A rigorous formalism for solving the Coulomb scattering problem is presented in this thesis. The approach is based on splitting the interaction potential into a finite-range part and a long-range tail part. In this representation the scattering problem can be reformulated to one which is suitable for applying exterior complex scaling. The scaled problem has zero boundary conditions at infinity and can be implemented numerically for finding scattering amplitudes. The systems under consideration may consist of two or three charged particles. The technique presented in this thesis is first developed for the case of a two body single channel Coulomb scattering problem. The method is mathematically validated for the partial wave formulation of the scattering problem. Integral and local representations for the partial wave scattering amplitudes have been derived. The partial wave results are summed up to obtain the scattering amplitude for the three dimensional scattering problem. The approach is generalized to allow the two body multichannel scattering problem to be solved. The theoretical results are illustrated with numerical calculations for a number of models. Finally, the potential splitting technique is further developed and validated for the three body Coulomb scattering problem. It is shown that only a part of the total interaction potential should be split to obtain the inhomogeneous equation required such that the method of exterior complex scaling can be applied. The final six-dimensional equation is reduced to a system of three dimensional equations using the full angular momentum representation. Such a system can be numerically implemented using the existing full angular momentum complex exterior scaling code (FAMCES). The code has been updated to solve the three body scattering problem. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: Submitted. Paper 5: Manuscript.

Aquesta tesi doctoral està emmarcada en el camp de l'astrodinàmica. Presenta solucions a problemes identificats en el disseny de missions que utilitzen òrbites entorn dels punts de libració, fent servir la teoria de sistemes dinàmics.El problema restringit de tres cossos és un model per estudiar el moviment d'un cos de massa infinitessimal sota l'atracció gravitatòria de dos cossos molt massius. Els cinc punts d'equilibri d'aquest model, en especial L1 i L2, han estat motiu de nombrosos estudis per aplicacions pràctiques en les últimes dècades (SOHO, Genesis...). Genèricament, qualsevol missió en òrbita al voltant del punt L2 del sistema Terra-Sol es veu afectat per ocultacions degudes a l'ombra de la Terra. Si l'òrbita és al voltant de L1, els eclipsis són deguts a la forta influència electromagnètica del Sol. D'entre els diferents tipus d'òrbites de libració, les òrbites de Lissajous resulten de la combinació de dues oscil.lacions perpendiculars. El seu principal avantatge és que les amplituds de les oscil.lacions poden ser escollides independentment i això les fa adapatables als requeriments de cada missió. La necessitat d'estratègies per evitar eclipsis en òrbites de Lissajous entorn dels punts L1 i L2 motivaren la primera part de la tesi. En aquesta part es presenta una eina per la planificació de maniobres en òrbites de Lissajous que no només serveix per solucionar el problema d'evitar els eclipsis, sinó també per trobar trajectòries de transferència entre òrbites d'amplituds diferents i planificar rendez-vous. Per altra banda, existeixen canals de baix cost que uneixen els punts L1 i L2 d'un sistema donat i representen una manera natural de transferir d'una regió de libració a l'altra. Gràcies al seu caràcter hiperbòlic, una òrbita de libració té uns objectes invariants associats: les varietats estable i inestable. Si tenim present que la varietat estable està formada per trajectòries que tendeixen cap a l'òrbita a la qual estan associades quan el temps avança, i que la varietat inestable fa el mateix però enrera en el temps, una intersecció entre una varietat estable i una d'inestable proporciona un camí asimptòtic entre les òrbites corresponents. Un mètode per trobar connexions d'aquest tipus entre òrbites planes entorn de L1 i L2 es presenta a la segona part de la tesi, i s'hi inclouen els resultats d'aplicar aquest mètode als casos dels problemes restringits Sol Terra i Terra-Lluna.La idea d'intersecar varietats hiperbòliques es pot aplicar també en la cerca de camins de baix cost entre les regions de libració del sistema Sol-Terra i Terra-Lluna. Si existissin camins naturals de les òrbites de libració solars cap a les lunars, s'obtindria una manera barata d'anar a la Lluna fent servir varietats invariants, cosa que no es pot fer de manera directa. I a l'inversa, un camí de les regions de libració lunars cap a les solars permetria, per exemple, que una estació