Analytical routes to chaos in nonlinear engineering:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester
Wiley
2014
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | X, 266 S. Ill., graph. Darst. |
| ISBN: | 9781118883945 |
Staff View
MARC
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| 245 | 1 | 0 | |a Analytical routes to chaos in nonlinear engineering |c Albert C. J. Luo |
| 246 | 1 | 3 | |a Analytical routes to chaos |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Chichester |b Wiley |c 2014 | |
| 300 | |a X, 266 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Systems engineering | |
| 650 | 4 | |a Chaotic behavior in systems | |
| 650 | 4 | |a Nonlinear systems | |
| 650 | 4 | |a Nonlinear control theory | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface jx
1
Introduction
ι
1.1
Analytical Methods
1
1.1.1 Lagrange
Standard Form
1.1.2
Perturbation Methods
2
1.13
Method of Averaging
5
1.1.4
Generalized Harmonic Balance
8
1.2
Book Layout
24
2
Bifurcation Trees in Duffing Oscillators
25
2.1
Analytical Solutions
25
2.2
Period-
1
Motions to Chaos
32
2.2.1
Period-
1
Motions
33
2.2.2
Period-
1
to Period^ Motions
35
2.2.3
Numerical Simulations
52
2.3
Period-3 Motions to Chaos
57
2.3.1
Independent, Symmetric Period-3 Motions
57
2.3.2
Asymmetric
Perìod
-З
Motions
64
2.5.5
Period-
3
to Period-6 Motions
71
2.3.4
Numerical Illustrations
82
3
Self-Excited Nonlinear Oscillators
87
3.1
van del Pol Oscillators
87
3.1.1
Analytical Solutions
87
3.1.2
Frequency-Amplitude Characteristics
97
3.1.3
Numerical Illustrations
110
3.2
van del Pol-Duffing Oscillators
1
1
4
3.2.1
Finite Fourier Series Solutions
114
3.2.2
Analytical Predictions
130
3.2.3
Numerical Illustrations
143
viii Contents
4
Parametric
Nonlinear Oscillators
151
4.1
Parametric, Quadratic Nonlinear Oscillators
151
4.1.1
Analytical Solutions
151
4.1.2
Analytical Routes to Chaos
156
4.1.3
Numerical Simulations
169
4.2
Parametric Duffing Oscillators
186
4.2.1
Formulations
186
4.2.2
Parametric Hardening Duffing Oscillators
194
5
Nonlinear Jcffcott Rotor Systems
209
5.1
Analytical Periodic Motions
209
5.2
Frequency-Amplitude Characteristics
225
5.2.1
Period-1 Motions
226
5.2.2
Analytical Bifurcation Trees
231
5.2.3
Independent Perwd-5 Motion
239
5.3
Numerical Simulations
246
References
26 !
Index
265
Nonlinear problems are of .nterest to engineers, physicists and mathematicians
and many other sc.ent.sts because most systems are inherently nonlinear in
nature. As nonlinear equations are difficult to solve, nonlinear systems are
commonly approximated by linear equations. This works well up to some
accuracy and some range for the input values, but some interesting phenomena
such as chaos and singularities are hidden by linearization and perturbation
analysis. It follows that some aspects of the behavior of a nonlinear system
appear commonly to be chaotic, unpredictable or counterintuitive. Although such
a chaotic behavior may resemble a random behavior, it is absolutely deterministic.
Analytical Routes to Chaos in Nonlinear Engineering discusses analytical
solutions of periodic motions to chaos or quasi-periodic motions in nonlinear
dynamical systems in engineering and considers engineering applications,
design, and control. It systematically discusses complex nonlinear phenomena in
engineering nonlinear systems, including the periodically forced Duffing oscillator,
nonlinear self-excited systems, nonlinear parametric systems and nonlinear rotor
syslems,
Nonlinear models used in engineering are also presented and a brief
history of the topic is provided.
•
Considers engineering applications, design and control
•
Presents analytical techniques to show how to find the periodic
motions to chaos in nonlinear dynamical systems
•
Systematically discusses complex nonlinear phenomena in
engineering nonlinear systems
•
Presents extensively used nonlinear models in engineering
АпаІуШІ
Routes to Chaos in Nonlinear Engineering is a practical reference for
/ese
chers
and practitioners across engineering, mathematics and physics
dZhnes. and «also a usefu. source of .formation for graduate and senior
undergraduate students in these areas.
|
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| dewey-sort | 3629.8 236 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
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| id | DE-604.BV042057595 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:11:36Z |
| institution | BVB |
| isbn | 9781118883945 |
| language | English |
| lccn | 014001974 |
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| physical | X, 266 S. Ill., graph. Darst. |
| publishDate | 2014 |
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| publisher | Wiley |
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| spelling | Luo, Albert C. J. 1964- Verfasser (DE-588)142378097 aut Analytical routes to chaos in nonlinear engineering Albert C. J. Luo Analytical routes to chaos 1. publ. Chichester Wiley 2014 X, 266 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Systems engineering Chaotic behavior in systems Nonlinear systems Nonlinear control theory Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027498549&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027498549&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Luo, Albert C. J. 1964- Analytical routes to chaos in nonlinear engineering Systems engineering Chaotic behavior in systems Nonlinear systems Nonlinear control theory |
| title | Analytical routes to chaos in nonlinear engineering |
| title_alt | Analytical routes to chaos |
| title_auth | Analytical routes to chaos in nonlinear engineering |
| title_exact_search | Analytical routes to chaos in nonlinear engineering |
| title_full | Analytical routes to chaos in nonlinear engineering Albert C. J. Luo |
| title_fullStr | Analytical routes to chaos in nonlinear engineering Albert C. J. Luo |
| title_full_unstemmed | Analytical routes to chaos in nonlinear engineering Albert C. J. Luo |
| title_short | Analytical routes to chaos in nonlinear engineering |
| title_sort | analytical routes to chaos in nonlinear engineering |
| topic | Systems engineering Chaotic behavior in systems Nonlinear systems Nonlinear control theory |
| topic_facet | Systems engineering Chaotic behavior in systems Nonlinear systems Nonlinear control theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027498549&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027498549&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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