Preface1 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 The Heavy Top 1.5 Incompressible Fluids 1.6 The Maxwell-Vlasov System 1.7 Nonlinear Stability 1.8 Bifurcation 1.9 The Poincare-MelnikovMethod 1.10 Resonances,Geometric Phases,and Control2 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 Chaos3 An Introduction to Infinite-Dimensional Systems 3.1 Lagrange'sandHamilton'sEquationsforFieldTheory 3.2 Examples：Hamilton's Equations 3.3 Examples：Poisson Brackets and Conserved Quantities4 Interlude：Manifolds，Vector Fields，Differential Forms5 Hamiltonian Systems on Symplectic Manifolds6 Cotangent Bundles7 Lagrangian Mechanics8 Variational Principles，Constraints，Rotating Systems9 An Introduction to Lie Groups10 Poisson Manifolds11 Momentum Maps12 Computation and Properties of Momentum Maps13 Euler-Poincare and Lie-Poisson Reduction14 Coadjoint Orbits15 The Free Rigid BodyReferencesIndex