Oscillations in planar dynamic systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1996
|
| Schriftenreihe: | Series on advances in mathematics for applied sciences
37 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 319 S. graph. Darst. |
| ISBN: | 9810222920 |
Internformat
MARC
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| 100 | 1 | |a Mickens, Ronald E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Oscillations in planar dynamic systems |c Ronald E. Mickens |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1996 | |
| 300 | |a XII, 319 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series on advances in mathematics for applied sciences |v 37 | |
| 650 | 7 | |a Approximation, Théorie de l' |2 ram | |
| 650 | 4 | |a Bifurcation Hopf | |
| 650 | 7 | |a Cinétique chimique |2 ram | |
| 650 | 4 | |a Méthode Krylov-Bogoljubov-Mitropolskij | |
| 650 | 7 | |a Oscillations non linéaires |2 ram | |
| 650 | 4 | |a Système dynamique plan | |
| 650 | 7 | |a Systèmes dynamiques - Problèmes et exercices |2 ram | |
| 650 | 7 | |a Équations différentielles non linéaires |2 ram | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Differential equations, Nonlinear |x Numerical solutions | |
| 650 | 4 | |a Nonlinear oscillations | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008662464 | ||
Datensatz im Suchindex
| _version_ | 1804127406638759936 |
|---|---|
| adam_text | TABLE OF CONTENTS
1 Oscillatory Systems 1
1.1 Introduction 1
1.2 Examples of Nonlinear Systems 2
1.2.1 The Pendulum 2
1.2.2 Mass Attached to a Stretched Wire 3
1.2.3 Vibrations of the Eardrum 3
1.2.4 Nonlinear Electrical Circuits 6
1.2.5 Negative Resistance Oscillator 10
1.2.6 Oscillations of a Diatomic Molecule 15
1.2.7 Nonlinear Oscillators with Damping 17
1.2.8 Brusselator Model 20
1.2.9 Glycolysis 22
1.2.10 Chlorine Dioxide Iodine Reaction 23
1.2.11 Advertising Model 24
1.2.12 Predator Prey 24
1.3 Dimensionless Form of Differential Equations 24
1.3.1 Linear Damped Oscillator 27
1.3.2 Nonlinear Oscillator 28
1.3.3 Rayleigh Equation 29
1.4 Nonlinear Equations Having Exact Solutions 30
1.4.1 Harmonic Oscillator 30
1.4.2 Particle in a Box 31
1.4.3 Antisymmetric, Constant Force Oscillator 35
1.4.4 tPy/dt2 + y + ey3 = 0 38
1.4.5 Exact Period of the Pendulum 41
1.4.6 Pendulum 44
Problems 47
References 50
2 Lindstedt Poincare Perturbation Method 54
2.1 Introduction 54
2.2 Seculax Terms 56
2.3 Lindstedt Poincare Method 58
2.4 Examples 61
2.4.1 Example A 61
2.4.2 Example B 64
2.4.3 Example C 65
2.4.4 Example D 66
2.4.5 Example E 68
ix
X
2.4.6 Discussion 71
2.5 Existence of a Periodic Solution 72
2.5.1 Two Conditions 72
2.5.2 F a Function Only of y 75
2.5.3 F = Fx{y) C(dy/dt) 76
2.5.4 F a Function Only of dy/dt 77
2.5.5 F = F3(y)dy/dt 78
2.6 Shohat Expansion 79
Problems 82
References 83
3 Method of Krylov Bogoliubov Mitropolsky 86
3.1 Introduction 86
3.2 First Approximation of Krylov and Bogoliubov 87
3.2.1 Technique 87
3.2.2 Two Special Cases 91
3.2.3 Stability Properties of Limit Cycles 92
3.2.4 Equivalent Linearization 95
3.3 Worked Examples Using the Method of Krylov and Bogoliubov . .99
3.3.1 Example A 99
3.3.2 Example B 100
3.3.3 Example C 100
3.3.4 Example D 101
3.3.5 Example E 101
3.3.6 Example F 102
3.3.7 Example G 103
3.3.8 Example H 104
3.4 Method of Krylov Bogoliubov Mitropolsky 106
3.4.1 y + y = eF(y,y) 107
3.4.2 y + y = eF(y,y)+e2G(y,y) 115
3.5 Worked Examples Using the Method of Krylov,
Bogoliubov, and Mitropolsky 117
3.5.1 Example A : 117
3.5.2 Example B 118
3.5.3 Example C 119
3.5.4 Example D 121
3.6 Spurious Limit Cycles 123
3.7 y + y3 = eF(y,y) 128
Problems 134
References 137
xi
4 Harmonic Balance 139
4.1 Introduction 139
4.2 General Method 140
4.2.1 Bounds on the Fourier Coefficients 140
4.2.2 Direct Harmonic Balance 147
4.2.3 Rational Representations 149
4.3 Worked Examples: First Approximation 152
4.3.1 Example A 153
4.3.2 Example B 153
4.3.3 Example C 154
4.3.4 Example D 155
4.3.5 Example E 156
4.3.6 Example F 158
4.3.7 Example G 159
4.3.8 Example H 160
4.4 Comparison with the Lindstedt Poincare Method 163
4.5 Worked Examples: Second Approximation 164
4.5.1 Example A 164
4.5.2 Example B 167
Problems 169
References 171
5 Multi Time Expansions 174
5.1 Introduction 174
5.2 Two Time Expansion 177
5.3 Worked Examples Using the Two Time Expansion 179
5.3.1 Example A 179
5.3.2 Example B 182
5.3.3 Example C 184
5.3.4 Example D 186
5.3.5 Example E 188
5.3.6 Example F 190
5.4 Derivative Expansion Procedure 191
5.5 Worked Examples Using the Derivative Expansion Procedure ... 192
5.5.1 Example A 192
5.5.2 Example B 195
5.5.3 Example C 196
Problems 197
References 198
