The method of normal forms:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Weinheim
Wiley-VCH
2011
|
| Ausgabe: | 2., updated and enl. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 329 S. Ill. |
| ISBN: | 9783527410972 9783527635788 9783527635801 9783527635771 |
Internformat
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| 250 | |a 2., updated and enl. ed. | ||
| 264 | 1 | |a Weinheim |b Wiley-VCH |c 2011 | |
| 300 | |a XII, 329 S. |b Ill. | ||
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Datensatz im Suchindex
| _version_ | 1804148380458287104 |
|---|---|
| adam_text | IMAGE 1
VII
CONTENTS
PREFACE XI
INTRODUCTION 1
1 SDOF AUTONOMOUS SYSTEMS 7
1.1 INTRODUCTION 7
1.2 DUFFING EQUATION 9
1.3 RAYLEIGH EQUATION 13 1.4 DUFFING-RAYLEIGH-VAN DER POL EQUATION 15
1.5 AN OSCILLATOR WITH QUADRATIC AND CUBIC NONLINEARITIES 17 1.5.1
SUCCESSIVE TRANSFORMATIONS 17 1.5.2 THE METHOD OF MULTIPLE SCALES 19
1.5.3 A SINGLE TRANSFORMATION 21 1.6 A GENERAL SYSTEM WITH QUADRATIC AND
CUBIC NONLINEARITIES 22 1.7 THE VAN DER POL OSCILLATOR 24 1.7.1 THE
METHOD OF NORMAL FORMS 25 1.7.2 THE METHOD OF MULTIPLE SCALES 26 1.8
EXERCISES 27
2 SYSTEMS OF FIRST-ORDER EQUATIONS 31 2.1 INTRODUCTION 31
2.2 A TWO-DIMENSIONAL SYSTEM WITH DIAGONAL LINEAR PART 34 2.3 A
TWO-DIMENSIONAL SYSTEM WITH A NONSEMISIMPLE LINEAR FORM 39 2.4 AN
N-DIMENSIONAL SYSTEM WITH DIAGONAL LINEAR PART 40 2.5 A TWO-DIMENSIONAL
SYSTEM WITH PURELY IMAGINARY EIGENVALUES 42 2.5.1 THE METHOD OF NORMAL
FORMS 43 2.5.2 THE METHOD OF MULTIPLE SCALES 47 2.6 A TWO-DIMENSIONAL
SYSTEM WITH ZERO EIGENVALUES 48 2.7 A THREE-DIMENSIONAL SYSTEM WITH ZERO
AND TWO PURELY IMAGINARY EIGENVALUES 52 2.8 THE MATHIEU EQUATION 54
2.9 EXERCISES 57
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1010591886
DIGITALISIERT DURCH
IMAGE 2
VIII I CONTENTS
3 MAPS 61
3.1 LINEAR MAPS 61
3.1.1 CASE OF DISTINCT EIGENVALUES 62 3.1.2 CASE OF REPEATED EIGENVALUES
64 3.2 NONLINEAR MAPS 66
3.3 CENTER-MANIFOLD REDUCTION 72 3.4 LOCAL BIFURCATIONS 76
3.4.1 FOLD OR TANGENT OR SADDLE-NODE BIFURCATION 76 3.4.2 TRANSCRITICAL
BIFURCATION 79 3.4.3 PITCHFORK BIFURCATION 80 3.4.4 FLIP OR
PERIOD-DOUBLING BIFURCATION 81
3.4.5 HOPF OR NEIMARK-SACKER BIFURCATION 85 3.5 EXERCISES 91
4 BIFURCATIONS OF CONTINUOUS SYSTEMS 97 4.1 LINEAR SYSTEMS 97
4.1.1 CASE OF DISTINCT EIGENVALUES 98 4.1.2 CASE OF REPEATED EIGENVALUES
99 4.2 FIXED POINTS OF NONLINEAR SYSTEMS 200 4.2.1 STABILITY OF FIXED
POINTS 100 4.2.2 CLASSIFICATION OF FIXED POINTS 101 4.2.3
HARTMAN-GROBMAN AND SHOSHITAISHVILI THEOREMS 102
4.3 CENTER-MANIFOLD REDUCTION 103 4.4 LOCAL BIFURCATIONS OF FIXED POINTS
107 4.4.1 SADDLE-NODE BIFURCATION 108 4.4.2 NONBIFURCATION POINT 230
4.4.3 TRANSCRITICAL BIFURCATION 111 4.4.4 PITCHFORK BIFURCATION 113
4.4.5 HOPF BIFURCATIONS 114 4.5 NORMAL FORMS OF STATIC BIFURCATIONS 117
4.5.1 THE METHOD OF MULTIPLE SCALES 117 4.5.2 CENTER-MANIFOLD REDUCTION
126
4.5.3 A PROJECTION METHOD 132 4.6 NORMAL FORM OF HOPF BIFURCATION 137
4.6.1 THE METHOD OF MULTIPLE SCALES 138 4.6.2 CENTER-MANIFOLD REDUCTION
141 4.6.3 PROJECTION METHOD 244 4.7 EXERCISES 146
