(has links) (PDF)
Thesis (Ph. D.)--Washington State University, May 2009. / Title from PDF title page (viewed on Feb. 12. day, 2010). "Department of Physics and Astronomy." Includes bibliographical references (p. 186-199).
Barkham, Peter George Douglas
Two fundamental problems of celestial mechanics are considered: the stellar or planetary three-body problem and a related form of the restricted four-body problem. Although a number of constraints are imposed, no assumptions are made which could invalidate the final solution. A consistent and rational approach to the analysis of four-body systems has not previously been developed, and an attempt is made here to describe problem evolution in a systematic manner. In the particular three-body problem under consideration two masses, forming a close binary system, orbit a comparatively distant mass. A new literal, periodic solution of this problem is found in terms of a small parameter e, which is related to the distance separating the binary system and the remaining mass, using the two variable expansion procedure. The solution is accurate within a constant error O(e¹¹) and uniformly valid as e tends to zero for time intervals 0(e¹⁴). Two specific examples are chosen to verify the literal solution, one of which relates to the sun-earth-moon configuration of the solar system. The second example applies to a problem of stellar motion where the three masses are in the ratio 20 : 1 : 1. In both cases a comparison of the analytical solution with an equivalent numerically-generated orbit shows .close agreement, with an error below 5 percent for the sun-earth-moon configuration and less than 3 percent for the stellar system. The four-body problem is derived from the three-body case by introducing a particle of negligible mass into the close binary system. Unique uniformly valid solutions are found for motion near both equilateral triangle points of the binary system in terms of the small parameter e, where the primaries move in accordance with the uniformly-valid three-body solution. Accuracy, in this case, is Q maintained within a constant error 0(e⁸), and the solutions are uniformly valid as e tends to zero for time intervals 0(e¹¹). Orbital position errors near L₄ and L₅ of the earth-moon system are found to be less than 5 percent when numerically-generated periodic solutions are used as a standard of comparison. The approach described here should, in general, be useful in the analysis of non-integrable dynamic systems, particularly when it is feasible to decompose the problem into a number of subsidiary cases. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate
Entanglement production in massive interacting two-particle system. / 有质量的相互作用双粒子系统产生的量子纠缠 / Entanglement production in massive interacting two-particle system. / You zhi liang de xiang hu zuo yong shuang li zi xi tong chan sheng de liang zi jiu chanJanuary 2006 (has links)
Wang Jia = 有质量的相互作用双粒子系统产生的量子纠缠 / 王佳. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 83-86). / Text in English; abstracts in English and Chinese. / Wang Jia = You zhi liang de xiang hu zuo yong shuang li zi xi tong chan sheng de liang zi jiu chan / Wang Jia. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Review of quantum entanglement --- p.3 / Chapter 2.1 --- Schmidt decomposition and entangled pure states --- p.3 / Chapter 2.2 --- Detecting the quantum entanglement of pure states --- p.7 / Chapter 2.3 --- Quantifying the quantum entanglement of pure states --- p.9 / Chapter 2.3.1 --- Von Neumann entropy --- p.10 / Chapter 2.3.2 --- Purity --- p.11 / Chapter 2.3.3 --- Effective Schmidt number --- p.12 / Chapter 2.4 --- Purity of systems consisting of two interacting particles --- p.13 / Chapter 3 --- The pseudopotential method of two-body interactions --- p.16 / Chapter 3.1 --- S-wave pseudopotential in free space --- p.17 / Chapter 3.2 --- An example --- p.19 / Chapter 3.3 --- Pseudopotential for bound states --- p.21 / Chapter 3.4 --- S-wave pseudopotential in harmonic traps --- p.23 / Chapter 3.5 --- Two examples --- p.26 / Chapter 3.5.1 --- Hard-sphere potential --- p.26 / Chapter 3.5.2 --- Square well potential --- p.28 / Chapter 3.6 --- Feshbach resonance and two-channel scattering --- p.30 / Chapter 4 --- Quantum entanglement of ultracold particles in a harmonic trap --- p.35 / Chapter 4.1 --- Regularized Hamiltonian and energy eigenstates --- p.37 / Chapter 4.2 --- Schmidt Decomposition of wave functions with spherical symmetry --- p.39 / Chapter 4.3 --- Numerical Results --- p.41 / Chapter 4.4 --- Infinite scattering length limit --- p.45 / Chapter 5 --- Entanglement generated by wave packet scattering at low energies --- p.47 / Chapter 5.1 --- Scattering between two gaussian wave packets --- p.48 / Chapter 5.2 --- Loss of purity --- p.50 / Chapter 5.3 --- Enhancement of entanglement by resonance --- p.54 / Chapter 6 --- Quantum entanglement in molecular dissociation process --- p.57 / Chapter 6.1 --- Morse potential model --- p.57 / Chapter 6.2 --- Numerical method --- p.60 / Chapter 6.3 --- Excitation and dissociation process --- p.61 / Chapter 6.3.1 --- Weak field transition and Rabi oscillations --- p.62 / Chapter 6.3.2 --- Multiphoton dissociation by a moderately strong field --- p.63 / Chapter 6.3.3 --- Strong field dissociation --- p.72 / Chapter 6.4 --- Schmidt decomposition of dissociated wave function --- p.74 / Chapter 6.4.1 --- Dissociated wave function for the moderated field strength --- p.75 / Chapter 6.4.2 --- Dissociated wave function for the strong field strength --- p.76 / Chapter 7 --- Summary and Conclusions --- p.81 / Bibliography --- p.83 / Chapter A --- Analytical solution of two coupled square-well potentials --- p.87
The two-body problem consists of determining the motion of two gravitationally interacting bodies with given masses and initial velocities. The problem was first solved by Isaac Newton in 1687 using geometric arguments. In this thesis, we present selected parts of Newton's solution together with an alternative geometric solution by Richard Feynman and a modern solution using differential calculus. All three solutions rely on the three laws of Newton and treat the two bodies as point masses; they differ in their approach to the the three laws of Kepler and to the inverse-square force law. Whereas the geometric solutions aim to prove some of these laws, the modern solution provides a method for calculating the positions and velocities given their initial values. It is notable that Newton in his most famous work Principia, where the general law of gravity and the solution to the two-body problem are presented, used mathematics that is not widely studied today. One might ask if today's low emphasis on classical geometry and conic sections affects our understanding of classical mechanics and calculus.
Anderson, Keegan Doig
02 November 2012
M.Sc. / Important ideas from dynamical systems theory and the restricted three-body problem are introduced. The intention is the application of dynamical systems theory techniques to the restricted three-body problem to better understand the phenomenon of gravitational capture. Chapter 1 gives a much deeper review of the purpose of this dissertation. Chapter 2 introduces and reviews important concepts from dynamical systems. Chapter 3 reviews the restricted three-body problem and all important aspects of the problem. In chapter 4 we define and study the phenomenon of gravitational capture. We take a novel approach by applying a symplectic method, namely the implicit midpoint method, to model trajectories in the restricted three-body problem. As far as we know, this is the first time such a method has actually been applied, with other authors preferring to apply explicit methods in trajectory modelling. In the closing of this chapter we review our whole discourse and suggest topics for future research. The disseration is concluded with two appendix chapters. In the first chapter we list all the computer code we have written for this dissertation. The second appendix chapter reviews the n-body problem and we show a full solution of the two-body problem.
Goodhart, Gregory J.
Three methods for solving the orbital intercept problem in the presence of an oblate earth are presented. Both iterative and direct approaches for solving the problem were compared in the bases of computational time and relative accuracy of the results. The two iterative methods were found to agree to eight significant figures for all elliptic intercept orbits studied. The results obtained from the direct approach were found to agree with the iterative methods's results to eight significant figures for low intercept eccentricities ( e < 0.2), and to five significant figures for high intercept orbit eccentricities (e = 0.9). However, the direct method was found to be twice as fast, computationally, as either of the two iterative methods. The iterative methods each take essentially the same amount of computational time. Neither type of routine yields accurate results for half-revolution intercept and hyperbolic intercept orbits. The method for developing these procedures, the computer code implementing the methods, and selected results are included. / M.S.
