of Jupiter and its Galilean satellites.In parallel to this work, we have developed a local shear-box model, inclined with respect to the axis ofrotation of the studied body, in order to understand the complex interaction between tidal inertial waves and zonal flows in the vicinity of critical layers, and in particular at the corotation resonance, which are regions where the tidal wave frequency vanishes or is commensurable with the local rotation frequency of the considered body. This model has allowed us to study the impact of different realistic rotation profiles, such as those observed in solar-type stars, or in giant planets such as Jupiter and Saturn. Thanks to this work, we have identified different transmission regimes of the wave energy flux, for which the wave can, in the vicinity of a critical layer, either deposit energy and be damped, or extract energy from the mean flow and thus be amplified. These different transmission regimes exist for each of the examined conical and cylindrical rotational profiles, and depend on the critical level encountered, the wave properties and the mean flow profile

Les variations de l'orientation de la terre dans l'espace sont aujourd'hui mesurees par differentes techniques astrometriques ; radio-interferometrie a tres longue base, tirs lasers sur la lune, et mesures de positionnement des satellites artificiels. Les parametres de rotation de la terre, utilises pour decrire les variations d'orientation sont determines avec une precision inferieure a 1 milliseconde de degre, et une resolution temporelle de 1 jour. Nous presentons les resultats de mesure des variations a courte periode de l'orientation (variations diurnes et subdiurnes) et nous montrons comment ces mesures permettent d'obtenir une description complete des variations du vecteur instantane de rotation de la terre. Cette etape est indispensable pour modeliser les observations obtenues par les instruments inertiels (qui sont sensibles aux variations du vecteur instantane de rotation). Nous etudions dans cette these l'apport des gravimetres supraconducteurs et des gyroscopes a la mesure de la rotation terrestre. L'utilisation conjointe de mesures classiques d'orientation et de mesures gravimetriques nous conduit a la determination des effets de non-rigidite de la terre. Les resultats obtenus a partir des mesures gravimetriques demontrent l'interet des gyroscopes qui sont, eux, des instruments inertiels specifiquement dedies aux mesures des variations de la rotation terrestre. Apres la presentation des realisations historiques et recentes des gyroscopes, nous etudions leurs futures applications astrometriques et geodesiques.

La qualité actuelle des techniques de Géodésie Spatiale permet d'estimer des séries temporelles de produits géodésiques tels que les paramètres de rotation et les positions de stations terrestres. Ces nouveaux produits doivent être utilisés dans la matérialisation des Systèmes de Référence Terrestres, en constantes évolution et amélioration. Ils doivent aussi mettre en évidence les phénomènes, globaux ou locaux, régissant la rotation terrestre et les mouvements de la croûte. C'est dans ce contexte riche d'enjeux divers que s'inscrivent ces travaux. Leur but premier a été l'élaboration et l'application d'une méthode d'estimation de séries temporelles de positions de stations et de paramètres de rotation de la Terre par l'analyse de données de télémétrie laser sur satellites. Cette technique est en effet une des clefs de voûte du Repère de Référence Terrestre International (ITRF). En guise de validation de cette méthode, douze ans de données (1993-2004) sur les deux satellites LAGEOS ont été traités et analysés. Si les techniques géodésiques présentent certes des forces individuellement, c'est dans leur combinaison qu'elles montrent réellement toutes leurs potentialités. À ce titre, le Groupe de Recherche en Géodésie Spatiale (GRGS) a mené une expérience de combinaison de cinq techniques géodésiques (SLR/LLR/GPS/DORIS/VLBI) au niveau des observations sur l'année 2002. J'ai activement participé à cette expérience dont le but principal était de démontrer la force d'une telle approche pour la détermination de séries temporelles de coordonnées du pôle et du Temps Universel.

La qualité actuelle des techniques de géodésie spatiale permet d'estimer des séries temporelles de produits géodésiques tels que les paramètres de rotation et les positions de stations terrestres. Ces nouveaux produits doivent être utilisés dans la matérialisation des systèmes de référence terrestres, en constantes évolution et amélioration. Ils doivent aussi mettre en évidence les phénomènes, globaux ou locaux, régissant la rotation terrestre et les mouvements de la croûte. C’est dans ce contexte riche d’enjeux divers que s’inscrivent ces travaux. Leur but premier a été l’élaboration et l’application d’une méthode d’estimation de séries temporelles de positions de stations et de paramètres de rotation de la terre par l’analyse de données de télémétrie laser sur satellites. Cette technique est en effet une des clefs de voûte du repère de référence terrestre international(ITRF). En guise de validation de cette méthode, douze ans de données (1993-2004) sur les deux satellites LAGEOS ont été traités et analysés. Si les techniques géodésiques présentent certes des forces individuellement, c’est dans leur combinaison qu’elles montrent réellement toutes leur potentialités. A ce titre, le Groupe de recherche en géodésie spatiale (GRGS) a mené une expérience de combinaison de cinq techniques géodésiques (SLR/LLR/DORIS/VLBI) au niveau des observations sur l’année 2002. J'ai activement participé à cette expérience dont le but principal était de démontrer la force d’une telle approche pour la détermination de séries temporelles de coordonnées du pôle et du temps universel.

La distribution des masses à l'intérieur de la Terre régit la vitesse de rotation terrestre, ainsi que le comportement de l'axe de rotation terrestre dans la Terre, et dans l'espace. Ces distributions de masses peuvent être mesurées depuis l'espace grâce aux satellites artificiels, dont l'orbitographie donne accès à la détermination du champ de gravité terrestre. Par conséquent, les variations temporelles du champ de gravité peuvent être reliées aux variations des paramètres d'orientation terrestre (via le tenseur d'inertie). Des progrès considérables ont été effectués ces dernières années dans la modélisation des effets des couches fluides. Et de nos jours, les mesures d'orientation terrestre dans l'espace obtenues par Interférométrie à très Longue Base (VLBI) ont une exactitude meilleure qu'une milliseconde de degré. Ceci permet de progresser dans la connaissance de la dynamique globale de la Terre. Mon travail de thèse a eu pour but d'utiliser la mesure du champ de gravité et de ses variations comme outil pour compléter la modélisation de la rotation terrestre. D'une part, en vue de l'utilisation des mesures du satellite GRACE, d'une grande précision, nous avons effectué des comparaisons précises des méthodes numériques d'intégration d'orbite de Cowell et d'Encke dans le logiciel GINS du GRGS. D'autre part, nous avons établi les liens théoriques entre les Paramètres d'Orientation Terrestres (EOP) et les variations des coefficients du champ de gravité. Ainsi, nous avons utilisé les données de variations temporelles des coefficients de degré 2 du géopotentiel pour en déduire leur influence sur la longueur du jour, le mouvement du pôle et la précession de l'équateur.