xii
6 General Second Order Systems 200
6.1 Introduction 200
6.2 Glycolytic Oscillator 202
6.3 Hopf Bifurcation Theorem 210
6.3.1 The Theorem 210
6.3.2 Example 215
6.4 General Procedure for Two Variable Systems 218
6.5 The Recipe 225
6.6 Worked Examples 226
6.6.1 van der Pol Equation 226
6.6.2 WCM Oscillator 227
6.6.3 Batch Fermentation 228
6.6.4 Brusselator Model 229
Problems 232
References 233
Appendix A. Mathematical Relations 236
Appendix B. Series Expansions 243
Appendix C. Fourier Series 251
Appendix D. Asymptotics Expansions 256
Appendix E. Basic Theorems of the Theory of Second Order
Differential Equations 265
Appendix F. Linear Second Order Differential Equations 270
Appendix G. Existence of Periodic Solutions for Certain
Second Order Differential Equations 280
Appendix H. Stability of Limit Cycles 285
Appendix I. Qualitative Theory of Differential Equations 295
General Bibliography 307
Index 315
|
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| indexdate | 2024-07-09T18:32:51Z |
| institution | BVB |
| isbn | 9810222920 |
| language | English |
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| physical | XII, 319 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | World Scientific |
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| series2 | Series on advances in mathematics for applied sciences |
| spelling | Mickens, Ronald E. Verfasser aut Oscillations in planar dynamic systems Ronald E. Mickens Singapore [u.a.] World Scientific 1996 XII, 319 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on advances in mathematics for applied sciences 37 Approximation, Théorie de l' ram Bifurcation Hopf Cinétique chimique ram Méthode Krylov-Bogoljubov-Mitropolskij Oscillations non linéaires ram Système dynamique plan Systèmes dynamiques - Problèmes et exercices ram Équations différentielles non linéaires ram Approximation theory Differential equations, Nonlinear Numerical solutions Nonlinear oscillations Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Nichtlineare Schwingung (DE-588)4042100-4 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 s Nichtlineare Schwingung (DE-588)4042100-4 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Series on advances in mathematics for applied sciences 37 (DE-604)BV004569239 37 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008662464&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mickens, Ronald E. Oscillations in planar dynamic systems Series on advances in mathematics for applied sciences Approximation, Théorie de l' ram Bifurcation Hopf Cinétique chimique ram Méthode Krylov-Bogoljubov-Mitropolskij Oscillations non linéaires ram Système dynamique plan Systèmes dynamiques - Problèmes et exercices ram Équations différentielles non linéaires ram Approximation theory Differential equations, Nonlinear Numerical solutions Nonlinear oscillations Numerisches Verfahren (DE-588)4128130-5 gnd Nichtlineare Schwingung (DE-588)4042100-4 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4042100-4 (DE-588)4205536-2 |
| title | Oscillations in planar dynamic systems |
| title_auth | Oscillations in planar dynamic systems |
| title_exact_search | Oscillations in planar dynamic systems |
| title_full | Oscillations in planar dynamic systems Ronald E. Mickens |
| title_fullStr | Oscillations in planar dynamic systems Ronald E. Mickens |
| title_full_unstemmed | Oscillations in planar dynamic systems Ronald E. Mickens |
| title_short | Oscillations in planar dynamic systems |
| title_sort | oscillations in planar dynamic systems |
| topic | Approximation, Théorie de l' ram Bifurcation Hopf Cinétique chimique ram Méthode Krylov-Bogoljubov-Mitropolskij Oscillations non linéaires ram Système dynamique plan Systèmes dynamiques - Problèmes et exercices ram Équations différentielles non linéaires ram Approximation theory Differential equations, Nonlinear Numerical solutions Nonlinear oscillations Numerisches Verfahren (DE-588)4128130-5 gnd Nichtlineare Schwingung (DE-588)4042100-4 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| topic_facet | Approximation, Théorie de l' Bifurcation Hopf Cinétique chimique Méthode Krylov-Bogoljubov-Mitropolskij Oscillations non linéaires Système dynamique plan Systèmes dynamiques - Problèmes et exercices Équations différentielles non linéaires Approximation theory Differential equations, Nonlinear Numerical solutions Nonlinear oscillations Numerisches Verfahren Nichtlineare Schwingung Nichtlineare Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008662464&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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