Asteroid missions are gaining interest from the scientific community and many new missions are planned. The Didymos binary asteroid is a Near-Earth Object and the target of the Asteroid Impact and Deflection Assessment (AIDA). This joint mission, developed by NASA and ESA, brings the possibility to build one of the first CubeSats for deep space missions: the ASPECT satellite. Navigation systems of a deep space satellite di er greatly from the common planetary missions. Orbital environment close to an asteroid requires a case-by-case analysis. In order to develop the Attitude Determination Control System (ADCS) for the mission, one needs detailed information about orbital disturbances in the vicinity of the asteroid. This work focuses on the development of a simulator that characterises the orbital disturbances a ecting the ASPECT satellite in the space environment near the Didymos asteroid. In this work, a model of orbital conditions and disturbances near the Didymos system was defined. The model integrates several classical and modern models of spacecraft motion and disturbance. An existing Low Earth Orbit (LEO) simulator was modified and updated accordingly to the ASPECT mission scenario. The developed simulator can be used to analyse the disturbances to be counteracted by the ADCS of the ASPECT satellite. The objective of the study was to quantify the e ect of both non-gravitational and gravitational disturbances. The simulator was used to analyse di erent orbit scenarios related to the period of the mission and to the relative distance between the spacecraft and the asteroid system. In every scenario, the solar radiation pressure was found to be the strongest of the disturbance forces. With the developed simulator, suitable spacecraft configurations and control systems can be chosen to mitigate the e ect of the disturbances on the attitude and orbit of the ASPECT satellite.

This work investigates the possibility of obtaining attitude estimates by capturing images of stars using a SWIR camera. Today, many autonomous systems rely on the measurements from a GPS to obtain accurate position and attitude estimates. However, the GPS signals are vulnerable to both jamming and spoofing, making any system reliant on only GPS signals insecure. To make the navigation systems more robust, other sensors can be added to acquire a multisensor system. One of these sensors might be a ground based SWIR star camera that is able to provide accurate attitude estimates. To investigate if this is possible, an experimental setup with a SWIR camera was placed at the office of FOI Linköping, where the camera in a rigid position has captured images of the sky. The SWIR camera possesses several advantages over a camera operating in the visual spectrum. For example, the background radiation is weaker and the transmission through the atmosphere is higher in certain wavelength bands.  The images captured by the SWIR camera was provided to a star tracker software that has been developed. The star tracker software contains algorithms to detect stars, position them in the image at subpixel accuracy, match the stars to a star database and finally output an attitude based on the stars from the image and the identified stars in the database. To further improve the attitude estimates, an MEKF was applied. The results show that attitude estimates could be obtained consistently from late evenings to early mornings, when the sky was dark. However, this required that the weather conditions were good, i.e., a limited amount of clouds. When more clouds were present, no attitude estimates could be provided for a majority of the night. The SWIR camera was also compared to a camera operating in the visual spectrum when clouds were present, to see if the results were any different. With the camera settings applied in this work, the two cameras seemed to perform equally. The accuracy of the estimated attitudes is hard to validate, since no true attitude is available. However, the variance of the estimates was low, and the major differences in the attitude estimates over a night's measurements seemed to be a drift present in all angles. The maximum estimated error in declination during a night's measurements varied from about 40 to 60 arc seconds, depending on the data set. The maximum estimated error in right ascension varied between 200 and 2000 arc seconds, and the same metric in the roll estimate were about 100 to 2500 arc seconds. The reason for the drifts is assumed to be atmospheric effects not being accounted for, and astronomical effects moving the direction of the rotation axis of the earth, creating errors in the star positions given in the database.

Ants typically use path integration and vision for navigation when the environment precludes the use of pheromones for trails. Recent simulations have been able to accurately mimic the retinotopic navigation behaviour of these ants using simple models of movement and memory of unprocessed visual images. Naturally it is interesting to test these navigation algorithms in more realistic circumstances, particularly with actual route data from the ant, in an accurate facsimile of the ant world and with visual input that draws on the characteristics of the animal. While increasing the complexity of the visual processing to include skyline extraction, inhomogeneous sampling and motion processing was conjectured to improve the performance of the simulations, the reverse appears to be the case. Examining closely the assumptions about motion, analysis of ants in the field shows that they experience considerable displacement of the head which when applied to the simulation leads to significant degradation in performance. The family of simulations rely upon continuous visual monitoring of the scene to determine heading and it was decided to test whether the animals were similarly dependent on this input. A field study demonstrated that ants with only visual navigation cues can return the nest when largely facing away from the direction of travel (moving backwards) and so it appears that ant visual navigation is not a process of continuous retinotopic image matching. We conclude ants may use vision to determine an initial heading by image matching and then continue to follow this direction using their celestial compass, or they may use a rotationally invariant form of the visual world for continuous course correction.