La complexité des missions spatiales a augmenté de façon exponentielle, avec des exigences croissantes en matière de performance, de précision et de robustesse. Cette évolution est due à la fois aux progrès technologiques et à la nécessité de satisfaire de nouveaux défis, tels que les satellites en rotation (spinnés), l'assemblage en orbite et le service en orbite. Ces missions nécessitent l'intégration de systèmes mécaniques complexes, notamment des réservoirs de carburant liquide et ballotant, des systèmes de pointage précis et des structures flexibles qui présentent généralement des modes à basse fréquence, proches en fréquence et peu amortis. À mesure que les engins spatiaux deviennent plus modulaires avec plusieurs composants interconnectés tels que les antennes et les charges utiles, il est essentiel de modéliser et de contrôler avec précision ces systèmes multicorps complexes. Les interactions entre les structures flexibles et les systèmes de contrôle peuvent avoir un impact significatif sur les tâches critiques telles que le contrôle de l'attitude et la précision du pointage. Il est donc essentiel de prendre en compte les dynamiques couplées et les perturbations externes pour garantir le succès de la mission.Afin de résoudre ces problèmes, cette thèse présente une approche unifiée de la modélisation et du contrôle des systèmes multicorps flexibles dans les missions spatiales. Elle utilise des modèles de représentation fractionnaire linéaire (LFR) pour capturer efficacement la dynamique complexe et les incertitudes inhérentes à ces scénarios. La recherche commence par la dérivation d'un modèle LFR pour une poutre extsc{Euler}- extsc{Bernoulli} flexible et en rotation, prenant en compte les forces centrifuges et leur dépendance par rapport à la vitesse angulaire. Ce modèle à six degrés de liberté (DOFs) intègre les dynamiques de flexion, de traction et de torsion et est conçu pour être compatible avec l'approche des ports à deux entrées et deux sorties (TITOP), permettant de modéliser des systèmes multicorps complexes. Ce manuscrit présente également un modèle multicorps pour un scénario de mission de vaisseau spatial en rotation, suivi de la conception d'un système de contrôle.La thèse étend l'application des modèles LFR à une mission de service en orbite, en se concentrant sur le contrôle robuste de la dynamique d'attitude malgré les incertitudes et les paramètres variables du système. Une nouvelle approche de modélisation pour le mécanisme d'amarrage est introduite pour prendre en compte les propriétés dynamiques de rigidité et d'amortissement de la chaîne cinématique en boucle fermée formée par le véhicule chasseur et le véhicule cible. Un système de contrôle par rétroaction assurant une stabilité et des performances robustes pendant toutes les phases de la mission est proposé et validé par une analyse structurée des valeurs singulières.A partir de ces éléments, la thèse développe finalement une méthodologie complète pour la modélisation d'une mission d'assemblage en orbite impliquant un robot à bras multiples construisant une grande structure flexible. Ce travail aborde également la dynamique de couplage entre le robot et la structure évolutive tout en considérant les changements significatifs d'inertie et de flexibilité au cours du processus d'assemblage. Un algorithme d'optimisation de planification de tâches est finalement proposé pour assurer des opérations robotiques stables et efficaces, mettant en évidence l'efficacité de l'approche de modélisation basée sur la représentation LFR
Space missions have grown exponentially in complexity, with increasing demands for performance, precision and robustness. This evolution is driven by both technological advancements and the need for spacecraft to support diverse mission objectives, such as spinning spacecraft, on-orbit assembly and on-orbit servicing. These missions require the integration of large and complex designs, including dynamic fuel tanks, precise pointing systems and flexible structures that typically exhibit low-frequency, closely spaced and poorly damped modes. As spacecraft become more modular with multiple interconnected components like antennas and payloads, accurately modeling and controlling these complex multibody systems is crucial. The interactions between flexible structures and control systems can significantly impact mission-critical tasks such as attitude control and pointing accuracy, making it essential to address the coupled dynamics and external disturbances to ensure successful mission outcomes.In order to tackle these problems, this thesis presents a unified approach to the modeling and control of flexible multibody systems in space missions. It utilizes linear fractional representation (LFR) models to effectively capture the complex dynamics and uncertainties inherent in these scenarios. The research begins with the derivation of an LFR model for a flexible and spinning extsc{Euler}- extsc{Bernoulli} beam, fully accounting for centrifugal forces and their dependence on the angular velocity. This six degrees of freedom model integrates bending, traction and torsion dynamics and is designed to be compatible with the Two-Input-Two-Output Ports (TITOP) approach, enabling the modeling of complex multibody systems. This manuscript also introduces a multibody model for a spinning spacecraft mission scenario, followed by the design of a control system.The thesis further extends the application of LFR models to an on-orbit servicing mission, focusing on the robust control of attitude dynamics despite uncertainties and varying system parameters. A novel modeling approach for a docking mechanism is introduced, capturing the dynamic stiffness and damping properties of the closed-loop kinematic chain formed by the chaser and target spacecraft. The design of a feedback control system ensuring robust stability and performance across all mission phases is proposed, validated through structured singular value analysis.Building on this foundation, the thesis finally develops a comprehensive methodology for modeling an on-orbit assembly mission involving a multi-arm robot constructing a large flexible structure. This work also addresses the coupling dynamics between the robot and the evolving structure while considering significant changes in inertia and flexibility during the assembly process. A path optimization algorithm is ultimately proposed to ensure stable and efficient robotic operations, highlighting the effectiveness of the LFR-based modeling approach

Over recent years considerable advances have taken place in the field of space geodesy, resulting in a number of highly precise global positioning techniques. The increased resolution of many of the scientific products from the new observational techniques has stimulated the interest of not only geodesists but also geophysicists. Furthermore, their potential to determine the orientation of the earth's axis of rotation (polar motion) and the variations of the rate of rotation of the earth about that axis, was recognised by the scientific community. The result was the establishment of Project MERIT, to intercompare these new observational techniques. Satellite Laser Ranging, a method of measuring the distance from a point on the earth's surface to an artificial satellite by means of timing the flight of a short pulse of laser light, is currently the most accurate available means of tracking near earth satellites. However, in order to reach the accuracy requirements of current geodetic applications dedicated satellites, such as the NASA LAser GEOdynamic Satellite (LAGEOS), must be tracked and specialised processing software must be used. This Thesis describes the basic theory behind the analysis of Satellite Laser Ranging Observations, with a special emphasis on the determination of earth rotation parameters (the polar motion and the variations in the rate of rotation). The development and testing, at Nottingham, of the Satellite Orbit Determination and Analysis Package Of Programs, SODAPOP, for the processing of laser range data, is described. The thesis also presents and discusses the results of the analysis of laser range observations the LAGEOS satellite, from the short and main campaigns of project MERIT.

Cette thèse présente une théorie analytique de l'évolution d'attitude d'un satellite artificiel en rotation perturbée. La contrainte principale est celle d'une rotation lente fortement perturbée avec l'axe pointant loin d'une position d'équilibre. De plus les trois axes d'inertie du satellite peuvent être inégaux. Une solution formelle est développée au deuxième ordre suivant les puissances d'un petit paramètre caractéristique de l'ordre de grandeur des couples perturbateurs et la théorie peut convenir quelles que soient les forces perturbatrices intérieures ou extérieures susceptibles de créer des couples. Ces couples sont développées en série de Fourier et la théorie s'applique quelle que soit la longueur de ces séries. En effet les coefficients de la solution sont donnés par une loi de formation itérative. Ainsi, dans un premier temps, cette thèse propose les bases et le développement d'une théorie relativement générale tout en restant proche des configurations concrètes pour lesquelles Hipparcos, satellite astrométrique à balayage continu du ciel, est choisi pour référence. Dans un second temps, une application aux contraintes extrêmement exigeantes d'Hipparcos permet d'apprécier le degré d'exactitude et la validité de la solution, puis de montrer la convergence des expressions issues de la théorie, suivant les ordres croissants des développements, et enfin de confirmer et généraliser les hypothèses et l'algorithme établis dans les procédés numériques de calcul du mouvement d'attitude d'Hipparcos par le consortium FAST chargé de la réduction des données de ce satellite. L'influence du rapport intensité résultante des couples perturbateurs-énergie de rotation sur la dérive d'attitude, par rapport à une théorie donnée, est telle que plus celui-ci est faible, plus un ordre faible du développement de la théorie suffit à donner une bonne précision sur la connaissance de l'évolution de l'attitude.

