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Zusatztext Throughout the text the exposition is very clear, and this is in big part due to the extensive use of detailed examples, which is probably one of the strongest pedagogical points of this text when compared with other text books with similar subjects and targets...This makes this text the starting point for any researcher interested in getting started in the field of geometric models for continuum systems. Informationen zum Autor Darryl D Holm spent thirty four years at Los Alamos National Laboratory before moving in 2005 to Imperial College London as Professor of Applied Mathematics. During his career, Darryl developed a wide range of applications of the geometric approach to dynamical systems. His main interest is in deriving and analyzing nonlinear evolution equations for multiscale phenomena. Applications of these equations have ranged from nonlinear optical pulses used in telecommunications, to turbulence modeling for global ocean circulation and climate prediction, to template matching for the shapes of biomedical images, to directed self-assembly in nanoscience. The solution behavior of these equations includes solitons (governed by the Camassa-Holm equation), vortices and turbulence (modelled by the LANS-alpha equation) and emergent singularities (modelled by the EPDiff equation) representing the sharp edges that appear in biomedical images.Tanya Schmah completed her PhD in mathematics in 2001 at the Swiss Federal Institute of Technology in Lausanne. She has held lectureships at the University of Warwick (U.K.) and Macquarie University (Australia), and is currently working in the Department of Computer Science at the University of Toronto. She has a wide range of interests in mathematics and computer science, including symmetric Hamiltonian systems and machine learning.Cristina Stoica has a Diploma in Mathematics-Mechanics from the University of Bucharest (1991) and possesses a Doctor of Sciences degree in Astronomy awarded by the Astronomical Institute of the Romanian Academy (1997). She also holds a PhD in Applied Mathematics from the University of Victoria, Canada (2000). Currently she is a faculty member at Wilfrid Laurier University, Canada. Her main interests lie at the intersection of dynamical systems and mathematical physics. Klappentext A graduate level text based partly on lectures in geometry, mechanics, and symmetry given at Imperial College London, this book links traditional classical mechanics texts and advanced modern mathematical treatments of the subject. Zusammenfassung A graduate level text based partly on lectures in geometry, mechanics, and symmetry given at Imperial College London, this book links traditional classical mechanics texts and advanced modern mathematical treatments of the subject....
List of contents
- Preface
- Acknowledgements
- PART I
- 1: Lagrangian and Hamiltonian Mechanics
- 2: Manifolds
- 3: Geometry on Manifolds
- 4: Mechanics on Manifolds
- 5: Lie Groups and Lie Algebras
- 6: Group Actions, Symmetries and Reduction
- 7: Euler-Poincaré Reduction: Rigid body and heavy top
- 8: Momentum Maps
- 9: Lie-Poisson Reduction
- 10: Pseudo-Rigid Bodies
- PART II
- 11: EPDiff
- 12: EPDiff Solution Behaviour
- 13: Integrability of EPDiff in 1D
- 14: EPDiff in n Dimensions
- 15: Computational Anatomy: contour matching using EPDiff
- 16: Computational Anatomy: Euler-Poincaré image matching
- 17: Continuum Equations with Advection
- 18: Euler-Poincaré Theorem for Geophysical Fluid Dynamics
- Bibliography
Report
The book provides a very comprehensive presentation of ideas and methods from geometric mechanics, aimed at the graduate-student level, but it could also be of interest for specialists who want to refresh their knowledge in this modern, elegant and unifying formulation of Lagangrian and Hamiltonian mechanics. Jean-Francois Ganghoffer, Journal of Geometry and Symmetry in Physics
