Geometrical Theory Of Dynamical Systems And Fluid Flows

Download or read book Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) written by and published by World Scientific. This book was released on 2009 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."-

Download or read book Geometrical Theory Of Dynamical Systems And Fluid Flows written by Tsutomu (Jixin) Kambe and published by World Scientific Publishing Company. This book was released on 2004-09-09 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book An Introduction to the Geometry and Topology of Fluid Flows written by Renzo L. Ricca and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics written by Tian Ma and published by American Mathematical Soc.. This book was released on 2005 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Differential Geometry Applied To Dynamical Systems (With Cd-rom) written by Jean-marc Ginoux and published by World Scientific. This book was released on 2009-04-03 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory written by J.K. Hale and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Including: An Introduction to the Homotopy Theory in Noncompact Spaces

Download or read book Differential Dynamical Systems, Revised Edition written by James D. Meiss and published by SIAM. This book was released on 2017-01-24 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.