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 25 for “"Invariant manifolds"”.
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Pitchfork bifurcations of invariant manifolds
… the topological properties of fixed points and invariant manifolds of dynamical systems. A pitchfork bifurcation in R is said to have occurred when a stable fixed point becomes unstable and two new stable fixed points, separated by the unstable fixed point come into existence. In this thesis, a …
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Invariant Manifolds of a Toy Climate Model
… phenomena rely on bounded, structurally stable invariant manifolds that occur when a constant equilibrium solution becomes unstable. For the autonomous formulation, asymptotic analysis was performed to obtain analytic approximations. An outflowing manifold of a second saddle equilibrium formed a …
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High-order adaptive methods for computing invariant manifolds of maps
… and accurate numerical methods for computing invariant manifolds of maps which arise in the study of dynamical systems. In order to decrease the number of points needed to compute a given curve/surface, he proposes using higher-order interpolation/approximation techniques from geometric …
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Interplanetary Transfer Trajectories Using the Invariant Manifolds of Halo Orbits
… on a spacecraft, rather than just one. The invariant manifolds of halo orbits about Sun-planet Lagrange points are used to aid in the transfer from one planet to another, and can lead into orbital insertion about the destination planet or flyby trajectories to get to another planet. This …
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A numerical investigation of the global stability of ship roll: invariant manifolds, Melnikov's method, and transient basins
… is investigated through the numerical study of invariant manifolds, Melnikov's method, and transient basins. The calculation of the manifolds is facilitated through the development of a sophisticated algorithm for approximating the locations of the saddle points of the Poincaré map. For selected …
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Automated detection of invariant manifold intersections using grid based approach
… and the dynamical structure of interest are the invariant manifolds of the Euler-Lagrange points. The construction of LE trajectories in the CR3BP is most often accomplished by manually finding homoclinic and/or heteroclinic intersections of invariant manifolds located on specific Poincare …
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Finding and exploiting structure in complex systems via geometric and statistical methods
… the structure can be revealed by the study of invariant manifolds of fixed points and periodic orbits in the first system, there do not exist any fixed points (and hence invariant manifolds) in the second system. The use of statistical (or measure theoretic) and topological methods reveals the …
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Spacecraft trajectory design utilizing resonance orbits in a hybrid optimal control framework
… efforts to incorporate resonance orbits, their invariant manifolds, and associated families into an automated global optimization tool in order to create solutions of optimal impulsive spacecraft trajectories in multi-body environments. Previous work using this tool has shown the ability to use …
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Exact coherent structures in spatiotemporal chaos: From qualitative description to quantitative predictions
… governing dynamical equations, is shaped by the invariant sets such as equilibria, periodic orbits, and invariant tori. State space of partial differential equations is infinite dimensional, nevertheless, recent computational advancements allow us to find their invariant solutions (exact coherent …
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Astrodynamics of the Next Generation Space Weather Prediction Mission
… are discussed and Low Energy transfers using invariant manifolds are evaluated. Transfers from Earth to Sun-Earth L1 as well as Sun-Venus, and Sun-Mercury L1 are computed.</p>
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A Mathematical Model for the Transition in Firing Patterns Across Puberty of a Gonadotropin-Releasing Hormone Neuron
… questions pertaining to the geometry of invariant manifolds of the underlying dynamical system. Using geometric singular perturbation theory methods and mathematical software packages I analyze the MMOs arising in the GnRH model. This analysis is presented through a sequence of theorems …
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Bifurcations of maps: numerical algorithms and applications
… An aspect of this study is to identify the invariant objects and the local behaviour around them. This local information then needs to be assembled in a consistent way by means of geometric and topological arguments, to obtain a global picture of the system. At local bifurcations, the number …
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Significance of Specific Force Models in Two Applications: Solar Sails to Sun-Earth L4/L5 and GRAIL Data Analysis Suggesting Lava Tubes and Buried Craters on the Moon
… First, to construct low energy transfers, the invariant manifolds are explored that form an important tool in the computation and design of complex trajectories. The focus is the investigation of trajectory design options, incorporating solar sail dynamics, from the Earth parking orbit to the …
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Application of the Lagrangian descriptors method to Hamiltonian systems with emphasis to models of barred galaxies
… galactic type to highlight normally hyperbolic invariant manifolds (NHIMs), examining the impact of different pattern speeds and energy levels on the NHIMs' structure and determine how these features influence orbital morphologies seen in the model's configuration space. Thereafter, we apply the …
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Natural and artificial orbits around the Martian moon Phobos
… artificial equilibria - Libration Point orbits - Invariant Manifolds - Quasi-Satellite orbits - radiation shielding - Phobos origin - Phobos morphology - Dynamical Systems Theory - numerical continuation
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Nonlinear, conditionally stable, singularly perturbed boundary-relation problems
… operator. The proof makes use of the local invariant manifolds of the boundary layer equation along solutions of the reduced differential equation. The vectors x and y may belong to arbitrary Banach spaces.
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The Lorenz System Near the Loss of the Foliation Condition
… of the Lorenz system is organised by the global invariant manifolds of saddle equilibria and saddle periodic orbits. Speci cally, we explain and de ne two phenomena, observed by Sparrow in the 1980's. First, the so-called 'half-swing' of the one-dimensional stable manifolds Ws(p ) of the …
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Theoretical foundations for finite-time transient stability and sensitivity analysis of power systems
… based on the theory of normally hyperbolic invariant manifolds and finite time Lyapunov exponents, adopted from geometric theory of dynamical systems. The theory of normally hyperbolic surfaces allows us to characterize the rate of expansion and contraction of co-dimension one material …
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Topological chaos and chaotic mixing of viscous flows
… the flow, invariance or leakiness of the Almost Invariant Sets (AIS) playing the role of ghost rods is found to be in a direct relationship with the rate of homogenization of a scalar. The mixing caused by these AIS and the variations of their structure are explained from the point of view of …
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Nonlinear Models and Geometric Structure of Fluid Forcing on Moving Bodies
… in velocity space collapse to a 1-dimensional invariant manifold known as the terminal velocity manifold. This work presents methods to identify the terminal velocity manifold, investigates its properties, and extends it to a 2-dimensional invariant manifold in a 3-dimensional space. Finally, …
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