Bifurcation and chaos in engineering:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
London [u.a.]
Springer
1998
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 452 S. Ill., graph. Darst. |
| ISBN: | 3540762426 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Chapter 1 Dynamical Systems, Ordinary Differential Equations
and Stability of Motion 1
1.1 Concepts of Dynamical Systems 1
1.2 Ordinary Differential Equations 5
1.3 Properties of Flow 14
1.4 Limit Point Sets 17
1.5 Liapunov Stability of Motion 23
1.6 Poincare Bendixson Theorem and its Applications 29
Chapter 2 Calculation of Flows 35
2.1 Divergence of Flows 35
2.2 Linear Autonomous Systems and Linear Flows
and the Calculation of Flows about the IVP 38
2.3 Hyperbolic Operator (or Generality) 47
2.4 Non linear Differential Equations and the Calculation of their Flows 55
2.5 Stable Manifold Theorem 60
Chapter 3 Discrete Dynamical Systems 66
3.1 Discrete Dynamical Systems and Linear Maps 66
3.2 Non linear Maps and the Stable Manifold Theorem 68
3.3 Classification of Generic Systems 71
3.4 Stability of Maps and Poincare Mapping 73
3.5 Structural Stability Theorem 76
Chapter 4 Liapunov—Schmidt Reduction 84
4.1 Basic Concepts of Bifurcation 84
4.2 Classification of Bifurcations of Planar Vector Fields 88
4.3 The Implicit Function Theorem 91
4.4 Liapunov—Schmidt Reduction 93
4.5 Methods of Singularity 102
4.6 Simple Bifurcations 119
4.7 Bifurcation Solution of the 1/2 Subharmonic Resonance Case of
Non linear Parametrically Excited Vibration Systems 127
4.8 Hopf Bifurcation Analyzed by Liapunov—Schmidt Reduction 143
Chapter 5 Centre Manifold Theorem and Normal Form of Vector Fields 1S4
5.1 Centre Manifold Theorem 154
5.2 Saddle—Node Bifurcation 166
5.3 Normal Form of Vector Fields 169
Chapter 6 Hopf Bifurcation 176
6.1 Hopf Bifurcation Theorem 176
6.2 Complex Normal Form of the Hopf Bifurcation 179
6.3 Normal Form of the Hopf Bifurcation in Real Numbers 182
6.4 Hopf Bifurcation with Parameters 18 5
6.5 Calculating Formula for the Hopf Bifurcation Solution 192
¦ j Bifurcation and Chaos in Engineering
6.6 Stability of the Hopf Bifurcation Solution 194
6.7 Effective Method for Computing the Hopf Bifurcation
Solution Coefficients 198
6.8 Bifurcation Problem Involving Double Zero Eigenvalues 203
Chapter 7 Application of the Averaging Method in Bifurcation Theory 230
7.1 Standard Equation 230
7.2 Averaging Method and Poincare Maps 237
7.3 The Geometric Description of the Averaging Method 241
7.4 An Example of the Averaging Method — the Duffing Equation 248
7.5 The Averaging Method and Local Bifurcation 255
7.6 The Averaging Method, Hamiltonian Systems
and Global Behaviour 261
Chapter 8 Brief Introduction to Chaos 265
8.1 What is Chaos? 265
8.2 Some Examples of Chaos 268
8.3 A Brief Introduction to the Analytical Method of Chaotic Study 273
8.4 The Hamiltonian System 289
8.5 Some Statistical Characteristics 303
8.6 Conclusions 305
Chapter 9 Construction of Chaotic Regions 311
9.1 Incremental Harmonic Balance Method (IHB Method) 312
9.2 The Newtonian Algorithm 317
9.3 Number of Harmonic Terms 318
9.4 Stability Characteristics 318
9.5 Transition Sets in Physical Parametric Space 319
9.6 Example of the Duffing Equation with Multi—Harmonic Excitation 320
Chapter 10 Computational Methods 341
10.1 Normal Form Theory 341
10.2 Symplectic Integration and Geometric Non Linear Finite
Element Method 359
10.3 Construction of the Invariant Torus 375
Chapter 11 Non linear Structural Dynamics 399
11.1 Bifurcations in Solid Mechanics 399
11.2 Non Linear Dynamics of an Unbalanced Rotating Shaft 406
11.3 Galloping Vibration Analysis for an Elastic Structure 421
11.4 Other Applications of Bifurcation Theory 431
References 436
Index 451
|
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| discipline | Physik Mathematik |
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| id | DE-604.BV011775472 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:15:33Z |
| institution | BVB |
| isbn | 3540762426 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007947091 |
| oclc_num | 39887334 |
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| physical | XII, 452 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| spelling | Chen, Yushu Verfasser aut Bifurcation and chaos in engineering Yushu Chen and Andrew Y. T. Leung London [u.a.] Springer 1998 XII, 452 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bifurcation theory Chaotic behavior in systems Differentiable dynamical systems Engineering mathematics Dynamisches System (DE-588)4013396-5 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s DE-604 Verzweigung Mathematik (DE-588)4078889-1 s Chaostheorie (DE-588)4009754-7 s Leung, Andrew Y. T. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007947091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chen, Yushu Leung, Andrew Y. T. Bifurcation and chaos in engineering Bifurcation theory Chaotic behavior in systems Differentiable dynamical systems Engineering mathematics Dynamisches System (DE-588)4013396-5 gnd Chaostheorie (DE-588)4009754-7 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4009754-7 (DE-588)4078889-1 |
| title | Bifurcation and chaos in engineering |
| title_auth | Bifurcation and chaos in engineering |
| title_exact_search | Bifurcation and chaos in engineering |
| title_full | Bifurcation and chaos in engineering Yushu Chen and Andrew Y. T. Leung |
| title_fullStr | Bifurcation and chaos in engineering Yushu Chen and Andrew Y. T. Leung |
| title_full_unstemmed | Bifurcation and chaos in engineering Yushu Chen and Andrew Y. T. Leung |
| title_short | Bifurcation and chaos in engineering |
| title_sort | bifurcation and chaos in engineering |
| topic | Bifurcation theory Chaotic behavior in systems Differentiable dynamical systems Engineering mathematics Dynamisches System (DE-588)4013396-5 gnd Chaostheorie (DE-588)4009754-7 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd |
| topic_facet | Bifurcation theory Chaotic behavior in systems Differentiable dynamical systems Engineering mathematics Dynamisches System Chaostheorie Verzweigung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007947091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT chenyushu bifurcationandchaosinengineering AT leungandrewyt bifurcationandchaosinengineering |