Geometrical theory of dynamical systems and fluid flows
 Author/Creator
 Kambe, Tsutomu.
 Language
 English.
 Edition
 Rev. ed.
 Imprint
 New Jersey : World Scientific, c2010.
 Physical description
 xxi, 421 p. : ill. ; 24 cm.
 Series
 Advanced series in nonlinear dynamics ; v. 23.
Access
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 405412) and index.
 Contents

 Mathematical Bases: Manifolds, Flows, Lie Groups and Lie Algebras Geometry of Surfaces in R3 Riemannian Geometry Dynamical Systems: Free Rotation of a Rigid Body Water Waves and KdV Equation Hamiltonian Systems: Chaos, Integrability and Phase Transition Flows of Ideal Fluids: Gauge Principle and Variational Formulation of Fluid Flows VolumePreserving Flows of an Ideal Fluid Motion of Vortex Filaments Geometry of Integrable Systems: Geometric Interpretations of SineGordon Equation Integrable Surfaces: Riemannian Geometry and Group Theory.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 wellknown 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2010
 Responsibility
 Tsutomu Kambe.
 Series
 Advanced series in nonlinear dynamics ; v. 23
 Note
 Previous ed.: 2004.
 ISBN
 9789814282246
 9814282243