力學和對稱性導論（第2版）

內容介紹

《套用數學教材叢書·力學和對稱性導論(第2版)》是Springer《套用數學教材叢書》第17卷（全英文版），系一部經典力學基本教程，對動力系統中的活躍分支——可積系統、混沌系統、在制系統、穩定性、分歧理論，以及特殊剛體、流體、電漿和彈性系統的研究等近代理論及其套用作了詳細介紹，內容系統豐富。

作品目錄

Preface1 Introduction and Overview1.1 Lagrangian and Hamiltonian Formalisms1.2 Tile Rigid Body1.3 Lie-Poisson Brackets,Poisson Manifolds,Momentum Maps1.4 The Heavy Top1.5 Incompressible Fluids1.6 The Maxwell-Vlasov System1.7 Nonlinear Stability1.8 Bifurcation1.9 The Poincare-MelnikovMethod1.10 Resonances,Geometric Phases,and Control2 Hamiltonian Systems on Linear Syrnplectic Spaces2.1 Introduction2.2 Symplectic Forms on Vector Spaces2.3 Examples2.4 Canonical Transformations or Symplectic Maps2.5 The Abstract Hamilton Equations2.6 The Classical Hamilton Equations2.7 When Are Equations Hamiltonian?2.8 Hamiltonian Flows2.9 Poisson Brackets2.10 A Particle in a Rotating Hoop2.11 The Poincare-Melnikov Method and Chaos3 An Introduction to Infinite-Dimensional Systems3.1 Lagrange'sandHamilton'sEquationsforFieldTheory3.2 Examples：Hamilton's Equations3.3 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