动态域上的不连续动力学系统

所属分类:总论  
出版时间:2009-5   出版时间:高等教育出版社   作者:罗朝俊   页数:222  

前言

This book is about discontinuous dynamical systems on timevarying domains. Ihad not planed to write this book originally. As a scientist working on dynamicsand vibration, the 5.12 earthquake of Wenchuan (Sichuan province, China) shockedmy heart and made me feel guilty because my research cannot make any direct contributions to help them. Therefore, I would like to write two words "Zhenhan" inChinese calligraphy on the dedication page to express my passion. The meaningof "Zhenhan" is "Earthquake and Heartbreak" that shocks one's passion and spirit,and recalls everyone to a sense of duty. Herein, I would like to accumulate recent research developments of discontinuous dynamical systems on timevarying domains.One likes to use continuous models for discontinuous dynamical systems. However,sometimes such continuous modeling cannot provide adequate descriptions of discontinuous dynamical systems. Recently, researchers have gradually realized thatdiscontinuous modeling may provide an adequate and acceptable predication ofengineering systems. Currently, most research still focuses on discontinuous dynamical systems on timeinvariant domains. To better describe practical problems,some research on discontinuous systems on timevarying domains is scattered hereand there but without a systematical theory. The purpose of this book is to systematically present a theory of discontinuous dynamical systems on timevaryingdomains for university students and researchers.This book mainly focuses on the switchability of discontinuous dynamical systems on timevarying domains. Based on such concepts, principles of dynamicalsystem interactions without any connections are presented. This book consists ofseven chapters. Chapter 1 discusses two examples to show where discontinuous dynamical systems exist. Chapter 2 presents a basic theory for the switchability of aflow to the separation boundary in discontinuous dynamical systems, and switchingbifurcations are also addressed. In Chapter 3, transversality and sliding phenomena for a controlled dynamical system to an inclined line boundary of control logicare presented to show how to apply such a new theory. In Chapter 4, dynamics of africtional oscillator on a traveling belt with timevarying speeds is presented, whichis a simple example of discontinuous dynamical systems on the timevarying domains.

内容概要

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.

作者简介

Dr. Albert C. J. Luo is a professor at Southern Illinois University Edwardsville, USA. His research is involved in the nonlinear theory of dynamical systems. His main contributions are in the following aspects: a stochastic and resonant layer theory in nonlinear Hamiltonian systems, singularity on discontinuous dynamical systems, and approximate nonlinear theories for a deformable-body.

书籍目录

1
Introduction 1.1
Discontinuous
systems 1.2
Book
layout References2
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 References3
Transversality
and
Sliding
Phenomena 3.1
A
controlled
system 3.2
Transversality
conditions 3.3
Mappings
and
predictions 3.4
Periodic
and
chaotic
motions References4
A
Frictional
Oscillator
on
Time-varying
Belt 4.1
Mechanical
model 4.2
Analytical
conditions  4.2.1
Equations
of
motion  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
Generic
mappings  4.3.2
Sliding
flows
and
fragmentation
 
4.3.3
Grazing
flows 4.4
Periodic
motions 
4.4.1
Mapping
structures 
4.4.2
Illustrations 4.5
Numerical
simulations References5
Two
Oscillators
with
Impacts
and
Stick 5.1
Physical
problem 
5.1.1
Introduction
to
problem 
5.1.2
Equations
of
motion 5.2
Domains
and
vector
fields 
5.2.1
Absolute
motion
description 
5.2.2
Relative
motion
description 5.3
Mechanism
of
stick
and
grazing 
5.3.1
Analytical
conditions 
5.3.2
Physical
interpretation 5.4
Mapping
structures
and
motions 
5.4.1
Switching
sets
and
basic
mappings 
5.4.2
Mapping
equations 
5.4.3
Mapping
structures 
5.4.4
Bifurcation
scenario 5.5
Periodic
motion
prediction 
5.5.1
Approach 
5.5.2
Impacting
chatter 
5.5.3
Impacting
chatter
with
stick 
5.5.4
Parameter
maps 5.6
Numerical
illustrations 
5.6.1
Impacting
chatter 
5.6.2
Impacting
chatter
with
stick 
5.6.3
Further
illustrations References6
Dynamical
Systems
with
Frictions 6.1
Problem
statement 6.2
Switching
and
stick
motions
 
6.2.1
Equations
of
motion 
6.2.2
Analytical
conditions 6.3
Periodic
motions
 
6.3.1
Switching
planes
and
mappings 
6.3.2
Mapping
structures
and
motions 
6.3.3
Bifurcation
scenario 6.4
Numerical
illustrations  6.4.1
Periodic
motion
without
stick  6.4.2
Periodic
motion
with
stick  6.4.3
Periodic
motion
with
stick
only References7 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
comer
singularity ReferencesAppendix A.1
Basic
solution A.2
Stability
and
bifurcationIndex

章节摘录

插图:

编辑推荐

《动态上的不连续力学系统》编辑推荐:Nonlinear Physical Science focuses on the recent advancesof fundamental theories and principles, analytical andsymbolic approaches, as well as computational technniquesin nonlinear physical science and nonlinear mathematicswith engineering applications.

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  •     离散是近年来数学和应用科学研究的一个主题,本书在了历史方面读书一支。
  •     内容还是不错的,尽管都是一些Paper的堆砌,缺乏很强的连续性、可读性。了解前沿知识的人可能会更喜欢!
 

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