Dynamical Systems X
Subtitle: General Theory of Vortices
By: by V. V. Kozlov
Series: Encyclopaedia of Mathematical Sciences -- 67; Encyclopaedia of Mathematical Sciences -- 67
Publisher: Springer Berlin Heidelberg
Published: 2003
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] :
Number of pages: 184
ISBN-13: 9783642075841; 9783662068007
Subjects: Geometry; Mathematics; Global analysis (Mathematics); Mechanics
Description: This book contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. This theory highlights several general mathematical ideas that appeared in Hamiltonian mechanics, optics and hydrodynamics under different names. In addition, some interesting applications of the general theory of vortices are discussed in the book such as applications in numerical methods, stability theory, and the theory of exact integration of equations of dynamics. The investigation of families of trajectories of Hamiltonian systems can be reduced to problems of multidimensional ideal fluid dynamics. For example, the well-known Hamilton-Jacobi method corresponds to the case of potential flows. The book will be of great interest to researchers and postgraduate students interested in mathematical physics, mechanics, and the theory of differential equations.
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Table of contents: title: Introduction; title: 1. Hydrodynamics, Geometrical Optics, and Classical Mechanics; title: 2. General Vortex Theory; title: 3. Geodesics on Lie Groups with Left-Invariant Metrics; title: 4. Vortex Method of Integration of Hamilton Equations; title: Appendix 1. Invariants of Vorticity and Second Hydrodynamics; title: Appendix 2. Quantum Mechanics and Hydrodynamics; title: References; title: Index.