力學和對稱性導論

內容概要

本書是Springer《應用數學教材》從書第17卷，是一部經典力學基本教程。書中對動力系統(tǒng)中的活躍分支——可積系統(tǒng)、混沌系統(tǒng)、在制系統(tǒng)、穩(wěn)定性、分歧理論，以及特殊剛體、流體、等離子體和彈性系統(tǒng)等近代理論及其應用作了詳細介紹，內容系統(tǒng)豐富?？晒氖聭脭祵W、力學專業(yè)的高年級大學生和研究生使用，也可作為相關領域專家、學者的參考書。

書籍目錄

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

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