![刚体动力学哈密顿方法,可积性.混沌](http://image12.bookschina.com/2018/20181014/2/7911272.jpg)
包邮刚体动力学哈密顿方法,可积性.混沌
¥111.2
(8.0折)
?
1星价
¥111.2
2星价¥111.2
定价¥139.0
![](http://o.bookschina.com/images/ling2.png?id=1)
暂无评论
图文详情
- ISBN:9787040502350
- 装帧:一般胶版纸
- 册数:暂无
- 重量:暂无
- 开本:16
- 页数:581
- 出版时间:2018-08-01
- 条形码:9787040502350 ; 978-7-04-050235-0
内容简介
本书从现代的观点给出了刚体动力学的系统和完整的介绍,包括李代数、泊松结构、混沌理论和稳定理论。本书描述了位于位势场、流体(基尔霍夫方程)和充满流体的空腔中的刚体运动的主要方程形式。本书所描述的系统都可以用哈密顿函数描述,涉及几乎所有可积情况和目前所知的显式积分方法,对各种刚体动力学中的非可积情况和混沌现象也进行了分析。本书广泛地利用了计算机方法对运动模式进行描述,结合丰富的表格等直观的叙述方式使得读者更易理解本书的内容。 本书适合力学、数学和物理学专业的本科生和研究生,也可供数学物理和动力系统领域的专家参考。
目录
Introduction
The Creators of Rigid Body Dynamics
1 Rigid Body Equations of Motion and Their Integration
1.1 Poisson Brackets and Hamiltonian Formalism
1 Poisson manifolds
Poisson brackets and their properties (19). Nondegenerate brackets,
Symplectic structures (22). Symplectic foliations. Generalized Darboux theorem (22)
2 The Lie-Poisson bracket
1.2 PoincarE and PoincarE-Chetaev Equations
1 PoincarE Equations
2 PoincarE-Chetaev equations
3 Equations on Lie groups
4 Comments
1.3 Various Systems of Variables in Rigid Body Dynamics
1 Euler angles
2 Euler variables. Components of momentum and the direction cosines
3 Quaternion Rodrigues-Hamilton parameters
4 Andoyer variables
5 Comments
1.4 Different Forms of Equations of Motion
1 Equations of motion of a rigid body with a fixed point
Euler-PoincarE equations in the group SO(3) (39). Equations of motion in angular velocities and quaternions (41). Kinetic energy of a rigid body with a fixed point (41).
2 Hamiltonian form of equations of motion for different systems of variables
Equations of motion in algebraic form (42). Quaternion representation
of the equations of motion (44). Canonical equations in Euler angles
and Andoyer variables (44).
3 PoincarE section and chaotic motions
1.5 Equations of Motion of a Rigid Body in Euclidean Space
1 Lagrangian formalism and Poincare equations on the group E(3)
2 Kinetic energy of a rigid body in R3
3 Hamiltonian form of equations of motion of a rigid body in R3
1.6 Examples and Similar Problems
1 Motion of a rigid body with a fixed point in a superposition of constant uniform force fields
2 A free rigid body in a quadratic potential
3 Motion of a rigid body with a fixed point in a rotating coordinate system
Gyroscope and Foucault pendulum (56). A satellite on a circular earth orbit (56).
4 Relative motion of a rigid body with a fixed point
5 Motion of a rigid body sliding on a smooth plane
6 Gyroscope in the Cardan suspension
7 Motion of a rigid body in an ideal incompressible fluid and the Kirchhoff equations
8 Falling rigid body in an ideal fluid
9 The Levitron
1.7 Theorems on Integrability and Methods of Integration
1 Hamiltonian systems. The Liouville-Arnold theorem
2 Theory of the last multiplier. Euler-Jacobi theorem
3 Separation of variables. Hamilton-Jacobi method
Geodesic flow on the ellipsoid (Jacobi problem) (73). System with
quadratic potential on a sphere (Neumann problem) (74).
2 The Euler-Poisson Equations and Their Generalizations
3 The Kirchhoff Equations and Related Problems of Rigid Body Dynamics
4 Linear Integrals and Reduction
5 Generalizations of Integrability Cases. Explicit Integration
6 Periodic Solutions, Nonintegrability, and Transition to Chaos
A Derivation of the KirchhoffPoincare一Zhukovskii, and Four·Dimensional Top Equations
B The Lie Algebra e(4)and Its Orbits
C Quaternion Equations and L-A Pair for the Generalized Goryachev——Chaplygin Top
D The Hess Case and Quantization of the Rotation Number
E Ferromagnetic Dynamics in a Magnetic Field
F The Landau—Lifshitz Equation, Discrete Systems, and the Neumann Problem
G Dynamics of Tops and Material Points on Spheres and Ellipsoids
H On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation
I The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids
Bibliography
Glossary
Index
展开全部
作者简介
Alexey V.Borisov博士是俄罗斯科学家,Steklov数学研究所首席研究员、莫斯科物理和技术研究所资深研究员和Udmurt大学非线性和新类型交通工具设计实验室主任。Alexey V.Borisov博士发表了150余篇文章,出版了6本专著。
本类五星书
本类畅销
-
宇宙与人
¥13.0¥35.0 -
新太阳系
¥13.2¥35.0 -
世纪幽灵-走近量子纠缠
¥12.0¥28.0 -
物理学之美-插图珍藏版
¥27.6¥69.0 -
技术史入门
¥17.4¥48.0 -
昆虫的生存之道
¥16.4¥38.0 -
假设的世界:一切不能想当然
¥19.1¥45.0 -
东京文艺地图(九品)
¥14.2¥38.0 -
数学的魅力;初等数学概念演绎
¥12.5¥22.0 -
为了人人晓得相对论
¥6.9¥13.5 -
118个数学竞赛不等式
¥45.5¥78.0 -
刘薰宇的数学三书:原来数学可以这样学全3册
¥35.2¥118.0 -
沉积岩与沉积相
¥28.6¥41.0 -
量子宇宙:一切可能发生的正在发生
¥16.1¥32.8 -
科学与现代性:整体科学理论
¥18.2¥33.0 -
20世纪中国科学口述史:涂光炽回忆与回忆涂光炽
¥19.7¥46.5 -
运筹学原理与方法
¥24.0¥72.0 -
从一到无穷大
¥25.9¥46.0 -
普林斯顿微积分读本-(修订版)
¥69.3¥99.0 -
古文诗词中的地球与环境事件
¥12.0¥28.0