Geometric mechanics and symmetry : from finite to infinite dimensions
 Author/Creator
 Holm, Darryl D.
 Language
 English.
 Imprint
 Oxford [England] ; New York : Oxford University Press, 2009.
 Physical description
 xvi, 515 p., [4] p. of plates : ill. (some col.) ; 24 cm.
 Series
 Oxford texts in applied and engineering mathematics ; 12.
Access
Available online

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Unknown
QA807.5 .H65 2009

Unknown
QA807.5 .H65 2009
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Contributors
 Contributor
 Schmah, Tanya.
 Stoica, Cristina, 1967
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [503]508) and index.
 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. EulerPoincare Reduction: Rigid body and heavy top  8. Momentum Maps  9. LiePoisson Reduction  10. PseudoRigid 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: EulerPoincare image matching  17. Continuum Equations with Advection  18. EulerPoincare Theorem for Geophysical Fluid Dynamics  BIBLIOGRAPHY.
 (source: Nielsen Book Data)
 Publisher's Summary
 Classical mechanics, one of the oldest branches of science, has undergone a long evolution, developing hand in hand with many areas of mathematics, including calculus, differential geometry, and the theory of Lie groups and Lie algebras. The modern formulations of Lagrangian and Hamiltonian mechanics, in the coordinatefree language of differential geometry, are elegant and general. They provide a unifying framework for many seemingly disparate physical systems, such as nparticle systems, rigid bodies, fluids and other continua, and electromagnetic and quantum systems. Geometric Mechanics and Symmetry is a friendly and fastpaced introduction to the geometric approach to classical mechanics, suitable for a one or two semester course for beginning graduate students or advanced undergraduates. It fills a gap between traditional classical mechanics texts and advanced modern mathematical treatments of the subject. After a summary of the necessary elements of calculus on smooth manifolds and basic Lie group theory, the main body of the text considers how symmetry reduction of Hamilton's principle allows one to derive and analyze the EulerPoincare equations for dynamics on Lie groups. Additional topics deal with rigid and pseudorigid bodies, the heavy top, shallow water waves, geophysical fluid dynamics and computational anatomy. The text ends with a discussion of the semidirectproduct EulerPoincare reduction theorem for ideal fluid dynamics. A variety of examples and figures illustrate the material, while the many exercises, both solved and unsolved, make the book a valuable class text.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2009
 Responsibility
 Darryl D. Holm, Tanya Schmah, Cristina Stoica ; with solutions to selected exercises by David C.P. Ellis.
 Series
 Oxford texts in applied and engineering mathematics ; 12
 ISBN
 9780199212910
 0199212910
 9780199212903
 0199212902