Nonlinear dynamics: between linear and impact limits
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Series: | Lecture notes in applied and computational mechanics
52 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XI, 364 S. graph. Darst. |
| ISBN: | 9783642127984 |
Staff View
MARC
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| 100 | 1 | |a Pilipchuk, Valery N. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonlinear dynamics |b between linear and impact limits |c Valery N. Pilipchuk |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XI, 364 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture notes in applied and computational mechanics |v 52 | |
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Record in the Search Index
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CONTENTS INTRODUCTION 1 1.1 BRIEF LITERATURE OVERVIEW 1 1.2 ASYMPTOTIC
MEANING OF THE APPROACH 4 1.2.1 TWO SIMPLE LIMITS OF LYAPUNOV OSCILLATOR
4 1.2.2 OSCILLATING TIME AND HYPERBOLIC NUMBERS, STANDARD AND IDEMPOTENT
BASIS 6 1.3 QUICK 'TUTORIAL' 9 1.3.1 REMARKS ON THE BASIC FUNCTIONS 9
1.3.2 VISCOUS DYNAMICS UNDER THE SAWTOOTH FORCING 9 1.3.3 THE
RECTANGULAR COSINE INPUT 11 1.3.4 OSCILLATORY PIPE FLOW MODEL 12 1.3.5
PERIODIC IMPULSIVE LOADING 15 1.3.6 STRONGLY NONLINEAR OSCILLATOR 15 1.4
GEOMETRICAL VIEWS ON NONLINEARITY 17 1.4.1 GEOMETRICAL EXAMPLE 17 1.4.2
NONLINEAR EQUATIONS AND NONLINEAR PHENOMENA 19 1.4.3 RIGID-BODY MOTIONS
AND LINEAR SYSTEMS 21 1.4.4 REMARKS ON THE MULTI-DIMENSIONAL CASE 23
1.4.5 ELEMENTARY NONLINEARITIES 24 1.4.6 EXAMPLE OF SIMPLIFICATION IN
NONSMOOTH LIMIT 25 1.4.7 NON-SMOOTH TIME ARGUMENTS 26 1.4.8 FURTHER
EXAMPLES AND DISCUSSION 28 1.4.9 DIFFERENTIAL EQUATIONS OF MOTION AND
DISTRIBUTIONS 30 1.5 NON-SMOOTH COORDINATE TRANSFORMATIONS 33 1.5.1
CARATHEODORY SUBSTITUTION 33 1.5.2 TRANSFORMATION OF POSITIONAL
VARIABLES 33 1.5.3 TRANSFORMATION OF STATE VARIABLES 35 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/1001251830 DIGITALISIERT DURCH VIII
CONTENTS 2 SMOOTH OSCILLATING PROCESSES 37 2.1 LINEAR AND WEAKLY
NON-LINEAR APPROACHES 37 2.2 A BRIEF OVERVIEW OF SMOOTH METHODS 38 2.2.1
PERIODIC MOTIONS OF QUASI LINEAR SYSTEMS 38 2.2.2 THE IDEA OF AVERAGING
39 2.2.3 AVERAGING ALGORITHM FOR ESSENTIALLY NONLINEAR SYSTEMS 41 2.2.4
AVERAGING IN COMPLEX VARIABLES 43 2.2.5 LIE GROUP APPROACHES 44 3
NONSMOOTH PROCESSES AS ASYMPTOTIC LIMITS 51 3.1 LYAPUNOV' OSCILLATOR 51
3.2 NONLINEAR OSCILLATORS SOLVABLE IN ELEMENTARY FUNCTIONS 54 3.2.1
HARDENING CASE 56 3.2.2 LOCALIZED DAMPING 59 3.2.3 SOFTENING CASE 60 3.3
NONSMOOTHNESS HIDEN IN SMOOTH PROCESSES 61 3.3.1 NONLINEAR BEATS MODEL
62 3.4 NONLINEAR BEAT DYNAMICS: THE STANDARD AVERAGING APPROACH 64 3.4.1
ASYMPTOTIC OF EQUIPARTITION 69 3.4.2 ASYMPTOTIC OF DOMINANTS 71 3.4.3
NECESSARY CONDITION OF ENERGY TRAPPING 73 3.4.4 SUFFICIENT CONDITION OF
ENERGY TRAPPING 74 3.5 TRANSITION FROM NORMAL TO LOCAL MODES 74 3.6
SYSTEM DESCRIPTION 74 3.7 NORMAL AND LOCAL MODE COORDINATES 76 3.8 LOCAL
MODE INTERACTION DYNAMICS 81 3.9 AUTO-LOCALIZED MODES IN NONLINEAR
COUPLED OSCILLATORS 85 4 NONSMOOTH TEMPORAL TRANSFORMATIONS (NSTT) 93
4.1 NON-SMOOTH TIME TRANSFORMATIONS 93 4.1.1 POSITIVE TIME 94 4.1.2
'SINGLE-TOOTH' SUBSTITUTION 96 4.1.3 'BROKEN TIME' SUBSTITUTION 96 4.1.
