力学和对称性导论
1997-9
世界图书出版公司北京公司
Jerrold E.Marsden,Tudor S.Ratiu
500
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。
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 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 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 Forms 4.1 Manifolds 4.2 Differential Forms 4.3 The Lie Derivative 4.4 Stokes'Theorem5 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