Designs for geostationary (GEO) solar power satellites (SPS) are extremely large in scale, more than one order of magnitude larger than the International Space Station. In this thesis a detailed study of the orbit dynamics of SPS is performed. Analytical equations, derived by the process of averaging of the SPS equations of motion, are used to determine the long-term orbital evolution. Previous SPS studies have simply assumed a GEO as the operational orbit, and then designed control systems for maintaining the orbit within acceptable nominal values. It is found that an alternative SPS orbital location known as the geosynchronous Laplace plane orbit (GLPO) is superior to GEO in many aspects. An SPS in GLPO requires virtually no fuel to maintain its orbit, minimises the risk of debris creation at geosynchronous altitude, and is extremely robust operationally, i.e. loss of control is inconsequential. The GLPO SPS requires approximately 10^5 kg less fuel per year compared to a GEO SPS while providing near equivalent power delivery. Although savings in orbit control are achieved, depending on the mass distribution of the SPS, attitude control costs may be incurred by placing an SPS in GLPO. Consideration of the attitude dynamics of SPS has motivated the development of a model for the rotational dynamics of a body which includes energy dissipation and the effects of external torques. Multiple spring-damper masses are used to provide a mechanism for energy dissipation. This rotational dynamics model is used to assess the naturally stable attitude configurations of a SPS design in geosynchronous orbit subject to gravity gradient torque. It is found that for a large planar array, a dynamically stable configuration requiring nominal orbit-attitude control is possible. This involves rotating around the maximum axis of inertia at the orbit rate, with the minimal axis aligned in the radial direction. It will be shown that a SPS in this configuration while in GLPO requires virtually no orbit or attitude control. The most significant result of the research in this thesis is proving that a SPS can operate in GLPO with nominal orbit control and yet still deliver almost equivalent power to the Earth’s surface as the same SPS would in a controlled GEO.

In this thesis, rotation, scale and translation (RST) invariant automatic target recognition (ATR) for satellite imagery is presented. Template matching is used to realize the target recognition. However, unlike most of the studies of template matching in the literature, RST invariance is required in our problem, since most of the time we will have only a small number of templates of each target, while the targets to be recognized in the scenes will have various orientations, scaling and translations. RST invariance is studied in detail and implemented with some of the competing methods in the literature, such as Fourier-Mellin transform and bipectrum combined with log-polar mapping. Phase correlation and normalized cross-correlation are used as similarity metrics. Encountered drawbacks were overcome with additional operations and modifications of the algorithms. ATR using reconstruction of the target image with respect to the template, based on bispectrum, log-polar mapping and phase correlation outperformed the other methods and successful recognition was realized for various target types, especially for targets on relatively simpler backgrounds, i.e. containing little or no other objects.

Cette thèse porte sur la rotation et l'activité magnétique des étoiles sismiques de type solaire. Nous utilisons les données provenant du satellite Kepler pour étudier l'histoire rotationnelle d'étoiles de type solaire. Dans un premier temps, nous présentons le contexte de l'astérosismologie. Nous décrivons ensuite l'outil de mesure de la rotation que nous avons développé durant cette thèse. Nous le comparons aux autres méthodes utilisées et montrons que ses performances sont excellentes. Dans un deuxième temps, nous appliquons cet outil à 500 étoiles de type solaire en séquence principale et en phase sous-géante. Nous mesurons la rotation de surface et l'activité de 300 étoiles. De plus, nous montrons que les périodes de rotation mesurées et les âges estimés grâce à l'astérosismologie ne respectent pas les relations utilisées et proposons de les modifier pour les âges élevés. Nous utilisons également la mesure de la rotation de surface pour estimer la rotation interne de certaines étoiles en séquence principale et montrons qu'elles ont, comme le Soleil, un faible taux de rotation différentielle radiale. Enfin, dans un troisième temps nous appliquons notre outil à 17000 géantes rouges. Nous repérons 360 géantes rouges en rotation rapide et comparons nos taux de détection aux prévisions théoriques. Nous utilisons également la modélisation stellaire pour reproduire le profi de rotation d'une géante rouge. Nous montrons l'importance de considérer de nouveau processus de transport de moment cinétique dans les codes d'évolution stellaire. Ce travail pose des contraintes fortes sur l'évolution de la rotation et de l'activité des étoiles, largement utilisables par la communauté
This thesis concerns the study of seismic solar-like stars' rotation and magnetic activity. We use data from the Kepler satellite to study the rotational history of these stars throughout their evolution. In the first part, we present the context of asteroseismology. We continue by describing the tool we developed to measure surface rotation of stars. We compare it to other methods and show that its efficiency is very high. In the second part, we apply this tool to 500 main-sequence and sub-giant solar-like stars. We measure surface rotation periods and activity levels for 300 of them. We show that the measured periods and the ages from asteroseismology do not agree well with the standard period-age relationships and propose to modify these relationships for old stars. We also use thE surface rotation as a constraint to estimate the internai rotation of a small number of seismic targets. We demonstrate that these stars have, like the Sun, a very low differential rotation ratio. In the third part, we apply our surface rotation-measuring tool to 17,000 red giants. We identify 360 fast rotating red giants and compare our detection rates with the ones predicted by theory to better understand the reasons for this rapid rotation. We also use stellar modelling to reproduce the internai rotation profile of a particular red giant. This allows us to emphasize how important implementing new angular momentum transport mechanisms in stellar evolution codes is. This work offers new results that are useful to a very wide community of stellar physicists. It also puts strona constraints on the evolution of solar-like stars' rotation and maanetic activity

