Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) write by . This book was released on 2009. Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) available 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."-
Geometrical Theory Of Dynamical Systems And Fluid Flows
Geometrical Theory Of Dynamical Systems And Fluid Flows - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometrical Theory Of Dynamical Systems And Fluid Flows write by Tsutomu Kambe. This book was released on 2004-09-09. Geometrical Theory Of Dynamical Systems And Fluid Flows available 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.
Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics
Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics write by Tian Ma. This book was released on 2005. Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics available 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.
An Introduction to the Geometry and Topology of Fluid Flows
An Introduction to the Geometry and Topology of Fluid Flows - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to the Geometry and Topology of Fluid Flows write by Renzo L. Ricca. This book was released on 2012-12-06. An Introduction to the Geometry and Topology of Fluid Flows available 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.
Geometric Theory of Dynamical Systems
Geometric Theory of Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Theory of Dynamical Systems write by Jacob Palis. This book was released on 1998. Geometric Theory of Dynamical Systems available in PDF, EPUB and Kindle.
