Although the quasi-adiabatic calculations have led to an improved description of the measured observables, the theoretical justifications of the assumptions made in the model have not yet been studied. The first part of the work described in this thesis is therefore concerned with the clarification of these theoretical uncertainties by performing a rigorous investigation of the accuracy and the validity of the model. In addition, we reformulate the quasi-adiabatic theory to give a more general formalism, approaching the three-body problem in a different way. This alternative formulation provides a clear understanding of the assumptions made in the original quasi-adiabatic theory. Using the spirit of the new quasi-adiabatic formalism, we also develop alternative approximation schemes for the treatment of quantum mechanical three-body systems. The accuracy and the range of validity of the developments, together with the quasi-adiabatic theory, are investigated carefully and precisely by comparing their predictions with those essentially exact CDCC technique for the 66Zn (d,p)67Zn reaction at 88.2 MeV. It is found that the alternative models and quasi-adiabatic theory are reliable techniques for the treatment of deuteron breakup process at intermediate energies of interest. The remainder of this thesis is devoted to the investigation of the mechanism of (p,d*) reactions. As the treatment of the final state interactions in such reactions has not previously been studied consistently, we develop an adiabatic method and apply it to new data for the 13C(p,d)12C reaction with 35 MeV incident proton energy. Due to the weak coupling between spin channels of the continuum n-p system at the energies of interest, the singlet and triplet state pickup cross-sections for the final n-p system are analyzed separately. We find that the contribution from the singlet state is dominant for small relative energies while the triplet state dominates for large energies. This application clarifies the relationship between the three-body dynamics in the final state of (p,d) and (p,d*) reactions.

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

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 62-63). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 62-63). Also available on the Internet.

Thesis (Ph.D.)--Ohio University, June, 2008. / Title from PDF t.p. Includes bibliographical references.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 131-137). Also available in electronic version. Access restricted to campus users.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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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.