Preface
1 Introduction and Overview
1.1 Lagrangian and Hamiltonian Formalisms
1.2 Tile Rigid Body
1.3 Lie-Poisson Brackets,Poisson Manifolds,Momentum Maps
1.4 Incompressible Fluids
1.5 The Maxwell-Vlasov System
1.6 The Maxwell and Poisson-Vlasov Brackets
1.7 The Poisson-Vlasovto Fluid Map
1.8 The Maxwell-Vlasov Bracket
1.9 The Heavy Top
1.10 Nonlinear Stability
1.11 Bifurcation
1.12 The Poincare-MelnikovMethod and Chaos
1.13 Resonances,Geometric Phases,and Control
2 Hamiltonian Systems on Linear Syrnplectic Spaces
2.1 Introduction
2.2 Symplectic Forms on Vector Spaces
2.3 Examples
2.4 Canonical Transformations or Symplectic Maps
2.5 The Abstract Hamilton Equations
2.6 The Classical Hamilton Equations
2.7 When Are Equations Hamiltonian?
2.8 Hamiltonian Flows
2.9 Poisson Brackets
2.10 A Particle in a Rotating Hoop
2.11 The Poincare-Melnikov Method and Chaos
3 An Introduction to Infinite-Dimensional Systems
3.1 Lagrange'sandHamilton'sEquationsforFieldTheory
3.2 Examples:Hamilton's Equations
3.3 Examples:Poisson Brackets and Conserved Quantities
4 Interlude:Manifolds,Vector Fields,Differential Forms
4.1 Manifolds
4.2 Differential Forms
4.3 The Lie Derivative
4.4 Stokes'Theorem
5 Hamiltonian Systems on Symplectic Manifolds
6 Cotangent Bundles
7 Lagrangian Mechanics
8 Variational Principles,Constraints,Rotating Systems
9 An Introduction to Lie Groups
10 Poisson Manifolds
11 Momentum Maps
12 Computation and Properties of Momentum Maps
13 Euler-Poincare and Lie-Poisson Reduction
14 Coadjoint Orbits
15 The Free Rigid Body
References
Index