Heitzman, Michael Thomas. Chicone, Carmen Charles.
Title from PDF of title page (University of Missouri--Columbia, viewed on Feb 26, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Professor Carmen Chicone. Vita. Includes bibliographical references.
The dynamics of deployment and observation of a rigid body spacecraft system in the linear and non-linear two-body problemOttesen, David Ryan 04 March 2013 (has links)
Modern space situational awareness entails the detection, tracking, identification, and characterization of resident space objects. Characterization is typically accomplished through the use of ground and space based sensors that are able to identify some specific physical feature, monitor unique dynamical behaviors, or deduce some information about the material properties of the object. The present investigation considers the characterizaiton aspects of situational awareness from the perspective of a close-proximity formation reconnaissance mission. The present study explores both relative translational and relative rotational motion for deployment of a spacecraft and observation of a resident space object. This investigation is motivated by specific situations in which characterization with ground or fixed space based sensors is insufficient. Instead, one or more vehicles are deployed in the vicinity of the object of interest. These could be, for instance, nano-satellites with imaging sensors. Nano-satellites offer a low-cost and effective technological platform, which makes consideration of the proposed scenario more feasible. Although the motivating application is rooted in space situational awareness, the techniques explored are generally applicable to flight in the vicinity of asteroids, and both cooperative vs. non-cooperative resident space objects. The investigation is initially focused on identifying the key features of the relative dynamics that are relevant to space situational awareness applications. Subsequently, effective spacecraft control techniques are considered to achieve the reconnaissance goals. / text
Sistemas gravitacionais com massa variável : merger de galáxias / Gravitational systems with variable mass : galaxy mergerSilva, Tiago Amancio da 14 August 2018 (has links)
Orientadores: Patricio Anibal Letelier Sotomayor, Orlando Luis Goulart Peres / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-14T18:35:27Z (GMT). No. of bitstreams: 1 Silva_TiagoAmancioda_M.pdf: 4442121 bytes, checksum: 7ea395e4746a38ae4776bb4adff497f4 (MD5) Previous issue date: 2009 / Resumo: É estudado o processo de merger entre galáxias, onde as galáxias são consideradas como objetos compactos com massa dependendo do tempo. O estudo se dá por meio da análise das órbitas de tal sistema. Para isso, é desenvolvido o problema gravitacional de dois corpos que trocam massa com a atmosfera que os involve. O problema de Gylden-Mestschersky é revisado para servir como referência para este problema. Alguns modelos de variação de massa são propostos, tendo como base uma analogia com a hidrodinâmica e a análise microscópica do sistema. O problema de dois corpos estudado é aplicado ao problema de três corpos de massas variáveis. São encontradas soluções estacionárias correspondentes às que estão presentes no problema usual de massas constantes / Abstract: We study the process of galactic merger, where galaxies are regarded as compact objects with time-dependent masses. This study is made through the analysis of the system's orbit. For this purpose, we consider the gravitational problem of two bodies exchanging mass with a surrounding atmosphere. The Gylden-Mestschersky problem is reviewed in order to be used as a reference for that problem. We propose some models of mass variation, based on a hydrodynamics analogy and on a microscopic analysis of the system. The two-body problem considered is applied to the three-boby problem of varying masses. We found stationary solutions corresponding to the ones of the usual constant masses problem / Mestrado / Astrofisica / Mestre em Física
Clark, Clayton Jeremiah
16 August 2005
The two body problem and the rocket equation r̈ + ∊ α ṙ + k/r3r = 0 have been expressed in numerous ways. However, the combination of the rocket equation with the two-body problem has not been studied to any degree of depth due to the intractability of the resulting non-linear, non-homogeneous equations. The goal is to use perturbation techniques to approximate solutions to the combined two-body and rocket equations.
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