Geometric mechanics, and symmetry : from finite to infinite dimensions
Title:
Geometric mechanics, and symmetry : from finite to infinite dimensions
Author:
Holm, Darryl D., author.
ISBN:
9780199212903
9780199212910
Personal Author:
Physical Description:
xvi, 515 pages : illustrations (some color) ; 24 cm.
Series:
Oxford texts in applied and engineering mathematics ; 12
Oxford texts in applied and engineering mathematics ; 12.
Contents:
Lagrangian and Hamiltonian mechanics -- Manifolds -- Geometry on manifolds -- Mechanics on manifolds -- Lie groups and Lie algebras -- Group actions, symmetries, and reduction -- Euler-Poincare reduction : rigid body and heavy top -- Momentum maps -- Lie-Poisson reduction -- Pseudo-rigid bodies -- EPDiff -- EPDiff solution behavior -- Integrability of EPDiff in 1D -- EPDiff in n dimensions -- Computational anatomy : contour matching using EPDiff -- Computational anatomy : Euler-Poincare image matching -- Continuum equations with advection -- Euler-Poincarâe theorem for geophysical fluid dynamics.
Abstract:
After a summary of the necessary elements of calculus on smooth manifolds and basic Lie group threory, the main body of the text considers how symmetry reduction of Hamilton's principle allows one to derive and analyse the Euler-Poincarâe equations.