CONTENTS IX 4.3 IDEMPOTENT BASIS GENERATED BY ASYMMETRIE TRIANGULAR WAVE
112 4.3.1 DEFINITION AND ALGEBRAIC PROPERTIES 112 4.3.2 DIFFERENTIATION
RULES 114 4.3.3 OSCILLATORS IN THE IDEMPOTENT BASIS 115 4.3.4
INTEGRATION IN THE IDEMPOTENT BASIS 116 4.4 DISCUSSIONS, REMARKS AND
JUSTIFICATIONS 117 4.4.1 REMARKS ON NONSMOOTH SOLUTIONS IN THE CLASSICAL
DYNAMICS 118 4.4.2 CARATHEODORY EQUATION 119 4.4.3 OTHER VERSIONS OF
PERIODIC TIME SUBSTITUTIONS 122 4.4.4 GENERAL CASE OF NON-INVERTIBLE
TIME AND ITS PHYSICAL MEANING 125 4.4.5 NSTT AND CNOIDAL WAVES 125 5
SAWTOOTH POWER SERIES 131 5.1 MANIPULATIONS WITH THE SERIES 131 5.1.1
SMOOTHING PROCEDURES 131 5.2 SAWTOOTH SERIES FOR NORMAL MODES 135 5.2.1
PERIODIC VERSION OF LIE SERIES 135 5.3 LIE SERIES OF TRANSFORMED SYSTEMS
138 5.3.1 SECOND-ORDER NON-AUTONOMOUS SYSTEMS 138 5.3.2 NSTT OF
LAGRANGIAN AND HAMILTONIAN EQUATIONS . 141 5.3.3 REMARK ON MULTIPLE
ARGUMENT CASES 144 6 NSTT FOR LINEAR AND PIECEWISE-LINEAR SYSTEMS 145
6.1 FREE HARMONIC OSCILLATOR: TEMPORAL QUANTIZATION OF SOLUTIONS 145 6.2
NON-AUTONOMOUS CASE 147 6.2.1 STANDARD BASIS 147 6.2.2 IDEMPOTENT BASIS
148 6.3 SYSTEMS UNDER PERIODIC PULSED EXCITATION 149 6.3.1 REGULAR
PERIODIC IMPULSES 149 6.3.2 HARMONIC OSCILLATOR UNDER THE PERIODIC
IMPULSIVE LOADING 151 6.3. X CONTENTS 6.6.3 PHASE SOLUTION 168 6.6.4
REMARKS ON GENERALIZED TAYLOR EXPANSIONS 172 6.7 MULTIPLE
DEGREES-OF-FREEDOM CASE 173 6.8 THE AMPLITUDE-PHASE PROBLEM IN THE
IDEMPOTENT BASIS . 177 7 PERIODIC AND TRANSIENT NONLINEAR DYNAMICS
UNDER DISCONTINUOUS LOADING 179 7.1 NONSMOOTH TWO VARIABLES METHOD 179
7.2 RESONANCES IN THE DUFFING'S OSCILLATOR UNDER IMPULSIVE LOADING 182
7.3 STRONGLY NONLINEAR OSCILLATOR UNDER PERIODIC PULSES 185 7.4 IMPACT
OSCILLATORS UNDER IMPULSIVE LOADING 189 8 STRONGLY NONLINEAR VIBRATIONS
195 8.1 PERIODIC SOLUTIONS FOR FIRST ORDER DYNAMICAL SYSTEMS 195 8.2
SECOND ORDER DYNAMICAL SYSTEMS 196 8.3 PERIODIC SOLUTIONS OF
CONSERVATIVE SYSTEMS 198 8.3.1 THE VIBROIMPACT APPROXIMATION 198 8.3.2
ONE DEGREE-OF-FREEDOM GENERAL CONSERVATIVE OSCILLATOR 202 8.3.3 A
NONLINEAR MASS-SPRING MODEL THAT BECOMES LINEAR AT HIGH AMPLITUDES 205
8.3.4 STRONGLY NON-LINEAR CHARACTERISTIC WITH A STEP-WISE DISCONTINUITY
AT ZERO 207 8.3.5 A GENERALIZED CASE OF ODD CHARACTERISTICS 209 8.4
PERIODIC MOTIONS CLOSE TO SEPARATRIX LOOP 211 8.5 SELF-EXCITED
OSCILLATOR 214 8.6 STRONGLY NONLINEAR OSCILLATOR WITH VISCOUS DAMPING
218 8.6.1 REMARK ON NSTT COMBINED WITH TWO VARIABLES EXPANSION 222 8.6.2
OSCILLATOR WITH TWO NONSMOOTH LIMITS 225 8.7 BOUNCING BALL 230 8.8 THE
KICKED ROTOR MODEL 234 8. CONTENTS XI 10.5.1 A DOUBLE-PENDULUM WITH
AMPLITUDE LIMITERS 258 10.5.2 A MASS-SPRING CHAIN UNDER CONSTRAINT
CONDITIONS 260 10.6 SYSTEMS WITH MULTIPLE IMPACTING PARTICLES 262 11
PRINCIPAL TRAJECTORIES OF FORCED VIBRATIONS 265 11.1 INTRODUCTORY
REMARKS 265 11.2 PRINCIPAL DIRECTIONS OF LINEAR FORCED SYSTEMS 267 11.3
DEFINITION FOR PRINCIPAL TRAJECTORIES OF NONLINEAR DISCRETE SYSTEMS 268
11.4 ASYMPTOTIC EXPANSIONS FOR PRINCIPAL TRAJECTORIES 269 11.5
DEFINITION FOR PRINCIPAL MODES OF CONTINUOUS SYSTEMS 271 12 NSTT AND
SHOOTING METHOD FOR PERIODIC MOTIONS 275 12.1 INTRODUCTORY REMARKS 275