fos col.locada en òrbita entorn del punt L2 lunar i servís com a base per donar servei a les missions que operen en òrbites de libració del sistema Sol-Terra. A la tercera part de la tesi es presenten mètodes per trobar trajectòries de baix cost que uneixen la regió L2 del sistema Terra-Lluna amb la regió L2 del sistema Sol-Terra, primer per òrbites planes i més endavant per òrbites de Lissajous, fent servir dos problemes de tres cossos acoblats. Un cop trobades les trajectòries en aquest model simplificat, convé refinar-les per fer-les més realistes. Una metodologia per obtenir trajectòries en efemèrides reals JPL a partir de les trobades entre òrbites de Lissajous en el model acoblat es presenta a la part final de la tesi. Aquestes trajectòries necessiten una maniobra en el punt d'acoblament, que és reduïda en el procés de refinat, arribant a obtenir trajectòries de cost zero quan això és possible. / This PhD. thesis lies within the field of astrodynamics. It provides solutions to problems which have been identified in mission design near libration points, by using dynamical systems theory. The restricted three body problem is a well known model to study the motion of an infinitesimal mass under the gravitational attraction of two massive bodies. Its five equilibrium points, specially L1 and L2, have been the object of several studies aimed at practical applications in the last decades (SOHO, Genesis...). In general, any mission in orbit around L2 of the Sun-Earth system is affected by occultations due to the shadow of the Earth. When the orbit is around L1, the eclipses are caused by the strong electromagnetic influence of the Sun. Among all different types of libration orbits, Lissajous type ones are the combination of two perpendicular oscillations. Its main advantage is that the amplitudes of the oscillations can be chosen independently and this fact makes Lissajous orbits more adaptable to the requirements of each particular mission than other kinds of libration motions. The need for eclipse avoidance strategies in Lissajous orbits around L1 and L2 motivated the first part of the thesis. It is in this part where a tool for planning maneuvers in Lissajous orbits is presented, which not only solves the eclipse avoidance problem, but can also be used for transferring between orbits having different amplitudes and for planning rendez-vous strategies.On the other hand, there exist low cost channels joining the L1 and L2 points of a given sistem, which represent a natural way of transferring from one libration region to the other one. Furthermore, there exist hyperbolic invariant objects, called stable and unstable manifolds, which are associated with libration orbits due to their hyperbolic character. If we bear in mind that the stable manifold of a libration orbit consists of trajectories which tend to the orbit as time goes by, and that the unstable manifold does so but backwards in time, any intersection between a stable and an unstable manifold will provide an asymptotic path between the corresponding libration orbits. A methodology for finding such asymptotic connecting paths between planar orbits around L1 and L2 is presented in the second part of the dissertation, including results for the particular cases of the Sun-Earth and Earth-Moon problems. Moreover, the idea of intersecting hyperbolic manifolds can be applied in the search for low cost paths joining the libration regions of different problems, such as the Sun-Earth and the Earth-Moon ones. If natural paths from the solar libration regions to the lunar ones was found, it would provide a cheap way of transferring to the Moon from the vicinity of the Earth, which is not possible in a direct way using invariant manifolds. And the other way round, paths from the lunar libration regions to the solar ones would allow for the placement of a station in orbit around the lunar L2, providing services to solar libration missions, for instance. In the third part of the thesis, a methodology for finding low cost trajectories joining the lunar L2 region and the solar L2 region is presented. This methodology was developed in a first step for planar orbits and in a further step for Lissajous type orbits, using in both cases two coupled restricted three body problems to model the Sun-Earth-Moon spacecraft four body problem. Once trajectories have been found in this simplified model, it is convenient to refine them to more realistic models. A methodology for obtaining JPL real ephemeris trajectories from the initial ones found in the coupled models is presented in the last part of the dissertation. These trajectories need a maneuver at the coupling point, which can be reduced in the refinement process until low cost connecting trajectories in real ephemeris are obtained (even zero cost, when possible).

