Dynamical Systems X: General Theory of Vortices

ISBN-13: 9783642075841 / Angielski / Miękka / 2010 / 184 str.

V. V. Kozlov

Opis

This book contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. In addition, it details some interesting applications of the general theory of vortices, such as applications in numerical methods, stability theory, and the theory of exact integration of equations of dynamics.

Recenzje

From the reviews:

"This is a very interesting, nicely written book on deep mathematical analogies between hydrodynamics, geometric optics and mechanics. [...] The book will surely be of interest to researchers and postgraduate students in mathematical physics and mechanics."

EMS Newsletter December 2005

"... Kozlov's very valuable contribution to the Encyclopaedia of Mathematical Sciences explores the world from the point of view of the vortex, its role in a variety of theories with an acknowledgement of the history of the argument originating in the rivalry of the Cartesian and Newtonian views of the world. ..."

C.Athorne, University of Glasgow, Contemporary Physics 2004, Vol. 45, Issue 5

"Kozlov's very valuable contribution to the Encyclopedia of Mathematical Sciences explores the world from the point of view of the vortex, its role in a variety of theories with an acknowledgement of the history of the argument originating in the rivalry of the Cartesian and Newtonian views of the world. Thus, the impulse behind the book is to make precise and formalize analogies between the motions of ideal fluids and the classical mechanics of conservative systems."

Dr. C. Athorne, Contemporary Physics, Vol. 45 (5), 2004

"The book is a translation from the 1998 original work appeared in Russian. ... the author highlights some analogies between hydrodynamics, classical mechanics, geometrical optics, and symplectic geometry. ... The book will be of great interest to researchers working on this or related subjects."

G.Schneider, ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 84 (10-11), 2004

"This book is devoted to a mathematical description of analogies between hydrodynamics, geometrical optics and classical mechanics. The basic idea is that the study of families of trajectories of Hamiltonian systems can be reduced to the investigation of multidimensional ideal fluid dynamics. The book contains four chapters and three appendices. ... can be recommended to researchers and graduate students interested in mathematical physics, mechanics and differential equations." (Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol. 74, 2008)

Spis treści

1. Hydrodynamics, Geometric Optics, and Classical Mechanics.- 2. General Vortex Theory.- 3. Geodesics on Lie Groups with a Left-Invariant Metric.- 4. Vortex Method for Integrating Hamilton Equations.- Supplement 1: Vorticity Invariants and Secondary Hydrodynamics.- Supplement 2: Quantum Mechanics and Hydrodynamics.- Supplement 3: Vortex Theory of Adiabatic Equilibrium Processes.- References.