Perturbation methods:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Weinheim
Wiley-VCH
2004
|
| Schriftenreihe: | Physics textbook
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016746457&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XII, 425 S. |
| ISBN: | 0471399175 9780471399179 |
Internformat
MARC
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| 245 | 1 | 0 | |a Perturbation methods |c Ali Hasan Nayfeh |
| 264 | 1 | |a Weinheim |b Wiley-VCH |c 2004 | |
| 300 | |a XII, 425 S. | ||
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| 650 | 0 | 7 | |a Störungstheorie |0 (DE-588)4128420-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1819269755144503296 |
|---|---|
| adam_text | 1.
Introduction
1
1.1. Parameter
Perturbations,
1
1.1.1.
An
Algebraic
Equation,
2
1.1.2.
The van
der Pol
Oscillator,
3
1.2.
Coordinate Perturbations,
4
1.2.1.
The Bessel Equation ofZeroth Order,
5
1.2.2.
A Simple Example,
6
1.3.
Order Symbols and Gauge Functions,
7
1.4.
Asymptotic Expansions and Sequences,
9
1.4.1.
Asymptotic Series,
9
1.4.2.
Asymptotic Expansions,
12
1.4.3.
Uniqueness of Asymptotic Expansions,
14
1.5.
Convergent versus Asymptotic Series,
15
1.6.
Nonuniform
Expansions,
16
1.7.
Elementary Operations on Asymptotic Expansions,
18
Exercises,
19
2.
Straightforward Expansions and Sources of Nonuniformity
23
2.1.
Infinite Domains,
24
2.1.1.
The Duffing Equation,
24
2.1.2.
A Model for Weak Nonlinear Instability,
25
2.1:3.
Supersonic Flow Past a Thin Airfoil,
26
2.1.4.
Small Reynolds Number Flow Past a Sphere,
28
2.2.
A Small Parameter Multiplying the Highest Derivative,
31
2.2.1.
A Second-Order Example,
31
2.2.2.
High Reynolds Number Flow Past a Body,
33
2.2.3.
Relaxation Oscillations,
34
2.2.4.
Unsymmetrical Bending of Prestressed Annular
Plates,
35
vii
Vlil
CONTENTS
2.3.
Type Change of a Partial Differential Equation,
37
2.3.1.
A Simple Example,
38
2.3.2.
Long Waves on Liquids Flowing down Incline
Planes,
38
2.4.
The Presence of Singularities,
42
2.4.1.
Shift in Singularity,
42
2.4.2.
The Earth-Moon-Spaceship Problem,
43
2.4.3.
Thermoelastic Surface Waves,
45
2.4.4.
Turning Point Problems,
48
2.5.
The Role of Coordinate Systems,
49
Exercises,
52
3.
The Method of Strained Coordinates
56
3.1.
The Method of Strained Parameters,
58
3.1.1.
The
Lindstedt-Poincaré
Method,
58
3.1.2.
Transition Curves for the
Mathieu
Equation,
60
3.1.3.
Characteristic Exponents for the
Mathieu
Equation
(Whittaker s Method),
62
3.1.4.
The Stability of the Triangular Points in the Elliptic
Restricted Problem of Three Bodies,
64
3.1.5.
Characteristic Exponents for the Triangular Points in
the Elliptic Restricted Problem of Three Bodies,
66
3.1.6.
A Simple Linear Eigenvalue Problem,
68
3.1.7.
A Quasi-Linear Eigenvalue Problem,
71
3.1.8.
The Quasi-Linear Klein-Gordon Equation,
76
3.2.
Lighthilľs
Technique,
77
3.2.1.
A First-Order Differential Equation,
79
3.2.2.
The One-Dimensional Earth-Moon-Spaceship Problem,
82
3.2.3.
A Solid Cylinder Expanding Uniformly in Still Air,
83
3.2.4.
Supersonic Flow Past a Thin Airfoil,
86
3.2.5.
Expansions by Using Exact Characteristics
—
Nonlinear
Elastic Waves,
89
3.3.
Temple s Technique,
94
3.4.
Renormalization Technique,
95
3.4.1.
The Duffing Equation,
95
3.4.2.
A Model for Weak Nonlinear Instability,
96
3.4.3.
Supersonic Flow Past a Thin Airfoil,
97
3.4.4.
Shift in Singularity,
98
3.5.
Limitations of the Method of Strained Coordinates,
98
5.5./.
A Model for Weak Nonlinear Instability,
99
CONTENTS IX
3.5.2.