12.2 PROBLEM FORMULATION 277 12.3 SAMPLE PROBLEMS AND DISCUSSION 279
12.3.1 SMOOTH LOADING 279 12.3.2 STEP-WISE DISCONTINUOUS INPUT 286
12.3.3 IMPULSIVE LOADING 286 12.4 OTHER APPLICATIONS 290 12.4.1 PERIODIC
SOLUTIONS OF THE PERIOD - N 290 12.4.2 TWO-DEGREES-OF-FREEDOM SYSTEMS
293 12.4.3 THE AUTONOMOUS CASE 294 13 ESSENTIALLY NON-PERIODIC PROCESSES
295 13.1 NONSMOOTH TIME DECOMPOSITION AND PULSE PROPAGATION IN A CHAIN
OF PARTICLES 295 13.2 IMPULSIVELY LOADED DYNAMICAL SYSTEMS 298 13.2.1
HARMONIC OSCILLATOR UNDER SEQUENTIAL IMPULSES 301 13.2.2 RANDOM
SUPPRESSION OF CHAOS 303 14 SPATIALLY-OSCILLATING STRUCTURES 305 14. |
| any_adam_object | 1 |
| author | Pilipchuk, Valery N. |
| author_facet | Pilipchuk, Valery N. |
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| author_sort | Pilipchuk, Valery N. |
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| dewey-ones | 530 - Physics |
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| dewey-search | 530.15 |
| dewey-sort | 3530.15 |
| dewey-tens | 530 - Physics |
| discipline | Maschinenbau / Maschinenwesen Physik Mathematik |
| format | Book |
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| institution | BVB |
| isbn | 9783642127984 |
| language | English |
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| physical | XI, 364 S. graph. Darst. |
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| series2 | Lecture notes in applied and computational mechanics |
| spelling | Pilipchuk, Valery N. Verfasser aut Nonlinear dynamics between linear and impact limits Valery N. Pilipchuk Berlin [u.a.] Springer 2010 XI, 364 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in applied and computational mechanics 52 Literaturangaben Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 s DE-604 Lecture notes in applied and computational mechanics 52 (DE-604)BV017110729 52 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3449992&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021157770&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pilipchuk, Valery N. Nonlinear dynamics between linear and impact limits Lecture notes in applied and computational mechanics Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| subject_GND | (DE-588)4126141-0 |
| title | Nonlinear dynamics between linear and impact limits |
| title_auth | Nonlinear dynamics between linear and impact limits |
| title_exact_search | Nonlinear dynamics between linear and impact limits |
| title_full | Nonlinear dynamics between linear and impact limits Valery N. Pilipchuk |
| title_fullStr | Nonlinear dynamics between linear and impact limits Valery N. Pilipchuk |
| title_full_unstemmed | Nonlinear dynamics between linear and impact limits Valery N. Pilipchuk |
| title_short | Nonlinear dynamics |
| title_sort | nonlinear dynamics between linear and impact limits |
| title_sub | between linear and impact limits |
| topic | Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| topic_facet | Nichtlineare Dynamik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3449992&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021157770&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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