1 (p1): 1 Introduction 1 (p2): 1.1 Discontinuous systems 5 (p3): 1.2 Book layout 6 (p4): References 9 (p5): 2 Flow Switchability 9 (p6): 2.1 Discontinuous dynamic systems 11 (p7): 2.2 G-functions 15 (p8): 2.3 Passable flows 19 (p9): 2.4 Non-passable flows 28 (p10): 2.5 Tangential flows 39 (p11): 2.6 Switching bifurcations 52 (p12): References 55 (p13): 3 Transversality and Sliding Phenomena 55 (p14): 3.1 A controlled system 57 (p15): 3.2 Transversality conditions 60 (p16): 3.3 Mappings and predictions 67 (p17): 3.4 Periodic and chaotic motions 75 (p18): References 77 (p19): 4 A Frictional Oscillator on Time-varying Belt 77 (p20): 4.1 Mechanical model 80 (p21): 4.2 Analytical conditions 80 (p22): 4.2.1 Equations of motion 83 (p23): 4.2.2 Passable flows to boundary 85 (p24): 4.2.3 Sliding flows on boundary 89 (p25): 4.24 Grazing flows to boundary 91 (p26): 4.3 Generic mappings and force product criteria 91 (p27): 4.3.1 Generic mappings 93 (p28): 4.3.2 Sliding flows and fragmentation 96 (p29): 4.3.3 Grazing flows 98 (p30): 4.4 Periodic motions 98 (p31): 4.4.1 Mapping structures 100 (p32): 4.4.2 Illustrations 112 (p33): 4.5 Numerical simulations 113 (p34): References 115 (p35): 5 Two Oscillators with Impacts and Stick 115 (p36): 5.1 Physical problem 115 (p37): 5.1.1 Introduction to problem 117 (p38): 5.1.2 Equations of motion 119 (p39): 5.2 Domains and vector fields 119 (p40): 5.2.1 Absolute motion description 125 (p41): 5.2.2 Relative motion description 127 (p42): 5.3 Mechanism of stick and grazing 128 (p43): 5.3.1 Analytical conditions 133 (p44): 5.3.2 Physical interpretation 134 (p45): 5.4 Mapping structures and motions 134 (p46): 5.4.1 Switching sets and basic mappings 137 (p47): 5.4.2 Mapping equations 141 (p48): 5.4.3 Mapping structures 144 (p49): 5.4.4 Bifurcation scenario...

zlibzh/no-category/罗朝俊著, Albert C. J Luo/动态域上的不连续动力学系统：英文版_37763288.pdf

Discontinuous Dynamical Systems on Time-varying Domains (Nonlinear Physical Science)

Discontinuous dynamical systems in time varying domains

Albert C J Luo; SpringerLink (Online service)

Luo, Albert C. J.

