Geometrical Theory of Dynamical Systems and Fluid Flows (Revised Edition) (Hardcover) (ISBN-13: 9789814282246)

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: Kambe
ISBN-10: 9814282243
ISBN-13: 9789814282246
Publisher: World Scientific Publishing Company
Language: English
Published: 12/29/2009
Pages: 444
Format: Hardcover
Weight: 1.70lbs
Size: 9.10h x 6.10w x 1.20d