This thesis evaluates decommissioning strategies for the International Space Station ISS. A permanent solution is attempted by employing energy efficient invariant manifolds that arise in the circular restricted three body problem CRTBP to transport the ISS from its low Earth orbit LEO to a lunar orbit. Although the invariant manifolds provide efficient transport, getting the the ISS onto the manifolds proves quite expensive, and the trajectories take too long to complete. Therefore a more practical, although temporary, solution consisting of an optimal re-boost maneuver with the European Space Agency's automated transfer vehicle ATV is proposed. The optimal re-boost trajectory is found using control parameterization and the sequential quadratic programming SQP algorithm. The model used for optimization takes into account the affects of atmospheric drag and gravity perturbations. The optimal re-boost maneuver produces a satellite lifetime of approximately ninety-five years using a two ATV strategy.

<p>Measurements of the three-body photodisintegration of <super>3</super>He were performed at the High Intensity &gamma-ray Source (HI&gammaS). Neutrons emitted in this reaction inside a <super>3</super>He gas target were detected with seven 12.7 cm diameter liquid scintillator detectors. Time-of-flight (TOF) and pulse-shape discrimination (PSD) techniques were used to identify neutron events. The absolute differential cross sections for the <super>3</super>He(&gamma, n)pp reaction as a function of outgoing neutron scattering angle and energy were determined from the measurements at the incident &gamma-ray energies of 11.4, 12.8, 13.5, and 14.7 MeV to within a precision better than +/- 6 %.</p><p>The absolute cross sections at each incident energy are compared to the results of Gorbunov [Gor74], phase space calculations, and state-of-the-art three-body calculations. The inclusion of the Coulomb interaction in the three-body problem has been a long-standing challenge in theoretical nuclear physics. The present experimental data were found to be in good agreement with the state-of-the-art theory, which includes a full treatment of the Coulomb interaction between</p><p>the protons in the final state [Del05].</p> / Dissertation

Thèse : Mécanique : Faculté des sciences de Paris : 1854. Thèse : Astronomie : Faculté des sciences de Paris : 1854. / Titre provenant de l'écran-titre. Notes bibliogr.

Αντικείμενο της παρούσης διπλωματικής εργασίας αποτελεί το Φωτοβαρυτικό Πρόβλημα των Τριών Σωμάτων, ένα άλυτο πρόβλημα που απασχόλησε και εξακολουθεί να απασχολεί τον τομέα των Εφαρμοσμένων Μαθηματικών και της Κλασικής Αστροφυσικής τουλάχιστον τους τελευταίους δύο αιώνες. Διεξάγεται μελέτη των σημείων ισορροπίας του συστήματος και προσδιορίζονται οικογένειες περιοδικών λύσεων, οι οποίες στην περίπτωσή μας διακρίνονται σε δύο κατηγορίες που χαρακτηρίζονται από το μέγεθος της περιόδου τους. / The topic of this thesis deals with the Restricted Photogravitational Three Body Problem, which is an unsolved problem in Astrophysics and Celestial Mechanics. Research is carried out concerning the equilibrium points, around which families of periodic solutions can be identified.

The research on tribology and wear of the metals and composites has always been the topic of interest to understand the behavior and life of them. The wear of the materials with three-body contact has been of particular interest because the wear debris generated due to the wear and tear between the contact surfaces in constant motion will aggravate the wear rate of the contact surfaces. Hence it would be interesting to understand the stress distribution inside the materials with three-body contact. The current research presents the stress distribution within the materials which are in three-body contact modeling them as plain-strain problems with three different models viz., point force model, uniform pressure model and Hertzian Pressure model. The stress distribution of all the three cases are numerically computed and compared and the stress intensity factor is calculated in each case.

The wear process in three-body contact causes problems of abrasion such as volume loss and changes of geometry of the triboelements. The wear problem leads to increased failure and high costs for repairing or replacing equipment. To understand the nature of the wear behaviour and to predict the wear rate in advance, experimental investigation and numerical simulation of the wear process are required. In this work, the wear process is analysed and the influencing parameters governing the wear behaviour are investigated experimentally to develop a new wear model. Main influential factors are considered such as kinematics of abrasive particles, contact stiffness of the particle layer, friction characteristics, and wear factors. The experiments to study kinematics of particle layers are performed on a new observation tester. To define the contact stiffness of abrasive particles, experiments are conducted by the uniaxial spindle compression tester. Moreover, a tribometer test rig with applied load up to 200 N and velocity up to 1000 mm/s is used to investigate the friction characteristics and the wear behaviour of three-body tribosystem. Analyses of influential factors on the wear behaviour in dependency of predefined process parameter are carried out. Additionally, based on the results of the experimental investigations, approximation equations representing the relation of the influential factors and the process parameters are determined. A three-body wear model is build up to represent the wear behaviour by physical wear laws. Furthermore, these approximation equations and the relevant parameters obtained by experimental investigations are included in the Fleischer’s wear equation to simulate the wear process. With the coupled model the wear process of the sample can be simulated twodimensional over the sliding distance. It is possible to predict the wear depth and the wear intensity, which can be used to estimate the wear rate. Additionally, from the results of the wear simulation the worn surface and the local contact pressure in the contact region are determined which provide a deeper insight into the wear process. With this simulation the understanding of the wear behaviour can be improved which is important to solve wear problems.

The quantum impulse approximation theory has been extended to the inelastic collision. The total inelastic cross sections for the degenerated states with different angular momenta was calculated. It was proved that summing over the transitions from nl to n' and from nl to n'l' would give us the total cross section of transition from n to n'. Rate coefficients were calculated for the common gases in the atmosphere being the third particle. The resonant effect of the rate coefficients had been observed. Recombination coefficients were then calculated in terms of rate coefficients. Previous calculations were carried out in compare with the net rate flow through certain excited levels, which were found to be more stable and reflected a clearer picture of the whole process. Results have been compared with the elastic collision. A dramatic decreasing of rates when temperature increased was also observed. More thermal energy increases the probability of electrons for being re-ionized. Similar calculations had been carried out for the upper atmosphere gases, such as N₂, O₂, CO, CO₂, and H₂O. The recombination coefficients for electron combining with metallic ion Na+ were also calculated.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.