Spektrum Akademischer Verlag. in Springer-Verlag GmbH

Higher Education Press Beijing ; Springer

Steinkopff. in Springer-Verlag GmbH

Springer-Verlag Berlin Heidelberg

Springer Nature

Nonlinear physical science (Print), Beijing, Dordrecht, cop. 2009

Nonlinear physical science, Beijing Berlin Heidelberg, 2009

Springer Nature, Berlin, Heidelberg, 2009

China, People's Republic, China

Germany, Germany

2, 20091106

Bookmarks: p1 (p1): 1 Introduction
p2 (p1): 1.1 Discontinuous systems
p3 (p5): 1.2 Book layout
p4 (p6): References
p5 (p9): 2 Flow Switchability
p6 (p9): 2.1 Discontinuous dynamic systems
p7 (p11): 2.2 G-functions
p8 (p15): 2.3 Passable flows
p9 (p19): 2.4 Non-passable flows
p10 (p28): 2.5 Tangential flows
p11 (p39): 2.6 Switching bifurcations
p12 (p52): References
p13 (p55): 3 Transversality and Sliding Phenomena
p14 (p55): 3.1 A controlled system
p15 (p57): 3.2 Transversality conditions
p16 (p60): 3.3 Mappings and predictions
p17 (p67): 3.4 Periodic and chaotic motions
p18 (p75): References
p19 (p77): 4 A Frictional Oscillator on Time-varying Belt
p20 (p77): 4.1 Mechanical model
p21 (p80): 4.2 Analytical conditions
p22 (p80): 4.2.1 Equations of motion
p23 (p83): 4.2.2 Passable flows to boundary
p24 (p85): 4.2.3 Sliding flows on boundary
p25 (p89): 4.24 Grazing flows to boundary
p26 (p91): 4.3 Generic mappings and force product criteria
p27 (p91): 4.3.1 Generic mappings
p28 (p93): 4.3.2 Sliding flows and fragmentation
p29 (p96): 4.3.3 Grazing flows
p30 (p98): 4.4 Periodic motions
p31 (p98): 4.4.1 Mapping structures
p32 (p100): 4.4.2 Illustrations
p33 (p112): 4.5 Numerical simulations
p34 (p113): References
p35 (p115): 5 Two Oscillators with Impacts and Stick
p36 (p115): 5.1 Physical problem
p37 (p115): 5.1.1 Introduction to problem
p38 (p117): 5.1.2 Equations of motion
p39 (p119): 5.2 Domains and vector fields
p40 (p119): 5.2.1 Absolute motion description
p41 (p125): 5.2.2 Relative motion description
p42 (p127): 5.3 Mechanism of stick and grazing
p43 (p128): 5.3.1 Analytical conditions
p44 (p133): 5.3.2 Physical interpretation
p45 (p134): 5.4 Mapping structures and motions
p46 (p134): 5.4.1 Switching sets and basic mappings
p47 (p137): 5.4.2 Mapping equations
p48 (p141): 5.4.3 Mapping structures
p49 (p144): 5.4.4 Bifurcation scenario
p50 (p144): 5.5 Periodic motion prediction
p51 (p145): 5.5.1 Approach
p52 (p147): 5.5.2 Impacting chatter
p53 (p150): 5.5.3 Impacting chatter with stick
p54 (p152): 5.5.4 Parameter maps
p55 (p153): 5.6 Numerical illustrations
p56 (p153): 5.6.1 Impacting chatter
p57 (p155): 5.6.2 Impacting chatter with stick
p58 (p158): 5.6.3 Further illustrations
p59 (p160): References
p60 (p161): 6 Dynamical Systems with Frictions
p61 (p161): 6.1 Problem statement
p62 (p164): 6.2 Switching and stick motions
p63 (p164): 6.2.1 Equations of motion
p64 (p166): 6.2.2 Analytical conditions
p65 (p172): 6.3 Periodic motions
p66 (p172): 6.3.1 Switching planes and mappings
p67 (p175): 6.3.2 Mapping structures and motions
p68 (p178): 6.3.3 Bifurcation scenario
p69 (p181): 6.4 Numerical illustrations
p70 (p181): 6.4.1 Periodic motion without stick
p71 (p184): 6.4.2 Periodic motion with stick
p72 (p189): 6.4.3 Periodic motion with stick only
p73 (p189): References
p74 (p191): 7 Principles for System Interactions
p75 (p191): 7.1 Two dynamical systems
p76 (p191): 7.1.1 Dynamical systems with interactions
p77 (p195): 7.1.2 Discontinuous description
p78 (p196): 7.1.3 Resultant dynamical systems
p79 (p199): 7.2 Fundamental interactions
p80 (p206): 7.3 Interactions with singularity
p81 (p210): 7.4 Interactions with corner singularity
p82 (p215): References
p83 (p217): Appendix
p84 (p217): A.1 Basic solution
p85 (p219): A.2 Stability and bifurcation
p86 (p221): Index

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"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. 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.

Nonlinear Physical Science
Erscheinungsdatum: 13.08.2009

2024-06-13