本书是Springer《应用数学教材》从书第17卷，是一部经典力学基本教程。书中对动力系统中的活跃分支——可积系统、混沌系统、在制系统、稳定性、分歧理论，以及特殊刚体、流体、等离子体和弹性系统等近代理论及其应用作了详细介绍，内容系统丰富。可供从事应用数学、力学专业的高年级大学生和研究生使用，也可作为相关领域专家、学者的参考书。

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 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 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

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