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.
Results
Showing 1 to 20 of 34 for “"Periodic orbit"”.
-
Periodic orbit analysis of the Helmholtz equation in two-dimensional enclosures
This thesis examines how periodic orbits may be used in acoustics to understand solutions of the Helmholtz equation. A review of the links between ray and wave mechanics is given including WKBJ (Wentzel, Kramers, Brillouin and Jeffreys) and EBK (Einstein, Brillouin, Keller) methods. It is also …
-
Station-keeping and orbital transfers in the vicinity of the Moon exploiting quasi-periodic orbit dynamics
… scenarios considering the use of low lunar orbits or transfer arcs to the surface are replaced by new mission scenarios exploiting the potentialities of the collinear Earth-Moon libration point orbits. In addition, solutions considering multiple coordinated spacecraft with disaggregated …
-
On stability and controllability of conjunctive Boolean networks
… of a finite dynamical system will enter a periodic orbit. Periodic orbits of a CBN are now completely understood. We first characterize in this thesis all periodic orbits of a CBN. In particular, we establish a bijection between the set of periodic orbits and the set of binary necklaces of …
-
Correlated trajectories in semiclassical approaches to quantum chaos
… form factor $K(\tau,x)$. Using a semiclassical periodic orbit expansion, we obtain a small $\tau$ expansion that agrees with random matrix theory for systems with and without time reversal symmetry. Then we consider correlations of the Wigner time delay in open systems. We study a form factor …
-
Coherent structures in incompressible fluid flows
… descriptions of turbulence is predicted by periodic orbit theory (POT) which expects to describe turbulence exactly, as opposed to approximately. The search for relative periodic orbits and traveling waves in pipe---the constituents solutions to periodic orbit theory---are discussed. The …
-
Dynamical systems approach to one-dimensional spatiotemporal chaos -- A cyclist's view
… turbulence(spatiotemporal chaos) based on the periodic orbit theory, emphasizing the role of recurrent patterns and coherent structures. After a brief review of the periodic orbit theory and its application to low-dimensional dynamics, we discuss its possible extension to study dynamics of …
-
Investigating multiphoton phenomena using nonlinear dynamics
… These phase-space structures may be periodic 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 …
-
The Geometry of Isochrons in Planar Systems
… the so-called isochrons of the underlying periodic orbit. Each isochron is the set of points that converge to the periodic orbit in phase with each other. In this thesis, we investigate planar systems, for which isochrons are curves that can have very complex geometries; we study how these …
-
Invariant Manifolds of a Toy Climate Model
… ice ages are caused by variations in the Earth's orbit. However, ice core data shows strong fluctuations in ice volume at a low frequency not significantly present in orbital variations. To understand how this might occur, the dynamics of a two dimensional nonlinear differential equation …
-
A dynamical-systems approach to understanding turbulence in plane Couette flow
… dynamics in terms of the local dynamics of its periodic solutions; these are the periodic orbits in state space. We considered the development of a model for the dynamics of plane Couette flow based on the theory. The proposed model is essentially a set of low-dimensional models for the local …
-
Transport geometry of the restricted three-body problem
… the Lagrange points in the CR3BP to time-periodic perturbations of the CR3BP, such as the bicircular problem (BCP) and the elliptic restricted three-body problem (ER3BP). The Lagrange points are no longer invariant under perturbation and are replaced by periodic orbits, which we call …
-
From the Earth to the Moon: A Multi-Domain Approach to Cislunar Space Domain Awareness
… configurations of optical sensors placed on periodic orbits within the Circular Restricted Three-Body Problem (CR3BP) through the development of a novel multivariate normal crossover technique for Genetic Algorithms that enables statistical local and global search of discrete populations. …
-
Control of a Chaotic Double Pendulum Model for a Ship Mounted Crane
… method is used to identify the unstable periodic orbit (UPO). Two different system parameters are used to control the motion. Minimum parameter constraints are studied. The use of discrete values for parameter changes is also investigated. Based on these investigations, a new on-off …
-
ΣΥΜΒΟΛΗ ΣΤΗ ΘΕΩΡΙΑ ΤΩΝ D+- ΕΥΣΤΑΘΩΝ ΔΥΝΑΜΙΚΩΝ ΣΥΣΤΗΜΑΤΩΝ ΣΕ ΔΙΔΙΑΣΤΑΤΕΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ
… D+ - STABLE DYNAMICAL SYSTEMS WITH AT LEAST ONE PERIODIC ORBIT. FROM THIS WE DEDUCE THAT THERE ARE ONLY FOUR COMPACT 2-MANIFOLDS WHICH CAN SUPPORT A (NON-TRIVIAL) D+ - STABLE DYNAMICAL SYSTEM. ON THE CONTRARY, ON EVERY NON-COMPACT 2-MANIFOLD WE CONSTRUCT A (NON-TRIVIAL) D+ - STABLE DYNAMICAL …
-
Geometrical Investigation on Escape Dynamics in the Presence of Dissipative and Gyroscopic Forces
… of a given energy is the invariant manifold of a periodic orbit. The process of obtaining such invariant manifold compromises two parts, including the computation of the periodic orbit by solving a proper boundary-value problem (BVP) and the globalization of the manifold. For the dissipative …
-
Spectral properties of planar helium under periodic driving
… packets which propagate along the associated periodic orbit. This represents a highly nontrivial qualitative confirmation of earlier calculations on a 1D model atom, though with important enhancements of the decay rate of these atomic eigenstates in the field, due to the transverse decay …
-
Modeling and Control of a Planar Bounding Quadrupedal Robot
… real-world behavior. The bounding gait (periodic orbit) of the robot is predicted by an optimization method based on the numerical integration of the differential equations of subsystems. To stabilize the gait, a switching controller is applied which can be split into two separate phases: …
-
Discrete dynamical systems in solving H-equations
… the mathematical structure and behavior of the orbits with respect to the parameter function, i.e. characteristic function. The dynamical system is controlled by a manifold. For n=2, stability of the fixed points is studied. The stable and unstable manifolds passing through the hyperbolically …
-
Cloud-Based Model Predictive Control: Establishing a Fully Distributed Architecture for Nonlinear MPC
… is capable of stabilizing a system to a periodic orbit when suitable constraints are applied.
-
From Measure Zero to Measure Hero: Periodic Kerr Orbits and Gravitational Wave Physics
… dynamical systems approach to the study of Kerr orbits, beginning with equatorial orbits. We deduce a topological taxonomy of orbits that hinges on a correspondence between periodic orbits and rational numbers. The taxonomy defines the entire dynamics, including aperiodic motion, since every …
Page 1 of 2