力学和对称性导论

Preface

1IntroductionandOverview

1.1LagrangianandHamiltonianFormalisms

1.2TileRigidBody

1.3Lie-PoissonBrackets,PoissonManifolds,MomentumMaps

1.4TheHeavyTop

1.5IncompressibleFluids

1.6TheMaxwell-VlasovSystem

1.7NonlinearStability

1.8Bifurcation

1.9ThePoincare-MelnikovMethod

1.10Resonances,GeometricPhases,andControl

2HamiltonianSystemsonLinearSyrnplecticSpaces

2.1Introduction

2.2SymplecticFormsonVectorSpaces

2.3Examples

2.4CanonicalTransformationsorSymplecticMaps

2.5TheAbstractHamiltonEquations

2.6TheClassicalHamiltonEquations

2.7WhenAreEquationsHamiltonian?

2.8HamiltonianFlows

2.9PoissonBrackets

2.10AParticleinaRotatingHoop

2.11ThePoincare-MelnikovMethodandChaos

3AnIntroductiontoInfinite-DimensionalSystems

3.1LagrangesandHamiltonsEquationsforFieldTheory

3.2Examples：HamiltonsEquations

3.3Examples：PoissonBracketsandConservedQuantities

4Interlude：Manifolds，VectorFields，DifferentialForms

5HamiltonianSystemsonSymplecticManifolds

6CotangentBundles

7LagrangianMechanics

8VariationalPrinciples，Constraints，RotatingSystems

9AnIntroductiontoLieGroups

10PoissonManifolds

11MomentumMaps

12ComputationandPropertiesofMomentumMaps

13Euler-PoincareandLie-PoissonReduction

14CoadjointOrbits

15TheFreeRigidBody

References

Index

　　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。