Engineering and technical challenges exist with the material transport of natural resources in space. One aspect of this transport problem is the design of an orbit architecture in the Earth-Moon system (EMS) that facilitates these resources through the mining cycle. In this thesis, it is proposed to use the Circular Restricted 3-Body Problem (CR3BP) to design an orbit architecture composed of L3 Lyapunov orbits, hyperbolic invariant stable and unstable manifolds, and geosynchronous (GEO) orbits. A single shooting method (SSM) and natural parameter continuation (NPC) numerical algorithm is used to compute a family of L3 Lyapunov orbits. Invariant Manifold Theory (IMT) is leveraged to find the set of feasible hyperbolic invariant stable and unstable manifolds associated with a L3 Lyapunov orbit. Ideal L3 Lyapunov orbits are chosen to construct an orbit architecture based off favorable metrics like orbital period, Jacobi Constant, and stability index. Manifolds that enter the GEO and xGEO (beyond GEO) volumes are identified. Finally, a ∆V analysis for GEO to manifold transfer is conducted. An achievement of this study is the computation of stable L3 Lyapunov orbits. The primary contribution of this paper lies in its modeling of a L3 Lyapunov orbit architecture using the CR3BP. / Master of Science / Engineering and technical challenges exist with the material transport of natural resources in space. One aspect of this transport problem is the design of an orbit architecture in the Earth-Moon system (EMS) that facilitates these resources through the mining cycle. In this thesis, it is proposed to use the Circular Restricted 3-Body Problem (CR3BP) to design an orbit architecture composed of L3 Lyapunov orbits, hyperbolic invariant stable and unstable manifolds, and geosynchronous (GEO) orbits. L3 is a unique point in space in a rotating frame of reference where the gravity of the Earth and Moon create a dynamical equilibrium point. Due to its location in a rotating frame of reference relative to the Earth and the Moon, orbits around L3 tend to greater stability than L1 or L2. A single shooting method (SSM) and natural parameter continuation (NPC), which are computational methods for finding solutions that connect discrete boundary conditions, numerical algorithm is used to compute a family of L3 Lyapunov orbits. Invariant Manifold Theory (IMT), which is a dynamical system structure that is invariant throughout the action of the system, is leveraged to find the set of feasible hyperbolic invariant stable and unstable manifolds associated with L3 Lyapunov orbits. Ideal L3 Lyapunov orbits and manifolds are chosen to construct an orbit architecture based off favorable metrics like orbital period, Jacobi Constant, and stability index. Manifolds that enter the GEO and xGEO (beyond GEO) volumes are identified. Finally, a ∆V analysis for GEO to manifold transfer is conducted. An achievement of this study is the computation of stable L3 Lyapunov orbits. The primary contribution of this paper lies in its modeling of a L3 Lyapunov orbit architecture using the CR3BP.

214 pages / The Fock-Tani (unitary) transformation of the second- quantized Hamiltonian gives a representation which treats reactants and products symmetrically, and composites exactly. Each term in the Fock-Tani potential corresponds to a specific physical process and contains terms orthogonalizing continuum states to the bound states. The difficulty in carrying out this transformation can be lessened by working in a center of mass system, giving (n-1) reduced mass particles. After a general analysis of such systems, the Fock- Tani transformations in the 3→2-body case are carried out for the reactions a⁺+(b⁺c⁻)→(a⁺c⁻)+b⁺ and a⁻+(b⁺c⁻)→(a⁻b⁺)+c⁻. It is found that for (2) the transformation in the symmetrical reduced mass system can easily be carried out, but the Jacobi reduced mass system requires the more complicated d-matrix approach. This transformation has not yet been attempted in the full 3-body system but is likely to be as difficult as that for (1). First order differential and total cross sections are computed for resonant charge transfer in (1) for a proton- hydrogen initial state. The Fock-Tani T-matrix for the initial-state Jacobi system is found to be identical to that for the full 3-body system. That for the symmetrical reduced mass system gives an error of order l/mprot in the incident wave vector. A comparison of the Jacobi version and a previous special case Fock-Tani transformation, where the proton mass is taken as infinite, is also made. Cross sections for (ls→ls) positronium formation in positron-hydrogen collisions, calculated using the same program as for the proton-hydrogen case, are found to disagree with the previous Fock-Tani result, probably due to lack of convergence of the previous result. Cross sections for reactions (1) involving muons in hydrogenic isotopes (of interest in quantum electrodynamics and catalyzed fusion) are also calculated. Finally, extension of the results to higher order is considered. Polarized Schrodinger wave functions for a system containing a hydrogenic atom and a fully kinetic external charge are found to first order. These would be used in the Fock-Tani matrix elements to account for some initial- and final-state effects. Calculations of distorted second-quantized states and second and third order T-matrix elements are also outlined.