A Small Parameter Multiplying the Highest Derivative,
100
3.5.3.
The Earth-Moon-Spaceship Problem,
102
Exercises,
103
4.
The Methods of Matched and Composite Asymptotic Expansions
110
4.1.
The Method of Matched Asymptotic Expansions, 111
4.1.1.
Introduction
—
Prandtľs
Technique, 111
4.1.2.
Higher Approximations and Refined Matching Pro¬
cedures,
114
4.1.3.
A Second-Order Equation with Variable Coefficients,
122
4.1.4.
Reynolds Equation for a Slider Bearing,
125
4.1.5.
Unsymmetrical Bending of Prestressed Annular Plates,
128
4.1.6.
Thermoelastic Surface Waves,
133
4.1.7.
The Earth-Moon-Spaceship Problem,
137
4.1.8.
Small Reynolds Number Flow Past a Sphere,
139
4.2.
The Method of Composite Expansions,
144
4.2.1.
A Second-Order Equation with Constant Coefficients,
145
4.2.2.
A Second-Order Equation with Variable Coefficients,
148
4.2.3.
An Initial Value Problem for the Heat Equation,
150
4.2.4.
Limitations of the Method of Composite Expansions,
153
Exercises,
154
5.
Variation of Parameters and Methods of Averaging
159
5.1.
Variation of Parameters,
159
5.1.1.
Time-Dependent Solutions of the
Schrödinger
Equation,
160
5.1.2.
A Nonlinear Stability Example,
162
5.2.
The Method of Averaging,
164
5.2.1.
Van
der Poľs
Technique,
164
5.2.2.
The Krylov-Bogoliubov Technique,
165
5.2.3.
The Generalized Method of Averaging,
168
5.3.
Struble s Technique,
171
5.4.
The Krylov-Bogoliubov-Mitropolski Technique,
174
5.4.1.
The Duffiing Equation,
175
5.4.2.
The van
der Pol
Oscillator,
176
5.4.3.
The Klein-Gordon Equation,
178
X
CONTENTS
5.5.
The Method of Averaging by Using Canonical Variables,
179
5.5.1.
The Duffing Equation,
182
5.5.2.
The
Mathieu
Equation,
183
5.5.3.
A Swinging Spring,
185
5.6.
Von Zeipeľs
Procedure,
189
5.6.1.
The Duffing Equation,
192
5.6.2.
The
Mathieu
Equation,
194
5.7.
Averaging by Using the Lie Series and Transforms,
200
5.7.1.
The Lie Series and Transforms,
201
5.7.2.
Generalized Algorithms,
202
5.7.3.
Simplified General Algorithms,
206
5.7.4.
A Procedure Outline,
208
5.7.5.
Algorithms for Canonical Systems,
212
5.8.
Averaging by Using Lagrangians,
216
5.8.1.
A Model for Dispersive Waves,
217
5.8.2.
A Model for Wave-Wave Interaction,
219
5.8.3.
The Nonlinear Klein-Gordon Equation,
221
Exercises,
223
6.
The Method of Multiple Scales
228
6.1.
Description of the Method,
228
6.1.1.
Many-Variable Version {The Derivative-Expansion
Procedure),
236
6.1.2.
The Two-Variable Expansion Procedure,
240
6.1.3.
Generalized Method—Nonlinear Scales,
241
6.2.
Applications of the Derivative-Expansion Method,
243
6.2.1.
The Duffing Equation,
243
6.2.2.
The van
der Pol
Oscillator,
245
6.2.3.
Forced Oscillations of the van
der Pol
Equation,
248
6.2.4.
Parametric Resonances
—
The
Mathieu
Equation,
253
6.2.5.
The van
der Pol
Oscillator with Delayed Amplitude
Limiting,
257
6.2.6.
The Stability of the Triangular Points in the Elliptic Re¬
stricted Problem of Three Bodies,
259
6.2.7.
A Swinging Spring,
262
6.2.8.
A Model for Weak Nonlinear Instability,
264
6.2.9.
A Model for Wave-Wave Interaction,
266
6.2.10.
Limitations of the Derivative-Expansion Method,
269
6.3.
The Two-Variable Expansion Procedure,
270
6.3.1.
The Duffing Equation,
270
6.3.2.
The van
der Pol
Oscillator,
272
CONTENTS Xl
6.3.3.
The Stability of the Triangular Points in the Elliptic
Restricted Problem of Three Bodies,
275
6.3.4.
Limitations of This Technique,
275
6.4.
Generalized Method,
276
6.4.1.
