GEOMETRIC MECHANICS

by Darryl D Holm (Imperial College London, UK)

Contents: Fermat's Principle for Ray Optics; Reviews of the Contributions of Newton Lagrange, Euler, Hamilton, Lie, Poincaré and Cartan in the Foundations of Geometric Mechanics; Rotations of a Rigid Body; Differential Forms; Lie Derivatives; Resonances and Symmetry Reduction; Geometric and Dynamic Phases; Elastic Spherical Pendulum; Maxwell-Bloch Equations for Laser-Matter Interaction.

GEOMETRIC MECHANICS

by Darryl D Holm (Imperial College London, UK)

Contents: Galilean Relativity; Newton, Lagrange and Hamilton's Treatments of the Rigid Body; Quaternions; Quaternionic Conjugacy and Adjoint Actions; The Special Orthogonal Group SO(3); The Special Euclidean Group SE(3); Euler-Poincare & Lie-Poisson Equations on SE(3); Heavy Top Equations; The Euler-Poincare Theorem; Euler-Poincare Reduction by Symmetry; Lie-Poisson Hamiltonian Form of the Classical Spin Chain; Momentum Maps; Round Rolling Rigid Bodies.