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Discontinuous Dynamical Systems on Time-varying Domains 动态域上的不连续动力学系统

Discontinuous Dynamical Systems on Time-varying Domains is the first monograph focusing on this topic. While in the classic theory of dynamical systems the focus is on dynamical systems on time-invariant domains， this book presents discontinuous dynamical systems on time-varying domains where the corresponding switchability of a flow to the time-varying boundary in discontinuous dynamical systems is discussed. From such a theory， principles of dynamical system interactions without any physical connections are presented. Several discontinuous systems on time-varying domains are analyzed in detail to show how to apply the theory to practical problems. The book can serve as a reference book for researchers， advanced undergraduate and graduate students in mathematics， physics and mechanics.

作者：

Albert C.J.Luo（罗朝俊）

定价：

46.00 元

出版时间：

2009-05-27

ISBN：

978-7-04-025759-5

物料号：

25759-00

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

动力系统

重点项目：

暂无

版面字数：

250千字

开本：

16开

装帧形式：

精装

页数：

222

最新
印次时间：

2009年01月

目录
- Front Matter
- 1 Introduction
  - 1.1 Discontinuous systems
  - 1.2 Book layout
  - References
- 2 Flow Switchability
  - 2.1 Discontinuous dynamic systems
  - 2.2 G-functions
  - 2.3 Passable flows
  - 2.4 Non-passable flows
  - 2.5 Tangential flows
  - 2.6 Switching bifurcations
  - References
- 3 Transversality and Sliding Phenomena
  - 3.1 A controlled system
  - 3.2 Transversality conditions
  - 3.3 Mappings and predictions
  - 3.4 Periodic and chaoticmotions
  - References
- 4 A Frictional Oscillator on Time-varying Belt
  - 4.1 Mechanicalmodel
  - 4.2 Analytical conditions
    - 4.2.1 Equations ofmotion
    - 4.2.2 Passable flows to boundary
    - 4.2.3 Sliding flows on boundary
    - 4.2.4 Grazing flows to boundary
  - 4.3 Generic mappings and force product criteria
    - 4.3.1 Genericmappings
    - 4.3.2 Sliding flows and fragmentation
    - 4.3.3 Grazing flows
  - 4.4 Periodicmotions
    - 4.4.1 Mapping structures
    - 4.4.2 Illustrations
  - 4.5 Numerical simulations
  - References
- 5 Two Oscillators with Impacts and Stick
  - 5.1 Physical problem
    - 5.1.1 Introduction to problem
    - 5.1.2 Equations ofmotion
  - 5.2 Domains and vector fields
    - 5.2.1 Absolutemotion description
    - 5.2.2 Relativemotion description
  - 5.3 Mechanismof stick and grazing
    - 5.3.1 Analytical conditions
    - 5.3.2 Physical interpretation
  - 5.4 Mapping structures andmotions
    - 5.4.1 Switching sets and basicmappings
    - 5.4.2 Mapping equations
    - 5.4.3 Mapping structures
    - 5.4.4 Bifurcation scenario
  - 5.5 Periodicmotion prediction
    - 5.5.1 Approach
    - 5.5.2 Impacting chatter
    - 5.5.3 Impacting chatterwith stick
    - 5.5.4 Parametermaps
  - 5.6 Numerical illustrations
    - 5.6.1 Impacting chatter
    - 5.6.2 Impacting chatterwith stick
    - 5.6.3 Further illustrations
  - References
- 6 Dynamical Systems with Frictions
  - 6.1 Problemstatement
  - 6.2 Switching and stick motions
    - 6.2.1 Equations ofmotion
    - 6.2.2 Analytical conditions
  - 6.3 Periodicmotions
    - 6.3.1 Switching planes andmappings
    - 6.3.2 Mapping structures andmotions
    - 6.3.3 Bifurcation scenario
  - 6.4 Numerical illustrations
    - 6.4.1 Periodic motion without stick
    - 6.4.2 Periodicmotionwith stick
    - 6.4.3 Periodicmotionwith stick only
  - References
- 7 Principles for System Interactions
  - 7.1 Two dynamical systems
    - 7.1.1 Dynamical systems with interactions
    - 7.1.2 Discontinuous description
    - 7.1.3 Resultant dynamical systems
  - 7.2 Fundamental interactions
  - 7.3 Interactions with singularity
  - 7.4 Interactions with corner singularity
  - References
- Appendix
  - A.1 Basic solution
  - A.2 Stability and bifurcation
- Index
- 彩图

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Discontinuous Dynamical Systems on Time-varying Domains 动态域上的不连续动力学系统

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