A Second-Order Equation with Variable Coefficients,
276
6.4.2.
A General Second-Order Equation with Variable
Coefficients,
280
6.4.3.
A Linear Oscillator with a Slowly Varying Restoring
Force,
282
6.4.4.
An Example with a Turning Point,
284
6.4.5.
The Duffing Equation with Slowly Varying Coefficients,
286
6.4.6.
Reentry Dynamics,
291
6.4.7.
The Earth-Moon-Spaceship Problem,
295
6.4.8.
A Model for Dispersive Waves,
298
6.4.9.
The Nonlinear Klein-Gordon Equation,
301
6.4.10.
Advantages and Limitations of the Generalized Method,
302
Exercises,
303
7.
Asymptotic Solutions of Linear Equations
308
7.1.
Second-Order Differential Equations,
309
7.1.1.
Expansions Near an Irregular Singularity,
309
7.1.2.
An Expansion of the Zeroth-Order Bessel Function for
Large Argument,
312
7.1.3.
Liouville s Problem,
314
7.1.4.
Higher
Approximations
for Equations Containing a
Large Parameter,
315
7.1.5.
A Small Parameter Multiplying the Highest Derivative,
317
7.1.6.
Homogeneous Problems with Slowly Varying Co¬
efficients,
318
7.1.7.
Reentry Missile Dynamics,
320
7.1.8.
Inhomogeneous Problems with Slowly Varying Co¬
efficients,
321
7.1.9.
Successive Liouville-Green (WKB) Approximations,
324
7.2.
Systems of First-Order Ordinary Equations,
325
Xli CONTENTS
7.2.1.
Expansions
Near an Irregular Singular Point,
326
7.2.2.
Asymptotic Partitioning of Systems of Equations,
327
7.2.3.
Subnormal Solutions,
331
7.2.4.
Systems Containing a Parameter,
332
7.2.5.
Homogeneous Systems with Slowly Varying Co¬
efficients,
333
7.3.
Turning Point Problems,
335
7.3.1.
The Method of Matched Asymptotic Expansions,
336
7.3.2.
The
Langer
Transformation,
339
7.3.3.
Problems with Two Turning Points,
342
7.3.4.
Higher-Order Turning Point Problems,
345
7.3.5.
Higher Approximations,
346
7.3.6.
An Inhomogeneous Problem with a Simple Turning
Point
—
First Approximation,
352
7.3.7.
An Inhomogeneous Problem with a Simple Turning
Point
—
Higher Approximations,
354
7.3.8.
An Inhomogeneous Problem with a Second-Order
Turning Point,
356
7.3.9.
Turning Point Problems about Singularities,
358
7.3.10.
Turning Point Problems of Higher Order,
360
7.4.
Wave Equations,
360
7.4.1.
The Born or Neumann Expansion and The Feynman
Diagrams,
361
7.4.2.
Renormalization Techniques,
367
7.4.3.
Rytov s Method,
373
7.4.4.
A Geometrical Optics Approximation,
374
7.4.5.
A Uniform Expansion at a Caustic,
377
7.4.6.
The Method of Smoothing,
380
Exercises,
382
References and Author Index
387
Subject Index
417
|
| 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 | BV035078178 |
| callnumber-first | Q - Science |
| callnumber-label | QA871 |
| callnumber-raw | QA871 |
| callnumber-search | QA871 |
| callnumber-sort | QA 3871 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 910 |
| ctrlnum | (OCoLC)254980034 (DE-599)BVBBV035078178 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035078178 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T13:19:37Z |
| institution | BVB |
| isbn | 0471399175 9780471399179 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016746457 |
| oclc_num | 254980034 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XII, 425 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Wiley-VCH |
| record_format | marc |
| series2 | Physics textbook |
| spellingShingle | Nayfeh, Ali Hasan 1933-2017 Perturbation methods Störungstheorie (DE-588)4128420-3 gnd |
| subject_GND | (DE-588)4128420-3 |
| title | Perturbation methods |
| title_auth | Perturbation methods |
| title_exact_search | Perturbation methods |
| title_full | Perturbation methods Ali Hasan Nayfeh |
| title_fullStr | Perturbation methods Ali Hasan Nayfeh |
| title_full_unstemmed | Perturbation methods Ali Hasan Nayfeh |
| title_short | Perturbation methods |
| title_sort | perturbation methods |
| topic | Störungstheorie (DE-588)4128420-3 gnd |
| topic_facet | Störungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016746457&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nayfehalihasan perturbationmethods |