力学和对称性导论

所属分类:力学  
出版时间:1997-9   出版时间:世界图书出版公司北京公司   作者:Jerrold E.Marsden,Tudor S.Ratiu   页数:500  

内容概要

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。

书籍目录

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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