Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 23 for “"Hamiltonian system"”.
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Stochastic Averaging Correctors for a Noisy Hamiltonian System With Discontinuous Statistics
… for stochastic averaging of a noisy planar Hamiltonian system containing a homoclinic orbit. The noise is assumed to be small and have skewness at the homoclinic orbit. Following Sowers, we center our efforts on a singular perturbations problem in a boundary layer near the homoclinic orbit. …
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Optimal control problems on lie groups with symmetry breaking cost functions
… this thesis, we consider smooth optimal control systems that evolve on Lie groups. Pontryagin's maximum principle allows us to search for local solutions of the optimal control problem by studying an associated Hamiltonian dynamical system. When the associated Hamiltonian function possess …
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Stochastic Geometric Mechanics and Symmetry
… in stochastically perturbed mechanical systems, in Hamiltonian as well as Lagrangian (variational) formulations. On the Hamiltonian side, we discuss a stochastic Kepler problem with a noisy angular momentum vector. We show that the radial distance and speed evolve deterministically. This …
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Volume Formula and Intersection Pairings of N-fold Reduced Products
… product of G is the symplectic quotient of the Hamiltonian system of the Cartesian product of N coadjoint orbits of G under diagonal coadjoint action of G. Under appropriate assumptions, it is a symplectic orbifold. Using the technique of nonabelian localization and the residue formula of …
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Group integrals in chaotic quantum systems
… recursion formula is an integral solution of a Hamiltonian system related to Calogero--Sutherland models for arbitrary coupling beta>0. We calculate closed expressions for some group integrals over the unitary symplectic group. Moreover we generalize the Gelfand--Tzetlin coordinate system and …
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Direct dynamical tunneling in systems with a mixed phase space
… generalizes the tunneling concept. A typical 1D Hamiltonian system has a mixed phase space. It contains regions of regular and chaotic dynamics, the so-called regular islands and the chaotic sea. These different phase space components are classically separated by dynamically generated barriers. …
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Vortices in sinusoidal shear, with applications to Jupiter
… to find vortex structures by integrating the Hamiltonian system has the drawback that the vortices lose enstrophy by filamentation and numerical dissipation, while continuing to deform and wobble. Adopting the local optimization technique of Hamiltonian Dirac Simulated Annealing overcomes this …
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Vortices in sinusoidal shear, with applications to Jupiter
… to find vortex structures by integrating the Hamiltonian system has the drawback that the vortices lose enstrophy by filamentation and numerical dissipation, while continuing to deform and wobble. Adopting the local optimization technique of Hamiltonian Dirac Simulated Annealing overcomes this …
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The nonlinear Schroedinger limit of the complex Ginzburg-Landau equation.
… the NLS equation is a completely integrable Hamiltonian system and a much larger family of its solutions can be written explicitly. The necessary conditions for the persistence of the NLS isospectral manifold are written explicitly as a system of equations for the simple periodic eigenvalues. …
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Application of the Lagrangian descriptors method to Hamiltonian systems with emphasis to models of barred galaxies
… permits the conversion of a dynamical system's phase space into a scalar field which can be used to distinguish regions of different dynamical behaviours and ultimately reveal structures in the system's phase space. In this work, we apply the LDs method to different dynamical systems. …
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Passivity-Based Control of Small Unmanned Aerial Systems
… range of autonomous motion of unmanned aerial systems without prohibitively {color{black}increasing the computational cost of the resultant controller}. Passivity-based control presents a method to implement a static, nonlinear state feedback control law that stabilizes the motion of an …
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Poisson structures and degenerations of integrable systems related to y (gl2)
The Toda lattice is an important dynamical system studied in the theory of integrable systems. It is known that the Toda lattice is related to other integrable systems: the DST system and the XXX model. We will generalize these three systems by attaching a Hamiltonian system to a nonincreasing …
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Anglo-American Relations, 1789-1794
… only essential to the success of the financial system erected by Hamilton but also necessary to prevent internal disunity and loss of territory as a result of a disastrous war. The Hamiltonian system rested on credit, and that credit was supported by import duties. By far the largest amount of …
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MIW Sequences
The Many Interacting Worlds (MIW) discrete Hamiltonian system approximation of the Schrödinger wave equation was introduced in [10]. Building on this work, convergence of MIW ground states to the normal ground state of the quantum harmonic oscillator has been shown via Stein's method [13, 5,15, …
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Quantization of Chirikov map and quantum KAM theorem
… eigenstates of the evolution operator of this system. We find that the wave functions in the coherent state representation (CSR) are very similar to the classical trajectories. In particular, some of these wave functions have wall-like structure at the locations of classical KAM curves. We also …
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Construction of frequency-energy plots for nonlinear dynamical systems from time-series data
… (FEP) is a useful tool in analyzing nonlinear system response, but previous methods of generating the FEP were limited to analytical calculations or use of the wavelet transform. Although these are acceptable methods of constructing the FEP, the former requires significant computation, and the …
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Geometric control and motion planning for three-dimensional bipedal locomotion
… stable hybrid limit cycles, we exploit system energetics, symmetry, and passivity through the energy-shaping method of controlled geometric reduction. This decouples a subsystem corresponding to a lower-dimensional robot through a passivity-based feedback transformation of the system …
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Plasma turbulence in the equatorial electrojet observations, theories, models, and simulations
… of describing both instabilities in a unified system. Numerical solution of the model in the linear regime demonstrates the capacity of the model to capture the salient characteristics of the two instabilities. Nonlinear simulations of the unified model of the equatorial electrojet …
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Geometric structures on the target space of Hamiltonian evolution equations
… with the relationship between integrable Hamiltonian partial differential equations and geometric structures on the manifold in which the dependent variables take their values. Chapters 1 and 2 are introductory chapters, and as such contain no original material. Chapter 1 covers some basic …
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On the N-body Problem
… of studying the 8 degrees of freedom Hamilton system for planar four-body problem, we reduce this number by means of some symmetry to derive a two degrees of freedom system which then can be used to determine the linear instability of the periodic solutions. After making a clever change of …
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