Geometric Mechanics and Symmetry is a friendly and fast-paced 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. The modern geometric approach illuminates and unifies many seemingly disparate mechanical problems from several areas of science and engineering. In particular, the book concentrates on the similarities between finite-dimensional rigid body motion and infinite-dimensional systems such as fluid flow. The illustrations and examples, together with a large number of exercises, both solved and unsolved, make the book particularly useful.

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-Poincare 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–Poincare image matching 17. Continuum Equations with Advection 18. Euler–Poincare Theorem for Geophysical Fluid Dynamics Bibliography

Darryl D. Holm , Professor, Mathematics Department, Imperial College London, Tanya Schmah , Department of Computer Science, University of Toronto and Department of Mathematics, Macquarie University, Australia, Cristina Stoica , Department of Mathematics, Wilfrid Laurier University, Canada