Dans le contexte du changement climatique mondial et la nécessité d'étudier les conséquences de l'ampleur de la fonte des glaces continentales sur le niveau des mers ainsi que sur la répartition des masses fluides à l'échelle du globe, notre travail de thèse s'intéresse aux phénomènes à très grande échelle qui modifient la forme de la Terre, son champ de gravité et l'équilibre de sa rotation. Il se focalise sur la stratégie à mettre en place pour observer et modéliser des variations très fines sur des termes géodynamiques (coefficients de bas degrés) qui sont encore aujourd'hui mal connus, et pourtant déterminants dans l'établissement des références terrestres fondamentales. La première partie de la thèse concerne l'observation du mouvement du géocentre par différentes techniques de mesures géodésiques. Ces travaux débouchent, par une meilleure maîtrise des sources d'erreurs, sur une explication des écarts entre les séries de mesures laser du mouvement du géocentre obtenues sur les satellites LAGEOS (référence actuelle pour l'origine du repère international, ITRF) et celles obtenues indépendamment sur le satellite altimétrique Jason-2 à partir d'observations DORIS/laser/GPS. La deuxième partie de la thèse s'intéresse à la détermination cohérente des coefficients de degrés 0 (coefficient gravitationnel GM), 1 (géocentre), et 2 (inertie/orientation) du champ de pesanteur terrestre. Nous utilisons pour cela les mesures de télémétrie laser disponibles depuis les années 1970 (par exemple, Starlette lancé en précurseur par le CNES dès 1975), car ce sont les seules mesures à caractère absolu qui donnent accès à ces trois premiers degrés. Nos analyses menées sur près de 35 ans aboutissent à une nouvelle valeur de la constante gravitationnelle géocentrique et la détection d'une réponse viscoélastique du manteau de notre planète aux échelles de temps décennales, par combinaison des termes de degré 2 et paramètres d'orientation de la Terre avec les équations d'Euler-Liouville
In the context of the overall climate change and the need to analyze the implications of the record ice-sheet melting for the sea level and global fluid mass redistribution budgets, our PhD work focuses on large-scale phenomena impacting the shape of the Earth, its gravity field, and the stability of its rotation pole. We explore strategies for the observation and modeling of subtle variations in geodynamic parameters (lowermost degree coefficients), which are still poorly constrained, despite their importance in determining fundamental terrestrial references. The first part of this PhD is dedicated to the observation of the geocenter motion, using different geodetic technics. The outcomes of this work provided explanations, through a correct handling of the dominant error sources, for the discrepancies between the reference laser-based LAGEOS geocenter time series (defining the origin of the international frame, ITRF) and independent solutions using DORIS/laser/GPS observations from the Jason-2 altimeter satellite. The second part of this PhD presents a self-consistent determination of the degrees 0 (gravitational coefficient GM), 1 (geocenter motion), and 2 (Earth's figure axis orientation) of the geopotential. To this end, we use the available laser data since the 1970s (e.g., the first geodetic satellite Starlette launched by CNES in 1975), as they are the only absolute measurements making possible the monitoring of the first three degree terms. Based on 35 years of satellite laser tracking, an updated value of the geocentric gravitational coefficient was obtained, and a viscoelastic behavior of the Earth's mantle manifesting at decadal time scales was exhibited, combining the derived figure axis variations of the Earth and polar motion observations with the Euler-Liouville equations

Resumo: Este trabalho tem por objetivo analisar a estabilidade do movimento rotacional de satélites arti…ciais simétricos (com dois momentos principais de inércia iguais), em órbita circular, sob a in‡uência do torque de gradiente de gravidade, usando as variáveis de Andoyer. O método utilizado neste trabalho para analisar a estabilidade é o teorema de Kovalev e Savchenko,o qual requer a redução da Hamiltoniana na forma normal até quarta ordem, por meio de transformações canônicas em torno dos pontos de equilíbrio. Os coe…cientes da Hamiltoniana normal são indispensáveis no estudo da estabilidade não linear de seus pontos de equilíbrio, de acordo com as três condições estabelecidas no teorema. Aplicações foram realizadas para satélites de médio e pequeno porte, com dados similares a satélites reais, utilizando o software MATHEMATICA. Diversos pontos de equilíbrio estáveis foram encontrados e regiões de equilíbrio ao redor destes pontos foram estabelecidas através de variações na inclinação orbital e nos momentos principais de inércia do satélite. Em comparação com trabalhos anteriores os resultados mostram um maior número de pontos de equilíbrio e uma otimização no algoritmo de determinação da forma normal e na análise de estabilidade, devido a possibilidade de inclusão de cálculo analítico dos coe…cientes da Hamiltoniana normal de 4a ordem. Assim, a utilização das variáveis de Andoyer se mostra adequada para a análise da estabilidade do movimento rotacional, podendo ser útil em análises de missões espaciais. Salienta-se que o lançamento do satélite em regiões de estabilidade pode contribuir para a manutenção da atitude do satélite, podendo gerar uma economia de combustível através de um menor número de manobras de atitude para manter a atitude desejada da missão
Abstract: This work aims to analyze the stability of the rotational motion of symmetrical arti…cial satellite (with two principal moments of inertia equal), in circular orbit with the in‡uence of gravity gradient torque, using the variables of Andoyer. The used method in this paper to analyze stability is the Kovalev-Savchenko theorem, which requires the reduction of the Hamiltonian in its normal form up to fourth order by means of canonical transformations around equilibrium points. The coe¢ cients of the normal Hamiltonian are indispensable in the study of nonlinear stability of its equilibrium points according the three established conditions in the theorem studied. The applications were made to satellites of medium and small size, with data similar to real satellites, using the software MATHEMATICA. Several stable equilibrium points were determined and regions around these equilibrium points have been established by variations in orbital inclination and the principal moments of inertia of the satellite. In comparison with previous results show a larger number of equilibrium points and an optimization in algorithm determining the normal form in the stability analysis, due the possibility of inclusion of analytical calculation of the coe¢ cients of the normal Hamiltonian of 4th order. Thus, the uses of variables Andoyer are adequate for the stability analysis of rotational motion, which can be useful for the analysis of space missions. Stresses those, the launch of the satellite regions of stability can contribute to the maintenance of the satellite attitude, which can generate a fuel economy through lower number of attitude maneuvers to maintain desired attitude of the mission
Orientador: Maria Cecília Franca de Paula Santos Zanardi
Coorientador: Jorge Kennety Silva Formiga
Banca: Ernesto Vieira
Banca: Mário Cesar Ricci
Mestre

Orientador: Maria Cecília F. P. S. Zanardi
Banca: Rodolpho Vilhena de Moraes
Banca: Sandro da Silva Fernandes
Resumo: A atitude de um satélite artificial representa sua orientação no espaço, de modo que através da atitude pode-se conhecer a orientação espacial do satélite pela relação entre dois sistemas de coordenadas, um dels fixo no corpo do setélite e o outro associado com umsistema de referência inercial. Apesar da atitude ser bem representada por vários conjuntos de variáveis, todos estes apresentam limitações em sua utilização. Focaliza-se neste trabalho um conjunto de variáveis canônicas não singulares, aplicáveis ao movimento racional de satélites artificiais. Estas variáveis são úteis para o caso em que o vetor momento angular de rotação coincide com o maior momento principal de inércia do satélite. As equações dinâmicas do movimento rotacional são deduzidas pelo formalismo hamiltoniano e então integradas para análise do movimento rotacional livre de torques externos. Soluções analíticas aproximadas são obtidas e comparadas com as soluções gerais, representadas em funções elípticas, e com soluções numéricas. A Hamiltoniana média associada ao Torque de Gradiente de Gravidade é também incluida e as equações diferenciais do movimento pertubado são deduzidas em termos das variáveis não singulares. A integração analítica e numérica destas equações permite uma análise qualitativa e quantitativa das variáveis não singulares utilizadas para o movimento rotacional, quando se considera a pertubação provocada pelo Torque da Gradiente de Gravidade. Ao mesmo tempo esta análise aponta para limitações de intervalos de tempo em que algumas soluções devem ser utilizadas. Aplicações são realizadas para satélites com características similares as dos Satélites Brasileirs de Coleta de Dados (SCD1 e SCD2).
Abstract: The attitude of an artificial satellite represents its orientation in the space, in way that through the attitude can be known the spatial orientation of the satellite for the relation between two systems of coordinates, one of them fixed in the satellite and other associate with an Inertial Referencce System. Many sets of variables are used to represent the satellite attitude, but some of them present limitations in its use. A set of non-singular canonical variables, applicable to the rotational motion of artificial satellites, is focused in this work. Thse variables are useful for the case where the rotational angular momentum vector coincides with the biggest principal moment of inertia of the satellite. The dynamic equations of the rotational motion are deduced by the Hamiltonian formalism and then they are integrated for the analysis of the torque-free rotational motion. Approximated analytical solutions are gotten and compared with the general solutions and numerical solutions. The associated mean Hamiltonian to the Gravity Gradient Torque also enclosed and the differential equations of the motion are deduced for the non-singular variables. The analytical and numeical integration of these equations allow a qualitative and quantitative analysis of these non-singular variables, when the disturbance of the Gravity Gradiente Torque is considered. At the same time this analysis point to limitations of time intervals where some solutions must be used. Applications are done for the satellite with similar characteristics of the Brzilian Satellites of Collection of Data (SCD1 and SCD2).
Mestre

