This thesis details the development and implementation of an attitude and orbit determining Kalman filter algorithm for a satellite in a Molniya orbit. To apply the Kalman Filter for orbit determination, the equations of motion of the two body problem were propagated using Cowell's formulation. Four types of perturbing forces were added to the propagated model in order to increase the accuracy of the orbit prediction. These four perturbing forces are Earth oblateness, atmospheric drag, lunar gravitational forces and solar radiation pressure. Two cases were studied, the first being the implementation of site track measurements when the satellite was over the ground station. It is shown that large errors, upwards of ninety meters, grow as time from last measurement input increases. The next case studied was continuous measurement inputs from a GPS receiver on board the satellite throughout the orbit. This algorithm greatly decreased the errors seen in the orbit determining algorithm due to the accuracy of the sensor as well as the continuous measurement inputs throughout the orbit. It is shown that the accuracy of the orbit determining Kalman filter also depends on the length of time between each measurement update. The errors decrease as the time between measurement updates decreases. Next the Kalman filter is applied to determine the satellite attitude. The rotational equations of motion are propagated using Cowell's Formulation and numerical integration. To increase the fidelity of the model four disturbing torques are included in the rotational equations of motion model: gravity gradient torque, solar pressure torque, magnetic torque, and aerodynamic torque. Four cases were tested corresponding to four different on board attitude determining sensors: magnetometer, Earth sensor, sun sensor, and star tracker. A controlled altitude path was chosen to test the accuracy of each of these cases and it was shown that the algorithm using star tracker measurements was three hundred times more accurate than that of the magnetometer algorithm. / Master of Science

Over 2.4 million eye injuries occur each year in the United States as a result of trauma. Eye injuries have been investigated for years; however, the role of the extraocular muscles in relation to eye injuries has yet to be quantified. In this research, Computed Tomography quasi-static tests were conducted to investigate the effect of the presence of the extraocular muscles on the biomechanical response of the human eye in situ. Three matched pairs of human eyes were displaced in 5 mm increments using a large flat cylindrical indenter to a maximum displacement of 30 mm. The loading was similar to what is experienced during a blunt impact, which is believed to cause the most serious eye injuries. In the matched pair, one eye had the extraocular muscles intact and the other had the extraocular muscles transected. Force, pressure, and displacement measurements were collected for each test. A trend was seen where a greater amount of force was created in the eye with the extraocular muscles intact than in the eye with the muscles transected, and a correlation between them was made. The greatest force measured in an eye with the extraocular muscles intact was 92 N, while the greatest force measured in an eye with the extraocular muscles transected was 80 N. An increase in intraocular pressure was also noticed for an eye with the extraocular muscles attached, rising steadily from 2 kPa to a maximum pressure of just over 50 kPa. It was also noted that during a quasi-static impact the eye can move out of the way of the imposing force. Since the test data set was small, analytical calculations were also conducted. / Master of Science

Title: Semigroups of operators and its orbits Author: Jan Vršovský Department: Institute of Mathematics of the Academy of Sciences of the Czech Republic Supervisor: prof. RNDr. Vladimír Müller, DrSc., Institute of Mathematics of the AS CR Abstract: The orbit of a bounded linear operator T on a Banach space is a se- quence T n x, n = 0, 1, 2, . . ., where x is a fixed vector. The orbits are closely connected to the dynamics of operator semigroups and to the invariant sub- spaces and subsets. The thesis studies the relation between the operator and its orbits. The subject of the first part is the relation between sequences T n x and T n , stability and orbits tending to infinity. The second part deals with dense orbits - hypercyclicity and related notions. In the third part, an ana- logue of reflexive algebras of operators, orbit reflexive operators are defined and studied. Apart from "normal" orbits of a single operator, the weak orbits and orbits of C0-semigroups are also touched. Keywords: operator, semigroup, orbit, hypercyclic, orbit reflexive