5 FORCED OSCILLATIONS OF THE DUFFING OSCILLATOR 161 5.1 PRIMARY
RESONANCE 161
5.2 SUBHARMONIC RESONANCE OF ORDER ONE-THIRD 164 5.3 SUPERHARMONIC
RESONANCE OF ORDER THREE 167 5.4 AN ALTERNATE APPROACH 169 5.4.1
SUBHARMONIC CASE 271
5.4.2 SUPERHARMONIC CASE 172
IMAGE 3
CONTENTS | IX
5.5 EXERCISES 172
6 FORCED OSCILLATIONS OF SDOF SYSTEMS 175 6.1 INTRODUCTION 175
6.2 PRIMARY RESONANCE 176 6.3 SUBHARMONIC RESONANCE OF ORDER ONE-HALF
178 6.4 SUPERHARMONIC RESONANCE OF ORDER TWO 180 6.5 SUBHARMONIC
RESONANCE OF ORDER ONE-THIRD 182
7 PARAMETRICALLY EXCITED SYSTEMS 187 7.1 THE MATHIEU EQUATION 187 7.1.1
FUNDAMENTAL PARAMETRIC RESONANCE 188 7.1.2 PRINCIPAL PARAMETRIC
RESONANCE 190 7.2 MULTIPLE-DEGREE-OF-FREEDOM SYSTEMS 191 7.2.1 THE CASE
OF Q NEAR W 2 + I 194
7.2.2 THE CASE OF Q NEAR 2 - I 194
7.2.3 THE CASE OF FL NEAR A 2 + U AND WT, - W 2 194 7.2.4 THE CASE OF
Q NEAR 2CU 3 AND CO 2 + FFLI 195 7.3 LINEAR SYSTEMS HAVING REPEATED
FREQUENCIES 195 7.3.1 THE CASE OF SS NEAR 2W! 198 7.3.2 THE CASE OF Q
NEAR O 3 + M X 199
7.3.3 THE CASE OF SS NEAR W3-W! 200 7.3.4 THE CASE OF Q NEAR TO I 200 7.4
GYROSCOPIC SYSTEMS 205 7.4.1 THE CASE OF Q NEAR 2W X 208
7.4.2 THE CASE OF Q NEAR W 2 - W I 208
7.5 A NONLINEAR SINGLE-DEGREE-OF-FREEDOM SYSTEM 208 7.5.1 THE CASE OF Q
AWAY FROM 2 209 7.5.2 THE CASE OF Q NEAR 2W 212 7.6 EXERCISES 212
8 MDOF SYSTEMS WITH QUADRATIC NONLINEARITIES 217 8.1 NONGYROSCOPIC
SYSTEMS 217 8.1.1 TWO-TO-ONE AUTOPARAMETRIC RESONANCE 220 8.1.2
COMBINATION AUTOPARAMETRIC RESONANCE 222
8.1.3 SIMULTANEOUS TWO-TO-ONE AUTOPARAMETRIC RESONANCES 223 8.1.4
PRIMARY RESONANCES 223 8.2 GYROSCOPIC SYSTEMS 225 8.2.1 PRIMARY
RESONANCES 226 8.2.2 SECONDARY RESONANCES 227 8.3 TWO LINEARLY COUPLED
OSCILLATORS 229 8.4 EXERCISES 232
9 TDOF SYSTEMS WITH CUBIC NONLINEARITIES 235 9.1 NONGYROSCOPIC SYSTEMS
235 9.1.1 THE CASE OF NO INTERNAL RESONANCES 236 9.1.2 THREE-TO-ONE
AUTOPARAMETRIC RESONANCE 238
IMAGE 4
X I CONTENTS
9.1.3 ONE-TO-ONE INTERNAL RESONANCE 239
9.1.4 PRIMARY RESONANCES 239 9.1.5 A NONSEMISIMPLE ONE-TO-ONE INTERNAL
RESONANCE 240 9.1.6 A PARAMETRICALLY EXCITED SYSTEM WITH A NONSEMISIMPLE
LINEAR STRUCTURE 244
9.2 GYROSCOPIC SYSTEMS 249 9.2.1 PRIMARY RESONANCES 250 9.2.2 SECONDARY
RESONANCES IN THE ABSENCE OF INTERNAL RESONANCES 251 9.2.3 THREE-TO-ONE
INTERNAL RESONANCE 255
10 SYSTEMS WITH QUADRATIC AND CUBIC NONLINEARITIES 257 10.1 INTRODUCTION
257
10.2 THE CASE OF NO INTERNAL RESONANCE 262 10.3 THE CASE OF THREE-TO-ONE
INTERNAL RESONANCE 263 10.4 THE CASE OF ONE-TO-ONE INTERNAL RESONANCE
264 10.5 THE CASE OF TWO-TO-ONE INTERNAL RESONANCE 266 10.6 METHOD OF
MULTIPLE SCALES 267 10.6.1 SECOND-ORDER FORM 268 10.6.2 STATE-SPACE FORM
272 10.6.3 COMPLEX-VALUED FORM 274 10.7 GENERALIZED METHOD OF AVERAGING
276 10.8 A NONSEMISIMPLE ONE-TO-ONE INTERNAL RESONANCE 279 10.8.1 THE
METHOD OF NORMAL FORMS 279 10.8.2 THE METHOD OF MULTIPLE SCALES 283 10.9
EXERCISES 285
11 RETARDED SYSTEMS 287
11.1 A SCALAR EQUATION 287 11.1.1 THE METHOD OF MULTIPLE SCALES 289
11.1.2 CENTER-MANIFOLD REDUCTION 291 11.2 A SINGLE-DEGREE-OF-FREEDOM
SYSTEM 295