ν Octantis is a spectroscopic binary with a semi-major axis and period of 2.55 AU and 2.9 years, respectively. Ramm et al. (2009) discovered a 52 ms^(-1) radial-velocity (RV) perturbation with a period of 417 days in this system. All evidence, both photometric and spectroscopic, suggests the perturbation is the result of a 2.5 MJ planet orbiting the primary star. However, when assuming a “normal” prograde coplanar orbit, celestial mechanics predicts this orbit is unstable, contradicting the observed stability. Simulations by Eberle and Cuntz (2010) showed a retrograde orbit for the planet to be stable for at least 10^7 years. In this thesis, we performed a 10^8 -yr simulation of the retrograde orbit, and found it remained stable. Simulations over a range of planetary semi-major axes, eccentricities, and primary/secondary masses showed that stable retrograde orbits are not possible past a semi-major axis of 1.315 +/- 0.092 AU . Therefore, planetary retrograde orbits are most likely inherently more stable than prograde orbits owing to the absence of stability at known mean-motion resonances. Eccentricity simulations showed that the period of the planet's dominant eccentricity variation is related to the planet's semi-major axis by a second order exponential. However, retrograde orbits tend to have longer eccentricity periods than prograde orbits at the same semi-major axis. There is also evidence that this eccentricity period is connected to the orbital stability. By fitting a keplerian to both Ramm et al. (2009) and current radial velocities, the period of the ν Octantis binary was determined to be 1050.04 +/- 0.02 days with an eccentricity of 0.2359 +/- 0.001 . The planetary orbital solution for just the data reduced in this thesis gave a period of 416.9 +/- 2.1 days and an eccentricity of 0.099 +/- 0.015 , with an RMS scatter of 9.6 ms^(-1). Therefore, the orbital elements are within 1σ of the Ramm et al. (2009) elements. Assuming a retrograde coplanar orbit about the primary star then the planet has a mass of M_pl = 2.3 M_J and a semi-major axis of a_pl = 1.21 +/- 0.09 AU.

Předkládaná disertační práce je zaměřena na \uv{Modelování propagačního kanálu pro off-body komunikaci v oblasti milimetrových vln}. Navzdory pokrokům v rámci bezdrátových sítí v přímé blízkosti člověka stále systémy 5. generace postrádají dostatečnou šířku pásma a dostatečně nízkou odezvu. To je způsobeno neefektivním využíváním rádiového spektra. Tento nedostatek je potřeba co nejdříve odstranit a právě z tohoto důvodu je hlavním cílem této práce navrhnout vylepšený model rádiového kanálů pro off-body komunikaci. Úkolem tohoto modelu je umožnit uživatelům efektivněji a přesněji simulovat propagaci signálu v rámci daného prostředí. Navržený model je dále optimalizován a ověřen vůči nejnovějším měřením, získaným z literatury. Nakonec je tento model implementován do simulačního nástroje NS-3, pomocí kterého je následně využit k simulaci množství scénářů. Hlavním výstupem této práce je ověřený model přenosového kanálu pro off-body komunikaci v rámci milimetrových vln, společně s jeho implementací do simulačního nástroje NS-3, díky čemuž je dostupný pro širokou veřejnost.

Topic: Comparison of three-point shoot trials occurence and effectivity in the aspects of FIBA rule changes in 2010 as well as in a relation with placement of the teams in Czech Women's basketball league Aim: The main aim of the thesis is to find out whether the following four- year-period as a result of rule changes applying to an extension of three- point line was sufficient enough to be able to adapt from the frequency and success in three-point shoot of view in the highest Czech Women's basketball league in the basic part of the Championship in between the selected teams. We take into account eight surveyed seasons in this study, where straight after the period of first four seasons following one after another there was a rule of three-point line extention established. The statistics of three-point shoots in the four seasons mentioned above, which means after establishing the rule, are the main source of data used for this survey and was accomplished according to statistical results and comparing these results. The mail goal is to create statistical analysis that would show how great impact the three-point line extention had during following four seasons of the change, which means the adaptability process applied for three- point shooting within the teams placed in the first, fourth, seventh...

L'objet de cette thèse est de proposer une étude numérique, fondée sur l'application de résultats de la théorie du contrôle optimal géométrique, des trajectoires spatiales du système Terre-Lune dans un contexte de poussée faible. Le mouvement du satellite est décrit par les équations du problème restreint des trois corps controlé. Nous nous concentrons sur la minimisation de la consommation énergétique et du temps de transfert. Les trajectoires optimales sont recherchées parmi les projections des courbes extrémales solutions du principe du maximum de Pontryagin et peuvent être calculées grâce à une méthode de tir. Ce procédé fait intervenir l'algorithme de Newton dont la convergence nécessite une initialisation précise. Nous surmontons cette difficulté au moyen de techniques homotopiques ou d'études géométriques du système de contrôle linéarisé. L'optimalité locale des trajectoires extrémales est ensuite vérifée en utilisant les conditions du second ordre liées au concept de point conjugué. Dans le cas du problème de minimisation de l'énergie, une technique de "recollement" de trajectoires optimales kepleriennes autour de la Terre et La Lune et d'une solution optimale de l'équation du mouvement linéarisée au voisinage du point d'équilibre L1 est également proposée pour approximer les transferts Terre-Lune à énergie minimale. / This PhD thesis provides a numerical study of space trajectories in the Earth-Moon system when low-thrust is applied. Our computations are based on fundamental results from geometric control theory. The spacecraft's motion is modelled by the equations of the controlled restricted three-body problem. We focus on minimizing energy cost and transfer time. Optimal trajectories are found among a set of extremal curves, solutions of the Pontryagin's maximum principle, which can be computed solving a shooting equation thanks to a Newton algorithm. In this framework, initial conditions are found using homotopic methods or studying the linearized control system. We check local optimality of the trajectories using the second order optimality conditions related to the concept of conjugate points. In the case of the energy minimization problem, we also describe the principle of approximating Earth-Moon optimal transfers by concatening optimal keplerian trajectories around The Earth and the Moon and an energy-minimal solution of the linearized system in the neighbourhood of the equilibrium point L1.