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 18 of 18 for “"unstable manifolds"”.
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Using the Circular Restricted Three-Body Problem to Design an Earth-Moon Orbit Architecture for Asteroid Mining
… 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 …
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Geometric Approaches in Phase Space Transport and Partial Control of Escaping Dynamics
… system is the codimension 1 stable and unstable manifolds associated with the hyperbolic fixed points. The manifolds separate regions with varied dynamical fates and their time evolution encodes how the initial conditions in a given region of phase space get transported to other regions. …
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An efficient algorithm for sensitivity analysis of chaotic systems
… chaotic attractors occur – with one-dimensional unstable manifolds. S3 can enable applications of the computed sensitivities to optimization, control theory and uncertainty quantification, in the realm of chaotic dynamics, wherein these applications remain nascent. We propose a transformation of …
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A new numerical optimization method based on Taylor series for challenging trajectory optimization problems
… problem (CR3BP), in particular the stable and unstable manifolds of a halo orbit about the interior L1 Lagrange point in the Earth-Moon system.
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Investigation into the Local and Global Bifurcations of the Whirling Planar Pendulum
… equilibrium point into three (two stable and one unstable), as the spin rate is increased. The global bifurcations lead to two independent types of chaotic oscillations which are induced by sinusoidal excitations. The types of chaos are each associated with one of two homoclinic orbits in the …
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Moduli spaces and cw structures arising from morse theory
… flow lines and gives a stratication of M by its unstable manifolds. The gluing of broken flow lines can also be constructed.</p> <p>We prove that, under certain assumptions, these moduli spaces can be compactified and the compactified spaces are smooth manifolds with corners. Moreover, these …
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A New Method to Predict Vessel Capsizing in a Realistic Seaway
… of solution orbits which lie in the stable or unstable manifolds and are then projected onto the phase plane.
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Chaotic transport by a turnstile mechanism in 4D symplectic maps
… of hyperbolic 1D-tori and their stable and unstable manifolds. We provide an approach to measure the volume of a turnstile in higher dimensions as well as the corresponding transport. From the very good agreement of the two measurements we conclude that these structures are a suitable …
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Nonlinear dynamics of three dimensional fluid flow separation
… and separation surface by locating nonhyperbolic unstable manifolds that collect and eject fluid particles from the boundary. We verify our theory on analytic flow models, in numerical simulations of important benchmark problems and in experiments. Our theory provides a systematic tool for …
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Discrete dynamical systems in solving H-equations
… of the fixed points is studied. The stable and unstable manifolds passing through the hyperbolically fixed point are obtained. Globally, the bounded orbits region is given. For parameter c in some region a periodic orbit of one dimension will cause periodic orbits in the higher dimensional …
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Leveraging the Linear Response Theory in Sensitivity Analysis of Chaotic Dynamical Systems and Turbulent Flows
… structure combined with the chain rule on smooth manifolds enables the derivation of ergodic-averaging schemes for sensitivities that rigorously converge in uniformly hyperbolic systems. Thus, S3 can be viewed as an LRT-based Monte Carlo method that averages data collected through regularized …
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Analysis of two- and three-dimensional flow separation
… as a material instability induced by an unstable manifold of a distinguished boundary point. In this general context, the unstable manifold is a time-dependent material line that shrinks to the separation point in backward time. In forward time, the unstable manifold attracts and ejects …
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Transport geometry of the restricted three-body problem
… particles, may be identified with the stable and unstable manifolds to the singularities of the CR3BP. We also study the arches in terms of particle orbital elements and demonstrate that the arches correspond to gravity assists in the two-body limit.
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Integrability, localisation and bifurcation of an elastic conducting rod in a uniform magnetic field
… to the transverse intersection of the stable and unstable manifolds and the loss of complete integrability. Consequently, the system admits spatially chaotic solutions and a multiplicity of multimodal homoclinic solutions exist. Poincare sections associated with the loss of integrability are …
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Investigating multiphoton phenomena using nonlinear dynamics
… orbits, invariant tori or their stable and unstable manifolds. One-electron systems and diatomic molecules are fundamental and important staging ground for new discoveries in nonlinear dynamics. In past years, increasing emphasis and effort has been put on the control or manipulation of …
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Chaotic advection, mixing, and property exchange in three-dimensional ocean eddies and gyres
… gyre boundary from segments of the stable and unstable manifolds emanating from two persistent hyperbolic trajectories on the coast at the eastern and western extent of the gyre. These manifolds are computed on several isopycnals and stacked vertically to construct a three-dimensional …
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Chaotic advection, mixing, and property exchange in three-dimensional ocean eddies and gyres
… gyre boundary from segments of the stable and unstable manifolds emanating from two persistent hyperbolic trajectories on the coast at the eastern and western extent of the gyre. These manifolds are computed on several isopycnals and stacked vertically to construct a three-dimensional …
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Bifurcation analysis near the cessation of complete chatter and Shilnikov homoclinic trajectories in a pressure relief valve model
The student, Erika Fotsch, submitted this Thesis for approval on 2016-01-19 at 09:37.