Thesis. 1978. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / Includes bibliographical references. / M.S.

The knowledge of the dynamics and characteristics of space plasma during solar-terrestrial coupling has been greatly enriched by process that aids the determination of the instantaneous frequencies which support the non-stationary and non-linear nature of signals. Such plasmas are observed in the magnetosheath in the downstream of bow shock. In this thesis a technique was applied which extracts the various contributing oscillatory modes reflecting the waveforms observed in the space by Cluster spacecraft instruments such as FGM, CIS and EFW, and decompose the frequency of each extracted mode using Instantaneous Frequency method that is based on Simple Hilbert Transform (SHT). This is achieved through the use of Empirical Mode Decomposition (EMD). To eliminate the negative frequency of the various extracted modes referred to as intrinsic mode function which appears with Fourier transform, we apply Hilbert transform leading to analytic representation of the signals. This process aids the determination of the instantaneous frequencies of the extracted modes. The combined process of EMD and Hilbert transform is called the Hilbert-Huang transform. The results in this thesis have been based on the improved EMD. To contribute to the understanding of plasma dynamics, the computed instantaneous frequencies are compared with the results obtained from the application of Simple Hilbert Transform. Instantaneous frequencies of overriding waves are easily separated as opposed to the application of just SHT. They offer the advantage of 3-dimensional study of the spatial characteristics of waves. The understanding of the instantaneous wave number has been achieved through the EMD and SHT combination. This provides the results which give the wave vector for a known frequency at a given instant of time. The instantaneous dispersion relation is determined using the knowledge of the instantaneous frequency and wave vector in the satellite frame, the plasma bulk velocity and the spacecraft velocity (found to be negligible compared with the plasma bulk velocity). This is accomplished using a Doppler shift relation. Wave modes identifications have been carried out by considering the proton temperature anisotropies, plasma beta and plasma bulk velocity and instantaneous phase velocity in the satellite frame. We report Alfvén mode close to the bow shock, spreading out to mirror mode which dominates the middle of magnetosheath. The mirror mode then diminishes towards the magnetopause.

This Ph.D. thesis is devoted to the development of a specific semi-analytical algorithm especially well-suited to derive the long-term evolution of near geosynchronous space debris and based on the concept of mean orbital motion. In a first approach, the semi-analytical theory is concerned with the singularity issues arising for circular and equatorial orbits as well as with the geostationary resonance modeling. In a second part, motivated by the discovery of high area-to-mass ratios space debris in high altitude Earth's orbit (mostly near the geosynchronous region), the direct radiation pressure models are revisited and completed. Within this context, the main effects of the direct solar radiation pressure for the mid- and long-term evolution of both the eccentricity and the inclination vectors are analyzed through a well-suited model. Moreover, by means of a smart extension, the passage in the Earth's shadow is taken into account in the computations of the orbits. Finally, a further insight into the intrinsic stability of such space debris is performed, by means of a recent numerical technique (MEGNO) which is based on the concept of ``variational chaos indicator'.

In this dissertation, we demonstrate the importance of invariant objects in many areas of applied research. The areas of application we consider are chemistry, celestial mechanics and aerospace engineering, plasma physics, and coupled map lattices. In the context of chemical reactions, stable and unstable manifolds of fixed points separate regions of phase space that lead to a certain outcome of the reaction. We study how these regions change under the influence of exposing the molecules to a laser. In celestial mechanics and aerospace engineering, we compute periodic orbits and their stable and unstable manifolds for a object of negligible mass (e.g. a satellite or spacecraft) under the presence of Jupiter and two of its moons, Europa and Ganymede. The periodic orbits serve as convenient spot to place a satellite for observation purposes, and computing their stable and unstable manifolds have been used in constructing low-energy transfers between the two moons. In plasma physics, an important and practical problem is to study barriers for heat transport in magnetically confined plasma undergoing fusion. We compute barriers for which heat cannot pass through. However, such barriers break down and lead to robust partial barriers. In this latter case, heat can flow across the barrier, but at a very slow rate. Finally, infinite dimensional coupled map lattice systems are considered in a wide variety of areas, most notably in statistical mechanics, neuroscience, and in the discretization of PDEs. We assume that the interaction amont the lattice sites decays with the distance of the sites, and assume the existence of an invariant whiskered torus that is localized near a collection of lattice sites. We prove that the torus has invariant stable and unstable manifolds that are also localized near the torus. This is an important step in understanding the global dynamics of such systems and opens the door to new possible results, most notably studying the problem of energy transfer between the sites. / text

