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21 
Separation of variables and integrabilityScott, Daniel R. D. January 1995 (has links)
No description available.

22 
Geometry of two degree of freedom integrable Hamiltonian systems.Zou, Maorong. January 1992 (has links)
In this work, several problems in the field of Hamiltonian dynamics are studied. Chapter 1 is a short review of some basic results in the theory of Hamiltonian dynamics. In chapter 2, we study the problem of computing the geometric monodromy of the torus bundle defined by integrable Hamiltonian systems. We show that for two degree of freedom systems near an isolated critical value of the energy momentum map, the monodromy group can be determined solely from the local data of the energy momentum map at the singularity. Along the way, we develop a simple method for computing the monodromy group which covers all the known examples that exhibit nontrivial monodromy. In chapter 3, we consider the topological aspects of the Kirchhoff case of the motion of a symmetric rigid body in an infinite ideal fluid. The bifurcation diagrams are constructed and the topology of all the invariant sets are determined. We show that this system has monodromy. We show also that this system undergoes a Hamiltonian Hopf bifurcation as the couple resultant passes through a certain value when the steady rotation of the rigid body about its symmetry axis changes stability. Chapter 4 is devoted to checking Kolmogorov's condition for the square potential pendulum. We prove, by essentially elementary methods, that Kolmogorov's condition is satisfied for all of the regular values of the energy momentum map. In chapter 5, we use Ziglin's theorem to prove rigorously that some of the generalized two degree of freedom Toda lattices are nonintegrable.

23 
Satellite tether systems dynamic modeling and control /Mankala, Kalyan K. January 2006 (has links)
Thesis (Ph.D.)University of Delaware, 2006. / Principal faculty advisor: Sunil K. Agrawal, Dept. of Mechanical Engineering. Includes bibliographical references.

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A Hamiltonian particlefinite element for elasticplastic impact simulation /Horban, Blaise Andrew, January 2001 (has links)
Thesis (Ph. D.)University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 118125). Available also in a digital version from Dissertation Abstracts.

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The role of the Van Hove singularity in the time evolution of electronic states in a lowdimensional superlattice semiconductorGarmon, Kenneth Sterling 28 August 2008 (has links)
Not available / text

26 
Coherent control of cold atoms in a[n] optical latticeHolder, Benjamin Peirce, 1976 28 August 2008 (has links)
The dynamics of noninteracting, ultracold alkali atoms in the presence of counterpropagating lasers (optical lattice systems) is considered theoretically. The center of mass motion of an atom is such a system can be described by an effective Hamiltonian of a relatively simple form. Modulation of the laser fields implies a parametric variation of the effective Hamiltonian's eigenvalue spectrum, under which avoided crossings may occur. We investigate two dynamical processes arising from these neardegeneracies, which can be manipulated to coherently control atomic motion. First, we demonstrate the mechanism for the chaosassisted, or multiplestate, tunneling observed in recent optical lattice experiments. Second, we propose a new method for the coherent acceleration of lattice atoms using the techniques of stimulated Raman adiabatic passage (STIRAP). In each case we use perturbation analysis to show the existence of a small, few level, subsystem of the full effective Schrödinger equation that determines the dynamics. / text

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The role of the Van Hove singularity in the time evolution of electronic states in a lowdimensional superlattice semiconductorGarmon, Kenneth Sterling, 1978 18 August 2011 (has links)
Not available / text

28 
Thermodynamics of the HenonHeiles oscillatorsAlberti, Mathias V. 08 1900 (has links)
No description available.

29 
On the construction of invariant tori and integrable HamiltoniansKaasalainen, Mikko K. J. January 1994 (has links)
The main principle of this thesis is to employ the geometric representation of Hamiltonian dynamics: in a broad sense, we study how to construct, in phase space, geometric structures that are related to a dynamical system. More specifically, we study the problem of constructing phasespace tori that are approximate invariant tori of a given Hamiltonian; also, using the constructed tori, we define an integrable Hamiltonian closely approximating the original one. The methods are generally applicable; as examples, we use gravitational potentials that are of interest in stellar dynamics. First, we construct tori for box and loop orbits in planar, barred potentials, thus demonstrating the applicability of the scheme to potentials that have more than one major orbit family. Also, we show that, in general, the construction scheme needs two types of canonical transformations together: point transformations as well as those expressed by generating functions. To complete the construction scheme, we show how to furnish the tori with consistent coordinate systems, i.e., how to recover the angle variables of a torus labelled by its actions. Next, the developed methods are employed in creating invariant phasespace tori in nonintegrable potentials supporting minororbit families. These tori are used to define an integrable Hamiltonian H<sub>0</sub>, and a modified form of the standard Hamiltonian perturbation theory is then used to demonstrate that a minororbit family can be treated as one made up of orbits trapped by a resonance of H<sub>0</sub>. Finally, we generalize the scheme further by constructing tori in timereversal asymmetric Hamiltonians (by considering the motion in a rotating frame of reference), and study the transition from locally contained stochasticity to global chaos. Using both nearintegrable 'laboratory' Hamiltonians and those for which we construct tori, we investigate the transition in the light of the resonance overlap criterion.

30 
Coherent control of cold atoms in a[n] optical latticeHolder, Benjamin Peirce, January 1900 (has links)
Thesis (Ph. D.)University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

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