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Este trabalho tem por objetivo analisar a estabilidade do movimento rotacional de satélites arti ciais simétricos (com dois momentos principais de inércia iguais), em órbita circular, sob a in uência do torque de gradiente de gravidade, usando as variáveis de Andoyer. O método utilizado neste trabalho para analisar a estabilidade é o teorema de Kovalev e Savchenko,o qual requer a redução da Hamiltoniana na forma normal até quarta ordem, por meio de transformações canônicas em torno dos pontos de equilíbrio. Os coe cientes da Hamiltoniana normal são indispensáveis no estudo da estabilidade não linear de seus pontos de equilíbrio, de acordo com as três condições estabelecidas no teorema. Aplicações foram realizadas para satélites de médio e pequeno porte, com dados similares a satélites reais, utilizando o software MATHEMATICA. Diversos pontos de equilíbrio estáveis foram encontrados e regiões de equilíbrio ao redor destes pontos foram estabelecidas através de variações na inclinação orbital e nos momentos principais de inércia do satélite. Em comparação com trabalhos anteriores os resultados mostram um maior número de pontos de equilíbrio e uma otimização no algoritmo de determinação da forma normal e na análise de estabilidade, devido a possibilidade de inclusão de cálculo analítico dos coe cientes da Hamiltoniana normal de 4a ordem. Assim, a utilização das variáveis de Andoyer se mostra adequada para a análise da estabilidade do movimento rotacional, podendo ser útil em análises de missões espaciais. Salienta-se que o lançamento do satélite em regiões de estabilidade pode contribuir para a manutenção da atitude do satélite, podendo gerar uma economia de combustível através de um menor número de manobras de atitude para manter a atitude desejada da missão
This work aims to analyze the stability of the rotational motion of symmetrical arti cial satellite (with two principal moments of inertia equal), in circular orbit with the in uence of gravity gradient torque, using the variables of Andoyer. The used method in this paper to analyze stability is the Kovalev-Savchenko theorem, which requires the reduction of the Hamiltonian in its normal form up to fourth order by means of canonical transformations around equilibrium points. The coe¢ cients of the normal Hamiltonian are indispensable in the study of nonlinear stability of its equilibrium points according the three established conditions in the theorem studied. The applications were made to satellites of medium and small size, with data similar to real satellites, using the software MATHEMATICA. Several stable equilibrium points were determined and regions around these equilibrium points have been established by variations in orbital inclination and the principal moments of inertia of the satellite. In comparison with previous results show a larger number of equilibrium points and an optimization in algorithm determining the normal form in the stability analysis, due the possibility of inclusion of analytical calculation of the coe¢ cients of the normal Hamiltonian of 4th order. Thus, the uses of variables Andoyer are adequate for the stability analysis of rotational motion, which can be useful for the analysis of space missions. Stresses those, the launch of the satellite regions of stability can contribute to the maintenance of the satellite attitude, which can generate a fuel economy through lower number of attitude maneuvers to maintain desired attitude of the mission

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Universidade Estadual Paulista (UNESP)
A atitude de um satélite artificial representa sua orientação no espaço, de modo que através da atitude pode-se conhecer a orientação espacial do satélite pela relação entre dois sistemas de coordenadas, um dels fixo no corpo do setélite e o outro associado com umsistema de referência inercial. Apesar da atitude ser bem representada por vários conjuntos de variáveis, todos estes apresentam limitações em sua utilização. Focaliza-se neste trabalho um conjunto de variáveis canônicas não singulares, aplicáveis ao movimento racional de satélites artificiais. Estas variáveis são úteis para o caso em que o vetor momento angular de rotação coincide com o maior momento principal de inércia do satélite. As equações dinâmicas do movimento rotacional são deduzidas pelo formalismo hamiltoniano e então integradas para análise do movimento rotacional livre de torques externos. Soluções analíticas aproximadas são obtidas e comparadas com as soluções gerais, representadas em funções elípticas, e com soluções numéricas. A Hamiltoniana média associada ao Torque de Gradiente de Gravidade é também incluida e as equações diferenciais do movimento pertubado são deduzidas em termos das variáveis não singulares. A integração analítica e numérica destas equações permite uma análise qualitativa e quantitativa das variáveis não singulares utilizadas para o movimento rotacional, quando se considera a pertubação provocada pelo Torque da Gradiente de Gravidade. Ao mesmo tempo esta análise aponta para limitações de intervalos de tempo em que algumas soluções devem ser utilizadas. Aplicações são realizadas para satélites com características similares as dos Satélites Brasileirs de Coleta de Dados (SCD1 e SCD2).
The attitude of an artificial satellite represents its orientation in the space, in way that through the attitude can be known the spatial orientation of the satellite for the relation between two systems of coordinates, one of them fixed in the satellite and other associate with an Inertial Referencce System. Many sets of variables are used to represent the satellite attitude, but some of them present limitations in its use. A set of non-singular canonical variables, applicable to the rotational motion of artificial satellites, is focused in this work. Thse variables are useful for the case where the rotational angular momentum vector coincides with the biggest principal moment of inertia of the satellite. The dynamic equations of the rotational motion are deduced by the Hamiltonian formalism and then they are integrated for the analysis of the torque-free rotational motion. Approximated analytical solutions are gotten and compared with the general solutions and numerical solutions. The associated mean Hamiltonian to the Gravity Gradient Torque also enclosed and the differential equations of the motion are deduced for the non-singular variables. The analytical and numeical integration of these equations allow a qualitative and quantitative analysis of these non-singular variables, when the disturbance of the Gravity Gradiente Torque is considered. At the same time this analysis point to limitations of time intervals where some solutions must be used. Applications are done for the satellite with similar characteristics of the Brzilian Satellites of Collection of Data (SCD1 and SCD2).