La mayor parte de los problemas de la Mecánica Celeste pueden reducirse a un problema perturbado de dos cuerpos. Esta memoria es una contribución a la comprensión y resolución de dichos problemas. En primer lugar se aborda la estructura del conjunto de órbitas del problema de dos cuerpos sin perturbar. Una adecuada definición de distancia entre órbitas permite, entre otros resultados, explicar las dificultades y singularidades que aparecen en los problemas perturbados en cuanto a las variables escogidas. Se demuestra a continuación la equivalencia formal de los métodos empleados en la teoría general de perturbaciones de la Mecánica Celeste (válidos en realidad para ecuaciones diferenciales ordinarias). Se explicitan los algoritmos que permiten el cálculo efectivo (mediante recurrencia) para todos los órdenes. En el caso del método clásico de Lagrange, Laplace y Poisson se obtienen las perturbaciones de orden cualquiera en forma explícita de manera directa. Se generaliza el teorema de Lagrange para la inversión de funciones. Su utilización es la base de diversas transformaciones. Otros conceptos introducidos en el último capítulo parecen tener interés en el estudio de la optimización y en el problema de los denominadores pequeños debidos a la dependencia de las frecuencias sobre el cuerpo racional. El detalle del contenido de los diversos capítulos se halla en la introducción que precede a cada uno de ellos. Como norma general se indica cuándo un resultado es conocido, omitiendo la demostración. Los conceptos de distancia entre órbitas, variedad de Kepler, elementos topológicos, operador de iteración, derivada contractiva, conjunto localmente accesible, desbloqueo de orden “k” y condición geométrica de desbloqueo, entre otros, se introducen en esta memoria. Si de un mismo concepto se citan varias referencias se debe a que en ellas se abordan distintos aspectos del mismo.

Thesis (M.S.)--Miami University, Dept. of Physics, 2008. / Title from first page of PDF document. Includes bibliographical references (p. 39-40).

Made available in DSpace on 2014-06-11T19:27:09Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-11-06Bitstream added on 2014-06-13T18:30:57Z : No. of bitstreams: 1 casteletti_jr_me_rcla.pdf: 1198028 bytes, checksum: 64d53c9ad4dac00f0f39d72fc52d6fae (MD5) / Secretaria de Educação do Estado de São Paulo / Realizamos neste trabalho o estudo de tópicos fundamentais de Mecânica Celeste visando a aplicação em problemas de interesse atual, tal como o estudo de ressonâncias de movimentos médios em sistemas planetários extrassolares. Ênfase foi dada nos seguintes tópicos: i) formulação do problema ressonante de dois planetas em interação mútua; ii) desenvolvimento e expansão da função perturbadora; iii) solução numérica de problemas de valor inicial; iv) aplicações ao par de planetas HD10180d,e, os quais estão próximos da ressonância 3:1. A abordagem dos problemas foi realizada analítica e numericamente. Na primeira parte deste trabalho formulamos o problema geral de três corpos e reproduzimos os principais passos do desenvolvimento da função perturbadora. Na segunda parte realizamos simulações dos sistemas em questão utilizando as equações exatas de movimento (Newton) e comparamos os resultados com soluções numéricas das equações de Lagrange, i.e., equações de variação dos elementos orbitais escritas em termos da função perturbadora envolvida. Os resultados das simulações numéricas realizadas neste trabalho poderão ser aplicados para três propostas: i) comparação dos resultados entre as soluções exatas e aproximadas (Lagrange) das equações de movimento para, com isso, obter evidências numéricas do domínio de validade da aplicação da função perturbadora expandida nos problemas ressonantes; ii) estudo de dinâmica ressonante, i.e., caracterização e evolução temporal de ângulos críticos associados às ressonâncias; iii) estabilidade dinâmica de longo período dos sistemas em questão / In this work we study a fundamental Celestial Mechanics in order to apply to problems of current interest, such as dynamics of extrasolar planetary systems. Emphasis is given on the following topics: i) formulation of the problem of two resonant planets in mutual interaction, ii) dedution and expansion of the disturbing function; iii) numerical solution of initial value problems, iv) applications to the pair of planets HD10180d,e which orbits are near to the 3:1 resonance. We adopt both, analytical and numerical approaches. In the first part, we formulate the general three-body problem, and reproduce the main steps of the expansion of the disturbing function. In the second part we show the results of a great deal of numerical simulations of the systems using both the exact equations of motion (Newton) Lagrange equations. The simulations have been done with three main goals: i) comparison of the results of the exact and approximate solutions (Lagrange) equations of motion, in order to obtain numerical evidences of the validity domain of the application of the expanded disturbing function to resonant problems, ii) study of the resonant dynamics, i.e., characterization and evolution of critical angles associated with resonances, iii) investigate long-term dynamic stability of the systems in question