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 12 of 12 for “"stable and unstable manifolds"”.
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Using the Circular Restricted Three-Body Problem to Design an Earth-Moon Orbit Architecture for Asteroid Mining
Engineering and technical challenges exist with the material transport of natural resources in space. One aspect of this transport problem is the design of an orbit architecture in the Earth-Moon system (EMS) that facilitates these resources through the mining cycle. In this thesis, it is proposed …
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Geometric Approaches in Phase Space Transport and Partial Control of Escaping Dynamics
… presents geometric approaches of understanding chaotic transport in phase space that is fundamental across many disciplines in physical sciences and engineering. This approach is based on analyzing phase space transport using boundaries and regions inside these boundaries in presence of …
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A new numerical optimization method based on Taylor series for challenging trajectory optimization problems
… constraints. Existing methods use only zeroth and first order derivatives of the system equations to formulate these constraints. The techniques of automatic differentiation allow the computation of the derivatives of the state equations to arbitrary order in reasonable time. The new methods …
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Investigation into the Local and Global Bifurcations of the Whirling Planar Pendulum
… This dynamical system exhibits both local and global bifurcations. The local pitchfork bifurcation leads to the splitting of a single stable equilibrium point into three (two stable and one unstable), as the spin rate is increased. The global bifurcations lead to two independent types of …
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Chaotic transport by a turnstile mechanism in 4D symplectic maps
Many systems in nature, e.g. atoms, molecules and planetary motion, can be described as Hamiltonian systems. In such systems, the transport between different regions of phase space determines some of their most important properties like the stability of the solar system and the rate of chemical …
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Discrete dynamical systems in solving H-equations
… dynamical models are used to solve the Chandrasekhar H-equation with a positive or negative characteristic function. Two of them produce series of continuous functions which converge to the solution of the H-equation. An iteration model of the nth approximation for the H-equation is …
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Transport geometry of the restricted three-body problem
This dissertation expands across three topics the geometric theory of phase space transit in the circular restricted three-body problem (CR3BP) and its generalizations. The first topic generalizes the low energy transport theory that relies on linearizing the Lagrange points in the CR3BP to …
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Integrability, localisation and bifurcation of an elastic conducting rod in a uniform magnetic field
… of a geometrically exact rod under end tension and moment are extended by incorporating the evolution of a fixed external vector (in the direction of the magnetic field) that interacts with the rod via a Lorentz force. The static equilibrium equations (in body cordinates) are found to be …
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Investigating multiphoton phenomena using nonlinear dynamics
… complex dynamics which has been studied and uncovered through nonlinear dynamical theory. The leitmotif of this thesis is changing phase-space structures and their (linear or nonlinear) stabilities by adding control functions (which act on the system as external perturbations) to the …
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Chaotic advection, mixing, and property exchange in three-dimensional ocean eddies and gyres
… flows: an overturning submesoscale eddy and the Western Alboran Gyre. In the first case, I focus on the importance of diffusion as compared to chaotic advection for tracers in this system. Three methods are used to quantify the relative contributions: scaling arguments including a …
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Chaotic advection, mixing, and property exchange in three-dimensional ocean eddies and gyres
… flows: an overturning submesoscale eddy and the Western Alboran Gyre. In the first case, I focus on the importance of diffusion as compared to chaotic advection for tracers in this system. Three methods are used to quantify the relative contributions: scaling arguments including a …
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A New Method to Predict Vessel Capsizing in a Realistic Seaway
… analytic solution, exact upto the rst order, and takes into account the the complete unperturbed (no damping or forcing) dynamics. Using this method very-large-amplitude nonlinear vessel motion in a random seaway can be analysed with techniques similar to those used to analyse nonlinear vessel …