Дисертаційна робота присвячена теоретичним та експериментальним дослідженням гідродинаміки процесу диспергування рідини при мимовільних і вимушених коливаннях, що виникають на поверхні струменя, що дасть можливість підвищити монодисперсність продукту, отриманого за допомогою обертового вібраційного гранулятора. Експериментально досліджено гідродинаміку витікання струменя і факторів, які впливають на режими його розпаду. Запропоновано аналітичні рівняння, які дозволяють аналізувати процес диспергування струменя. Отримані рівняння регулярного розпаду струменя, що дає можливість доповнити методику розрахунку обертових вібраційних грануляторів розплаву азотних добрив. Теоретичні розрахунки були підтверджені результатами експериментальних досліджень, тобто розроблена математична модель може бути застосована для розрахунку діаметра краплі при диспергуванні рідини методом накладення вимушених коливань на струмінь. Отримані результати стали основою для розробки генератора низьких частот, що дозволило модернізувати існуючу конструкцію і підвищити монодисперсність готової продукції. Основні результати дисертаційної роботи були впроваджені при виконанні госпдоговірних науково-дослідних робіт. Промислові випробування підтвердили ефективність роботи модернізованого гранулятора.
Диссертационная работа посвящена теоретическим и экспериментальным исследованиям гидродинамики процесса диспергирования жидкости при самопроизвольных и вынужденных колебаниях, возникающих на поверхности струи, которые приводят к его распаду на капли. Проведены экспериментальные исследования гидродинамики истечения струи в процессе диспергирования до ее распада на капли. Определено, что режимы распада струи зависят от скорости истечения и механических параметров генератора низких частот. На основании обобщенных экспериментальных данных было уточнено уравнение для описания изменения давления вдоль струи с учетом влияния собственных колебаний конструкции. Предложені аналитические уравнения для описания гидродинамических параметров истекающей струи из отверстия, позволящие анализировать процесс диспергирования. Получены закономерности регулярного распада струи жидкости, что позволяет дополнить методику расчета вращающихся вибрационных грануляторов расплавов азотных удобрений. Теоретические расчеты были подтверждены результатами экспериментальных исследований, т. е. разработанная математическая модель может быть применена для расчета диаметра капли при диспергировании жидкости методом наложения вынужденных колебаний на струю. Объединение полученных результатов стало основой для разработки генератора низких частот, что позволило модернизировать существующую конструкцию гранулятора. Улучшенная конструкция гранулятора позволяет автоматически определять и регулировать оптимальные частоты сигнала в зависимости от уровня расплава в грануляторе, что позволило повысить монодисперсность готовой продукции, уменьшить потери продукции в виде пыли, и, тем самым, улучшить экологическую обстановку вокруг предприятия. Проведены промышленные испытания модернизированого гранулятора. Анализ результатов испытаний гранулирования аммиачной селитры показал, что оптимальная скорость вращения гранулятора находится в интервале 0,8–0,97 с-1, при этом происходит равномерное распределение гранул по сечению грануляционной башни, что приводит к снижению ее тепловой нагрузки. Основные результаты диссертационной работы были внедрены при выполнении хоздоговорных научно-исследовательских работ. Промышленные испытания подтвердили эффективность работы модернизированного гранулятора.
Thesis is devoted to the theoretical and experimental studies of liquid dispersion hydrodynamics in spontaneous and forced vibrations arising on the surface of the jet, which enables to increase monodispersity of the granules obtained by using rotating vibro-granulator. Hydrodynamics of the jet efflux and factors affecting its disintegration modes are experimentally studied. Analytical equations for analyzing the jet dispersion are proposed. Equations of regular jet disintegration are obtained and it enables to update the calculation methodology of rotating vibro-granulators for fusion of nitrogen fertilizers. Theoretical calculations were proved by the experiments results which mean that the developed mathematical model can be used for the calculation of droplet diameter when dispersing liquid using the method of imposing the forced vibrations on the jet. Obtained results became the basis for the development of the special-frequency generator, which helped to modernize the existing device and increase monodispersity of the finished product. The main results of this thesis have been implemented for fulfilling of contractual research work. Industrial trials have confirmed the effectiveness of the modernized granulator.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Nowadays, despite the technological development experienced by science in general, a fact especially evident by the available powerful computer machines, the analytical and semi-analytical methods to study different space problems are still of great importance in the fields of astrodynamics and celestial mechanics. From the physical understanding of the motion of celestial bodies to the planing and designing of space missions, the use of mathematical models to deal with a very large number of contemporary problems plays a fundamental role in the progress of human knowledge. In this context, the present thesis presents the use of different mathematical techniques to deal with different various and current problems in astrodynamics and celestial mechanics. The studies developed throughout this work are applicable to both areas. The topics studied are the following ones: (1) The development of disturbing potentials using the double-averaging process, in order to be included in the Lagrange planetary which are numerically integrated to study features of orbits around Mercury and the Galilean moon Callisto; (2) The use of different perturbation integrals, techniques to identify and map different perturbations present in a planetary system, with focus on the analysis of systems of Giant planets with their massive moons; (3) The use of the concept of intermediary Hamiltonian and the use of a canonical transformation called elimination of the parallax, both to deal with binary systems in the context of the roto-orbital dynamics, this one as an approach of the fulltwo body problem; (4) An updated analysis of Gauss variational equations to study quasisatellite orbits around the Martian moon Phobos and with analytical predictions made after obtaining linear and averaged equations of motions. Therefore, this thesis intend not only to provide important analysis and results for each specific problem which it deals with along its pages, but also seeks to highlighting the merit and current relevance of different analytical and semi-analytical methods to be used in the fields of astrodynamics and celestial mechanics. Additionally, the author also hopes to offer an outcome of diverse interesting ideas and methods to be explored in future investigations in these research fields
Na atualidade, a despeito do desenvolvimento tecnológico experimentado pela ciência em geral, algo especialmente evidenciado por poderosas máquinas computacionais disponíveis, os métodos analíticos e semianalíticos para o estudo de diferentes problemas espaciais ainda são de grande importância nos campos de astrodinâmica e mecânica celeste. Desde a compreensão física do movimento de corpos celestes até ao planejamento e projeto de missões espaciais, o uso de modelos matemáticos para lidar com um grande número de problemas contemporâneos desempenha um papel fundamental no progresso do conhecimento humano. Neste contexto, a presente tese apresenta o uso de diferentes técnicas matemáticas para lidar com diversos e atuais problemas em astrodinâmica e mecânica celeste. Os estudos desenvolvidos ao longo deste trabalho são aplicáveis à ambas as áreas. Os tópicos estudados são os seguintes: (1) O desenvolvimento de potenciais perturbadores usando o processo de dupla média, de forma a serem incluídos nas equações planetárias de Lagrange que são integradas numericamente para estudar características de órbitas ao redor de Mercúrio e da lua galileana Calisto; (2) A utilização de diferentes integrais de perturbação, técnicas para identificar e mapear diferentes perturbações presentes em um sistema planetário, com foco na análise de sistemas de planetas gigantes com suas luas massivas; (3) A utilização do conceito de hamiltoniana intermediária e o uso de uma transformação canônica chamada eliminação da paralaxe, ambos para lidar com sistemas binários no contexto da dinâmica roto-orbital, essa sendo uma aproximação do problema completo de dois corpos; (3) Uma análise atualizada de equações variacionais de Gauss para o estudo de órbitas quasi-satélite ao redor da lua marciana Fobos e com predições analíticas realizadas após serem obtidas equações de movimento linearizadas e com média. Portanto, esta tese pretende não somente prover importantes análises e resultados para cada problema específico com os quais a mesma lida ao longo de suas páginas, mas também procura destacar o mérito e relevância atual de diferentes métodos analíticos e semianalíticos a serem utilizados nos campos de astrodinâmica e mecânica celeste. Adicionalmente, o autor também espera oferecer um produto de variadas ideias e métodos a serem explorados em futuras investigações nesses campos de pesquisa
2013/26652-4
2015/18881-9

