| Titre : |
Dynamical systems. X : general theory of vortices |
| Type de document : |
texte imprimé |
| Auteurs : |
Viktor Vladimirovich Kozlov, Auteur ; A. V. Ovchinnikov, Traducteur |
| Editeur : |
Berlin ; London ; Cham : Springer |
| Année de publication : |
2003 |
| Collection : |
Encyclopaedia of mathematical sciences num. 67 |
| Importance : |
VIII, 184 p |
| Présentation : |
ill. |
| Format : |
24 cm |
| ISBN/ISSN/EAN : |
978-3-540-42207-5 |
| Note générale : |
Bibliogr. p. 176-180. - Index
|
| Langues : |
Anglais (eng) |
| Mots-clés : |
Mechanics
Differentiable dynamical systems
Mécanique
Dynamique différentiable |
| Index. décimale : |
532.5 Mouvement des liquides. Hydrodynamique. |
| Résumé : |
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. Well-known first-rate author Treats a major topic in mathematical physics Text: 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 general vortex theory 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 ofdifferential equations. |
| Note de contenu : |
Summary :
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 |
Dynamical systems. X : general theory of vortices [texte imprimé] / Viktor Vladimirovich Kozlov, Auteur ; A. V. Ovchinnikov, Traducteur . - Berlin ; London ; Cham : Springer, 2003 . - VIII, 184 p : ill. ; 24 cm. - ( Encyclopaedia of mathematical sciences; 67) . ISBN : 978-3-540-42207-5 Bibliogr. p. 176-180. - Index
Langues : Anglais ( eng)
| Mots-clés : |
Mechanics
Differentiable dynamical systems
Mécanique
Dynamique différentiable |
| Index. décimale : |
532.5 Mouvement des liquides. Hydrodynamique. |
| Résumé : |
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. Well-known first-rate author Treats a major topic in mathematical physics Text: 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 general vortex theory 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 ofdifferential equations. |
| Note de contenu : |
Summary :
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 |
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