Geometrical Theory Of Dynamical Systems And Fluid Flows PDF Download
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Author | : |
Publisher | : World Scientific |
Total Pages | : 444 |
Release | : 2009 |
Genre | : Fluid dynamics |
ISBN | : 9814282251 |
Download Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) Book in PDF, ePub and Kindle
"This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows and certain integrable systems. The topics are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The main theme of this book is a unified formulation to understand dynamical evolutions of physical systems within mathematical ideas of Riemannian geometry and Lie groups by using well-known examples. Underlying mathematical concepts include transformation invariance, covariant derivative, geodesic equation and curvature tensors on the basis of differential geometry, theory of Lie groups and integrability. These mathematical theories are applied to physical systems such as free rotation of a top, surface wave of shallow water, action principle in mechanics, diffeomorphic flow of fluids, vortex motions and some integrable systems. In the latest edition, a new formulation of fluid flows is also presented in a unified fashion on the basis of the gauge principle of theoretical physics and principle of least action along with new type of Lagrangians. A great deal of effort has been directed toward making the description elementary, clear and concise, to provide beginners easy access to the topics."-
Author | : Tsutomu Kambe |
Publisher | : World Scientific Publishing Company |
Total Pages | : 436 |
Release | : 2004-09-09 |
Genre | : Science |
ISBN | : 981310628X |
Download Geometrical Theory Of Dynamical Systems And Fluid Flows Book in PDF, ePub and Kindle
This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows, and certain integrable systems. The subjects are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The underlying concepts are based on differential geometry and theory of Lie groups in the mathematical aspect, and on transformation symmetries and gauge theory in the physical aspect. A great deal of effort has been directed toward making the description elementary, clear and concise, so that beginners will have an access to the topics.
Author | : Tian Ma |
Publisher | : American Mathematical Soc. |
Total Pages | : 248 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821836935 |
Download Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics Book in PDF, ePub and Kindle
This monograph presents a geometric theory for incompressible flow and its applications to fluid dynamics. The main objective is to study the stability and transitions of the structure of incompressible flows and its applications to fluid dynamics and geophysical fluid dynamics. The development of the theory and its applications goes well beyond its original motivation of the study of oceanic dynamics. The authors present a substantial advance in the use of geometric and topological methods to analyze and classify incompressible fluid flows. The approach introduces genuinely innovative ideas to the study of the partial differential equations of fluid dynamics. One particularly useful development is a rigorous theory for boundary layer separation of incompressible fluids. The study of incompressible flows has two major interconnected parts. The first is the development of a global geometric theory of divergence-free fields on general two-dimensional compact manifolds. The second is the study of the structure of velocity fields for two-dimensional incompressible fluid flows governed by the Navier-Stokes equations or the Euler equations. Motivated by the study of problems in geophysical fluid dynamics, the program of research in this book seeks to develop a new mathematical theory, maintaining close links to physics along the way. In return, the theory is applied to physical problems, with more problems yet to be explored. The material is suitable for researchers and advanced graduate students interested in nonlinear PDEs and fluid dynamics.
Author | : Renzo L. Ricca |
Publisher | : Springer Science & Business Media |
Total Pages | : 346 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9401004463 |
Download An Introduction to the Geometry and Topology of Fluid Flows Book in PDF, ePub and Kindle
Leading experts present a unique, invaluable introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and links, the reader is gradually led to explore the fascinating world of geometric and topological fluid mechanics. Geodesics and chaotic orbits, magnetic knots and vortex links, continual flows and singularities become alive with more than 160 figures and examples. In the opening article, H. K. Moffatt sets the pace, proposing eight outstanding problems for the 21st century. The book goes on to provide concepts and techniques for tackling these and many other interesting open problems.
Author | : Jerrold E. Marsden |
Publisher | : American Mathematical Soc. |
Total Pages | : 466 |
Release | : 1984 |
Genre | : Mathematics |
ISBN | : 0821850288 |
Download Fluids and Plasmas: Geometry and Dynamics Book in PDF, ePub and Kindle
"The organizing committee envisioned bringing together three groups of people working on the following topics in fluid and plasma dynamics: 1. Geometric aspects : Hamiltonian structures, perturbation theory and nonlinear stability by variational methods, 2) Analytical and numerical methods: contour dynamics, spectral methods, and functional analytic techniques, 3) Dynamical systems aspects: experimental and numerical methods, bifurcation theory, and chaos."- introduction
Author | : Banavara N. Shashikanth |
Publisher | : Springer Nature |
Total Pages | : 192 |
Release | : 2021-10-28 |
Genre | : Science |
ISBN | : 3030826465 |
Download Dynamically Coupled Rigid Body-Fluid Flow Systems Book in PDF, ePub and Kindle
This book presents a unified study of dynamically coupled systems involving a rigid body and an ideal fluid flow from the perspective of Lagrangian and Hamiltonian mechanics. It compiles theoretical investigations on the topic of dynamically coupled systems using a framework grounded in Kirchhoff’s equations. The text achieves a balance between geometric mechanics, or the modern theories of reduction of Lagrangian and Hamiltonian systems, and classical fluid mechanics, with a special focus on the applications of these principles. Following an introduction to Kirchhoff’s equations of motion, the book discusses several extensions of Kirchhoff’s work, particularly related to vortices. It addresses the equations of motions of these systems and their Lagrangian and Hamiltonian formulations. The book is suitable to mathematicians, physicists and engineers with a background in Lagrangian and Hamiltonian mechanics and theoretical fluid mechanics. It includes a brief introductory overview of geometric mechanics in the appendix.
Author | : Jacob Palis |
Publisher | : |
Total Pages | : 198 |
Release | : 1998 |
Genre | : |
ISBN | : 9787515802800 |
Download Geometric Theory of Dynamical Systems Book in PDF, ePub and Kindle
Author | : Jean-marc Ginoux |
Publisher | : World Scientific |
Total Pages | : 341 |
Release | : 2009-04-03 |
Genre | : Mathematics |
ISBN | : 9814467634 |
Download Differential Geometry Applied To Dynamical Systems (With Cd-rom) Book in PDF, ePub and Kindle
This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory — or the flow — may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes).In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem.
Author | : Roger M. Samelson |
Publisher | : Springer Science & Business Media |
Total Pages | : 154 |
Release | : 2006-11-24 |
Genre | : Mathematics |
ISBN | : 0387462139 |
Download Lagrangian Transport in Geophysical Jets and Waves Book in PDF, ePub and Kindle
Written jointly by a specialist in geophysical fluid dynamics and an applied mathematician, this is the first accessible introduction to a new set of methods for analysing Lagrangian motion in geophysical flows. The book opens by establishing context and fundamental mathematical concepts and definitions, exploring simple cases of steady flow, and touching on important topics from the classical theory of Hamiltonian systems. Subsequent chapters examine the elements and methods of Lagrangian transport analysis in time-dependent flows. The concluding chapter offers a brief survey of rapidly evolving research in geophysical fluid dynamics that makes use of this new approach.
Author | : J.K. Hale |
Publisher | : Springer Science & Business Media |
Total Pages | : 203 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475744935 |
Download An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory Book in PDF, ePub and Kindle
Including: An Introduction to the Homotopy Theory in Noncompact Spaces