碩士
國立交通大學
工學院精密與自動化工程學程
100
For satellite antennas, this thesis mainly deals with spin mechanism design and speed control of an antenna in a radiometer to make sure it under stable operation is able to obtain measurement data. The spin mechanism of the satellite antenna involves vehicle payload, space constraints and extreme environment to drive payload at constant speed. During its mission, the radiometer itself has to rotate at the speed rate of 30rpm. Since the running between the box and the reflector has movable and immovable components, the signals delivery and spin mechanism design deserve study. This thesis uses a slip ring for both signal and power transfers. We choose a direct drive motor and control its speed. We adjust motor driver parameters to control speed stability and torque output. Measurement results of the antenna platform show that rotation speed is unstable when using small gain in speed control, and it takes longer time to achieve desired rotation speeds. Increasing gain to higher than 400 makes the antenna platform resonant and vibratory. Moreover, by using small integral constant in control, the antenna platform bearing sustains severe stress since the torque is not stable.

碩士
國立交通大學
機械工程學系
100
For satellite antennas, this thesis mainly deals with spin mechanism design and controls the spin rate of antennas in a radiometer. Based on communication or mission requirements, every satellite antenna has its own standard. Considering vehicle payload and space constraints, we need to fold the antenna before launch. After launching the satellite into an orbit, we will control the antenna attitude. During its mission, the radiometer itself has to rotate. Since the running between the box and the reflector has a lot of movable and immovable components, spin mechanism design has become a major issue. In this paper, we use the rotary joint and slip ring to design platform of the satellite antenna. In terms of motor control, the mission requires a high torque and low speed motor. This thesis uses a PID controller and a sliding mode controller to respectively control the velocity of a direct drive motor and make the radiometer rotate at 30RPM. We compare advantages and disadvantages of both methods in order to achieve the best control result.

碩士
國立中央大學
大氣物理研究所
95
In recent year, the damages caused by typhoons are more and more serious.The heavy rainfall from typhoons often causes inland flooding and mudslides that threaten lives and property which affect the livelihood of people. One of the most important areas of typhoon research focuses on the quantitative prediction of a typhoon’s precipitation. The forecasting from American agencies use the TRaP method to predict a hurricane’s accumulated rainfall for the next 24 hours. This technique is considered fast and practical. The main purpose of this study is to also apply the TRaP method, but take into account the influence from a typhoon’s rotation and intensity variation. This research uses SSM/I data, GOES-9 data and MTSAT data to estimate the instant rainfall brought forth by typhoons between 2003~2005 around Taiwan. The accumulated rainfall is projected every six hours, and compared with the actual rainfall data recorded from the island’s weather stations. The study’s results indicate that by also considering the rotation and intensity of a typhoon, it will further improve the accuracy of the rainfall estimates. The correlation coefficient of accumulated rainfall between station and the method only concern about advection is 0.79.If we consider the advection, rotation and intensity variation of typhoon, the correlation coefficient can increase to 0.96.

碩士
國立臺灣大學
電信工程學研究所
106
In this thesis, a Ka-band dual-circular polarization sequential antenna array design is proposed. The dual-circular polarization antenna element is a square microstrip patch antenna using dual probe-fed. In order to generate circular polarized wave, a compact 3 dB branch line coupler is used. Both microstrip lines with fractal design and open stub matched transmission line are applied to the propose dual-circular polarization sequential antenna array to minimize coupler size. In generally, sequential design can be used to maintain wide-band axial ratio response. The 128 elements single polarized sequential array which has a return loss better than 10 dB in operation frequency band is realized. Besides, the antenna radiation patterns and wide axial ratio bandwidth are similar to simulation results. To maintain good axial ratio, the proposed dual-circular polarization sequential antenna array employs two-layer sequential rotation technique. A 4×4 sequential array is proposed to demonstrate single layer feeding structure for dual-circular polarization without any crossover. The measurement results show that two-layer sequential rotation can achieve good axial ratio. Due to its compact size and planar construction, the proposed dual-circular polarization sequential antenna array is suitable for mobile satellite communication.