11.2.1 THE METHOD OF MULTIPLE SCALES 296 11.2.2 CENTER-MANIFOLD
REDUCTION 299 11.3 A THREE-DIMENSIONAL SYSTEM 304 11.3.1 THE METHOD OF
MULTIPLE SCALES 306 11.3.2 CENTER-MANIFOLD REDUCTION 308 11A CRANE
CONTROL WITH TIME-DELAYED FEEDBACK 311
11.5 EXERCISES 323
REFERENCES 315
FURTHER READING 319
INDEX 325
|
| any_adam_object | 1 |
| author | Nayfeh, Ali Hasan 1933-2017 |
| author_GND | (DE-588)151240388 |
| author_facet | Nayfeh, Ali Hasan 1933-2017 |
| author_role | aut |
| author_sort | Nayfeh, Ali Hasan 1933-2017 |
| author_variant | a h n ah ahn |
| building | Verbundindex |
| bvnumber | BV039557458 |
| classification_rvk | SK 520 SK 920 |
| ctrlnum | (OCoLC)725019902 (DE-599)DNB1010591886 |
| dewey-full | 515.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.39 |
| dewey-search | 515.39 |
| dewey-sort | 3515.39 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| edition | 2., updated and enl. ed. |
| format | Book |
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| id | DE-604.BV039557458 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:06:13Z |
| institution | BVB |
| isbn | 9783527410972 9783527635788 9783527635801 9783527635771 |
| language | English |
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| physical | XII, 329 S. Ill. |
| publishDate | 2011 |
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| spelling | Nayfeh, Ali Hasan 1933-2017 Verfasser (DE-588)151240388 aut The method of normal forms Ali Hasan Nayfeh 2., updated and enl. ed. Weinheim Wiley-VCH 2011 XII, 329 S. Ill. txt rdacontent n rdamedia nc rdacarrier Normalform (DE-588)4172025-8 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Methode (DE-588)4038971-6 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Normalform (DE-588)4172025-8 s DE-604 Differentialgleichung (DE-588)4012249-9 s 1\p DE-604 Methode (DE-588)4038971-6 s 2\p DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024409207&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nayfeh, Ali Hasan 1933-2017 The method of normal forms Normalform (DE-588)4172025-8 gnd Dynamisches System (DE-588)4013396-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Methode (DE-588)4038971-6 gnd |
| subject_GND | (DE-588)4172025-8 (DE-588)4013396-5 (DE-588)4012249-9 (DE-588)4038971-6 |
| title | The method of normal forms |
| title_auth | The method of normal forms |
| title_exact_search | The method of normal forms |
| title_full | The method of normal forms Ali Hasan Nayfeh |
| title_fullStr | The method of normal forms Ali Hasan Nayfeh |
| title_full_unstemmed | The method of normal forms Ali Hasan Nayfeh |
| title_short | The method of normal forms |
| title_sort | the method of normal forms |
| topic | Normalform (DE-588)4172025-8 gnd Dynamisches System (DE-588)4013396-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Methode (DE-588)4038971-6 gnd |
| topic_facet | Normalform Dynamisches System Differentialgleichung Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024409207&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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