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E-raamat: Singularity and Dynamics on Discontinuous Vector Fields

(Southern Illinois University, Department of Mechanical and Industrial Engineering, Edwardsville, USA)
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This book discussed fundamental problems in dynamics, which extensively exist in engineering, natural and social sciences. The book presented a basic theory for the interactions among many dynamical systems and for a system whose motions are constrained naturally or artificially. The methodology and techniques presented in this book are applicable to discontinuous dynamical systems in physics, engineering and control. In addition, they may provide useful tools to solve non-traditional dynamics in biology, stock market and internet network et al, which cannot be easily solved by the traditional Newton mechanics. The new ideas and concepts will stimulate ones' thought and creativities in corresponding subjects. The author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in dynamics.


· Challenging continuous Newton's dynamics
· Original theory and seeds of new researches in the field
· Brand-new concepts and ideas
· Wide spectrum of applications in science and engineering
· Systematic presentation and clear illustrations
· Very readable
· A unique book in the field
Preface vii
Chapter
1. Introduction
1(10)
1.1. Smooth dynamics
1(3)
1.2. Nonsmooth dynamics
4(3)
1.3. Book layout
7(4)
Chapter
2. Flow Passability and Tangential Flows
11(60)
2.1. Domain accessibility
11(1)
2.2. Discontinuous dynamic systems
12(2)
2.3. Oriented boundary and singular sets
14(9)
2.4. Local singularity and tangential flows
23(10)
2.5. A piecewise linear system
33(7)
2.6. A friction-induced oscillator
40(31)
Chapter
3. Flow Switching Bifurcations
71(42)
3.1. Set-valued vector fields
71(2)
3.2. Switching bifurcations
73(10)
3.3. Sliding fragmentation
83(10)
3.4. Sliding conditions in a friction oscillator
93(2)
3.5. Sliding criteria for a friction oscillator
95(18)
Chapter
4. Transversal Singularity and Bouncing Flows
113(34)
4.1. Transversal tangential flows
113(14)
4.2. Cusped and inflexed tangential flows
127(6)
4.3. Nonpassable tangential flows
133(2)
4.4. Bouncing flows
135(6)
4.5. A controlled piecewise linear system
141(6)
Chapter
5. Real and Imaginary Flows
147(40)
5.1. Singularity on boundary
147(1)
5.2. Hyperbolicity and parabolicity
148(7)
5.3. Boundary formation
155(7)
5.4. Real flows
162(6)
5.5. Imaginary flows
168(12)
5.6. An example
180(7)
Chapter
6. Discontinuous Vector Fields with Flow Barriers
187(26)
6.1. Flow barriers
187(6)
6.2. Switching bifurcations
193(4)
6.3. Sliding fragmentation
197(4)
6.4. A friction oscillator with flow barrier
201(12)
Chapter
7. Transport Laws and Mapping Dynamics
213(38)
7.1. Classification of discontinuity
213(5)
7.2. Transport laws
218(9)
7.3. Mapping dynamics
227(5)
7.4. An impacting piecewise system
232(19)
Chapter
8. Symmetry and Fragmentized Strange Attractor
251(38)
8.1. Symmetric discontinuity
251(2)
8.2. Switching sets and mappings
253(4)
8.3. Grazing and mappings symmetry
257(10)
8.4. Steady-state flow symmetry
267(9)
8.5. Strange attractor fragmentation
276(7)
8.6. Fragmentized strange attractors
283(6)
Appendix A 289(4)
References 293(6)
Subject Index 299


Albert C.J. Luo received his B.S. in Mechanical Engineering (1984) and M.S. in Engineering Mechanics (1990) in China and Ph.D. in Applied Mechanics (1996) in Canada. During 1996-1998, he was an NSERC (Canada) post-doctoral fellow at UC Berkeley. From 1998-present, Dr. Luo have worked at Southern Illinois University Edwardsville as Assistant/Associate Professor. During 20 year research experience, Dr. Luo developed stochastic and resonant layer theories in nonlinear Hamiltonian systems; a local theory for non-smooth dynamical systems on connectable domains. In addition, Dr, Luo also developed an approximate plate theory; a large damage theory for anisotropic materials and a generalized fractal theory. He has published over 130 peer-reviewed journal and conference papers. Dr. Luo has served editors for the Journal Communications in Nonlinear Science and Numerical simulation” and two book series on Nonlinear Science and Complexity. Dr. Luo is the editorial member for IMeCh E Part K Journal of Multibody Dynamics and Journal of Vibration and Control. He also organized over 10 international symposiums and conferences on Dynamics and Control.