The successful prediction of spacecraft motion is often heavily based upon assumptions used to simplify the problem without compromising solution accuracy. For many analyses, a primary assumption used is the decoupling of trajectory and attitude dynamics when calculating trajectories. In cases where spacecraft or objects have high area to mass ratios, non-conservative effects such as atmospheric drag and solar radiation pressure can greatly perturb spacecraft translational motion based on rotational state. A modular, six degree of freedom (6DOF) simulation with coupled orbit and attitude dynamics has been developed to model spacecraft and orbits of arbitrary geometries. First, the basis for the modular rotational and translational equations of motion are introduced. Next, formulations are provided for the gravity gradient torque, solar radiation pressure, aerodynamic, and non-spherical gravity potential sources of perturbations, and the Marshall Engineering Thermosphere atmospheric model used is described. A first test case is performed using the 6DOF simulation to simulate the deorbit of the spacecraft Lightsail 1, which flew in 2015. Next, predictive cases are demonstrated using the simulation for a theoretical sail-boom-rocket combination representative of a debris removal scenario, and for the Aerodynamic Deorbit Experiement, which will demonstrate a passively stable drag sail technology and characterize its effectiveness on orbit. All simulation cases have had aerodynamic perturbation formulations compared against high fidelity Direct Simulation Monte Carlo runs, and suggestions have been made for the future development of the simulation tool.

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The existence of the exact commensurability between the periods of rotation and revolution of a satellite orbiting a planet is not a rare phenomenon in the Solar system. In fact, there are several examples of such resonances with the Earth-Moon system being the most familiar example of a 1:1 (synchronous) resonance. In this report, I will discuss the questions of stability of five resonant systems (Moon – Earth, Enceladus - Saturn, Dione - Saturn, Rhea – Saturn, and Mercury – Sun (the only non – synchronous resonance among the evolved spin – orbit resonances in the Solar system). Several authors have investigated the stability of spin-orbit resonances, and, in this report, I will concentrate on the two most recent investigations. / text

Numerous wave and gap features observed in Voyager data of Saturn's rings are produced by resonances between the orbital frequencies of known external satellites and ring particle orbits. This thesis investigates the possibility that other, currently unassociated, ring features are generated by perturbations on ring participle orbits produced by non-axisymmetric gravitational fields resulting from acoustic oscillation modes of the planet. The frequencies of Saturnian low degree (l ≤ 8) fundamental (or f) mode oscillations are calculated for a variety of Saturn interior models which span the range of uncertainty of the interior structure of the planet. Corrections for rotation, oblateness, and possible differential rotation have been applied. Only the low degree f-modes are found to have frequencies and likely wave amplitudes in the range necessary to produce gap or wave features in the rings. The calculated positions of outer Lindblad resonances (OLR) for the degree l = 2,3,4, and 5 sectoral f-modes of a single Saturn model lie near four previously unassociated C-ring features. These features are the Maxwell gap and three waves identified as being forced at either OLR or inner vertical resonances. The outer vertical resonance (OVR) of the l = 5, m = 4 mode also overlaps the location of a wave which may be forced at either an OVR or an inner Lindblad resonance. Four other similar wave features, however, cannot be explained by oscillation mode resonances. This failure to account for all of the comparable unassociated C-ring waves is the principal inadequacy of the hypothesis. Other observed properties of the wave features, however, including their azimuthal wavenumbers m and the variation of amplitude with proposed oscillation mode degree are consistent with the proposed forcing. Planetary oscillation amplitudes of ∼1 m are required for gap opening; wave amplitudes of ∼10 cm are required for density wave production. The C-ring thus serves as a very sensitive f-mode detector. Observations by the Cassini spacecraft should unequivocally determine if the C-ring features are produced by planetary oscillation modes. If these observations confirm the association, significant new constraints could be placed on Saturnian energy transport, differential rotation, and core size.

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No description available.

El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado. / Objective: To report a case of orbital mass and proptosis, diagnosed as Rosai-Dorfman disease (RDD). Methods: Clinical case report based on the review of clinical charts, radiological images, and histopathology. Results: A 42-year-old male with orbital mass and proptosis of the right eye. A surgical biopsy was performed, and the diagnosis of RDD was established using microscopy and immunohistochemistry. Definitive management included open tumour cytoreduction, with good response. Discussion: The RDD is a rare, benign, proliferative condition of unknown origin. It rarely affects the cranial cavities, with the orbital presentation being very unusual. Diagnostic confirmation is essential for the best surgical management. / Revisión por pares / Revisión por pares