Two examples of planetary bodies that may have coupled thermal and dynamical evolutions are investigated. The work is presented in three individual papers. The first example is that of a tidally heated satellite in an orbital resonance, for which the tidal dissipation rate is a strongly increasing function of the internal temperature. For such a satellite, a feedback mechanism exists between the orbital and thermal energies, which may lead to periodic variations in tidal heating within the satellite and its orbital eccentricity. A simple model of this mechanism is presented in the first paper and is applied specifically to Io. The second example is that of an ice shell on Europa, which is decoupled from the silicate core by a layer of liquid water. In the second paper, the spatially varying thickness that such a shell would have in thermal equilibrium with tidal dissipation within it, surface solar insolation and heat flow from the core is calculated for reasonable rheological laws for ice. The contribution of these variations in ice thickness to Europa's inertia tensor is estimated, and the implications for nonsynchronous rotation of Europa are discussed. In the third paper, a detailed dynamical model is developed, which demonstrates that such a shell may exhibit large—scale polar wander as it approaches thermal equilibrium, because of the destabilizing effect of the variations in ice thickness on the inertia tensor of the shell. The abstracts of the three papers are reproduced below. Episodic Volcanism of Tidally Heated Satellites with Application to Io A simple model of the coupled thermal and orbital evolution of a tidally heated satellite in an orbital resonance is presented and applied specifically to Io. The model quantitatively demonstrates how a feedback mechanism between the orbital and thermal energy of such a satellite can lead to periodic variations in surface heatflow and orbital eccentricity. The convective heatflow and (k/Q) of the satellite are parameterized as local power laws of the temperature, where Q is the quality factor and k is the second-degree tidal potential Love number. The time evolution of the model is determined by two nonlinear equations: an equation governing the orbital eccentricity, and a simple heat-balance equation determining the temperature. A linear stability analysis reveals that the time-independent solution is unstable if n > m+p, where n and m are the exponents in the power laws for (k/Q) and convective heatflow, respectively, and p is the ratio of the convective cooling time scale to the time scale for equilibration of the eccentricity. Numerical integration of the nonlinear equations reveals behavior in qualitative agreement with this relation. Laboratory data on near-solidus peridotites suggest 20 ≾ n ≾ 30, and parameterized convection schemes suggest m ~ 10. Since p is of order unity, it follows that tidally heated satellites are probably in the unstable regime if they are operating near the solidus. It is thus probable that Io has no thermal steady state. The model is made more realistic by (1) arresting the reduction of (k/Q) at low temperature, and (2) arresting the growth of temperature at the mantle solidus and allowing volcanism to remove the excess heat. When the second modification is included, the unstable regime becomes periodic. In addition, a global k substantially larger than the elastic value is possible for a mostly solid Io because the body may begin to behave viscously when the tidal period is longer than, or comparable to, the Maxwell time. This requires a solid-state viscosity of ≾ 4 x 10^(15) Pa s, which may be achievable with a small amount of partial melt. The model can easily be adjusted to pass through Io's current observed heatflow (1-2 W m^(-2)) and eccentricity (~ 0.004) for reasonable choices of parameters (Q/k)_(min) ~ 100, (Q/k)_(max) ~ few x 10^3 solidus viscosity ~10^(15) – 10^(17) Pas, and Q_J within the required dynamical bounds. The periods of high heatflow and acceptable eccentricity typically have duration of ~20-20 myr, separated in time by ~ 80-100 myr. Spatial heterogeneities in Io's thermal structure are likely to make the behavior more complicated. The model predicts that Io's mean motion may be currently increasing, a possibility suggested by recent estimates of n_1 from eclipse data. Since Europa's eccentricity mimics that of Io, the model also implies that the tidal stresses in Europa's ice shell may have recently been large enough to produce the observed fracturing. The episodic heating mechanism may be responsible for the resurfacing of Enceladus < 10^9 years ago. Thermal State of an Ice Shell on Europa We consider a model of Europa consisting of an ice shell that is decoupled from a silicate core by a layer of liquid water. The thickness of the shell is calculated as a function of colatitude and longitude, assuming that a state of conductive equilibrium exists with the incident annual average solar insolation, tidal dissipation within the shell, and heat flow from the core. Ice thickness profiles are calculated for each of two plausible rheological behaviors for ice: the Maxwell rheology and the generalized flow law rheology. In both cases the strong temperature—dependence of the dissipation rate is explicitly included as well as the temperature—dependence of the thermal conductivity of ice. Because of the strong temperature dependence of the dissipation rate, nearly all of the tidal dissipation is concentrated in the lowermost few kilometers of the shell. Even though the effective Q of the greater part of the shell is >> 100 in our models, average shell thicknesses do not exceed 25 km. Thus, if the total thickness of H_2O which mantles Europa is ≳ 25 km, none of the models admit the possibility of a completely frozen H_2O layer. The total dissipation rates in our models are comparable to those of a constant Q model with Q ~ 10. The thickness profiles are relatively insensitive to heat flow from the core. The second degree spherical harmonic components of the ice thickness are given and the resulting contributions to the quantities B-A/C and B-C/A of Europa are estimated. Although the contribution to B-A/C is perhaps larger than the permanent value needed to prevent nonsynchronous rotation, its dependence on the shell's orientation relative to synchroneity suggests that very slow nonsynchronous rotation will persist, with reorientation of the shell relative to the satellite-planet direction occurring on a timescale ≳ the thermal diffusion timescale for the shell (~10^7 yr). The existence of a significant "fossil" bulge on the shell due to long-term elastic behavior of its outer, coldest regions would eliminate nonsynchronous rotation. Since the contribution to (B-C/A) of the thickness variations in most of our models is > 0, Europa may experience polar wander as thermal equilibrium is approached, if the above is the most important permanent contribution to (B-C/A). The magnitudes of the principal moment differences are insensitive to the details of the parameterization of the tidal dissipation. Polar Wander of a Synchronously Rotating Satellite with Application to Europa An ice shell on Europa that is decoupled from the silicate core by a layer of liquid water has a thermal-equilibrium thickness profile that varies with position over its surface, because of spatial variations in the surface temperature and tidal dissipation within the ice (see previous paper). The second spherical harmonic degree components of these thickness variations and of any fossil rotational and tidal bulges present on the shell contribute to the inertia tensor of the body. The problem is that of a planetary elastic lithosphere that is topographically loaded from below. Following the development of Willemann and Turcotte (1981) we develop equations describing the variations in the inertia tensor of a body, which are caused by the addition of second harmonic degree topography to the base of the crust. Applied to the case of an ice shell on Europa, it is found for many choices of parameters that a state of thermal equilibrium for the shell will involve an orientation of Europa's principal axes of inertia (when the hydrostatic bulges are relaxed), which is unusual for a synchronously rotating satellite. Specifically, the intermediate and maximum principal moments are reversed. To reach the preferred orientation for synchronous satellites, a thermal equilibrium ice shell must execute a net reorientation of ninety degrees about the satellite—planet direction. We present a simple model of a rigid, synchronously rotating satellite in a circular orbit for which the difference between the intermediate and maximum principal moments is linear in time, passing through zero when t = O. The model demonstrates that the expected reorientation is indeed dynamically favored. We then consider a more realistic model, including the effects of various torques which act to couple the motions of the core, shell, and liquid water layer, as well as the effect of viscous dissipation which arises in the shell due to the predicted polar wander. It is found that the Poincare torque, gravitational coupling, and the torque due to viscous shear in the liquid water layer are unable to induce significant motion of the core during polar wander of the shell. However, the Poincare torque exerted on the liquid water layer by the shell is believed to cause the liquid water layer to reorient in coincidence with the shell. The model suggests that viscous friction in the shell eliminates the possibility that polar wander will occur unless preexisting fractures (e.g., due to tidal stresses (Crawford and Stevenson, 1988)) extend from the surface to a depth where the ice behaves viscously on the polar wander time scale. If the temperature T_f at the base of the fractured region is as high as ~ 140-145 K, the model indicates that polar wander occurs on a time scale of 10^6-10^5 y (shorter as T_f increases) after the sign of the difference between the maximum and intermediate principal moments reverses. In the absence of dissipation, polar wander would occur in ~ few x 10^3 y. Polar wander must occur on a time scale significantly shorter than ~ 10^7 y, or the thickness profile of the ice will be in continuous equilibrium with its thermal environment regardless of its orientation, and the mechanism driving the polar wander will be virtually eliminated. It is likely that events of large scale polar wander occur episodically, separated in time by periods on the order of the time scale for thermal diffusion through the shell ~10^7 y), although a state of slow, continuous drifting of the pole is also possible. The time scale of viscous flow of topography at the base of the ice is also near 10^7 y. If dissipation in the shell due to polar wander is a few orders of magnitude smaller than our simple model suggests, polar wander as described here is a much more effective means for fracturing the ice than is tidal flexing, and it may contribute to producing the observed global fracture systems in Europa's ice.

Rotator cuff injury is a debilitating condition and when injury cannot be managed through non-operative procedures, surgery is required. To determine explanations for the failure of surgery to restore joint function, human muscle biopsies of supraspinatus were studied compared to deltoid. Histology showed atrophy and a tendency toward fibrosis/fatty infiltration in injured supraspinatus. Findings from AChR-subunit western blot and Sema3A localization around satellite cells suggest supraspinatus denervation. Nucleotide incorporation to quantify satellite cell activation in culture showed a significant increase in BrdU+(active) satellite cells in supraspinatus treated with a nitric oxide-donor drug, but not deltoid muscle. The application of principal component analysis to these data extracted components that suggest variables assaying muscle atrophy, satellite cell activity, and fibrosis contribute strongly to the observed variability. The results suggest supraspinatus muscle of the injured rotator cuff is atrophic, denervated, possibly subject to fibro-fatty infiltration, and support the idea that treatment could promote growth in atrophic supraspinatus to improve functional outcomes.
October 2015