Preface About the Authors 1 Introduction and Overview 2 Hamiltonian Systems on Linear Symplectic Spaces 3 An Introduction to Infinite-Dimensional Systems 4 Manifolds, Vector Fields, and Differential Forms 5 Hamiltonian Systems on Symplectic Manifolds 6 Cotangent Bundles 7 Lagrangian Mechanics 8 Variational Principles, Constraints, and Rotating Systems 9 An Introduction to Lie Groups 10 Poisson Manifolds 11 Momentum Maps 12 Computation and Properties of Momentum Maps 13 Lie-Poisson and Euler-Poincare Reduction 14 Coadjoint Orbits 15 The Free Rigid Body References
Preface * About the Authors * 1 Introduction and Overview * 2 Hamiltonian Systems on Linear Symplectic Spaces * 3 An Introduction to Infinite-Dimensional Systems * 4 Manifolds, Vector Fields, and Differential Forms * 5 Hamiltonian Systems on Symplectic Manifolds * 6 Cotangent Bundles * 7 Lagrangian Mechanics * 8 Variational Principles, Constraints, and Rotating Systems * 9 An Introduction to Lie Groups * 10 Poisson Manifolds * 11 Momentum Maps *12 Computation and Properties of Momentum Maps * 13 Lie-Poisson and Euler-Poincare Reduction * 14 Coadjoint Orbits * 15 The Free Rigid Body * References
A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering. This second edition has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available.