Stability analysis: nonlinear mechanics equations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Amsterdam [u.a]
Gordon and Breach
1995
|
| Schriftenreihe: | Stability and control
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 245 S. |
| ISBN: | 288449023X |
Internformat
MARC
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| 245 | 1 | 0 | |a Stability analysis |b nonlinear mechanics equations |c A. A. Martynyuk |
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| 300 | |a XII, 245 S. | ||
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Datensatz im Suchindex
| _version_ | 1804125171010764800 |
|---|---|
| adam_text | Contents
Introduction to the Series ix
Preface xi
1 Small Parameter Systems in General
1.1 Introductory remarks 1
1.2 General continuous small parameter systems 6
1.3 Limiting equations in nonlinear mechanics problems 13
1.4 Stability of solutions of small parameter systems of general form 23
1.5 Contraction principle 38
1.6 Comments and references 43
2 Standard Systems
2.1 Introductory remarks 45
2.2 Description of standard systems 45
2.3 Averaging in standard systems 47
2.4 Stability of solution of standard systems 65
2.5 Almost periodic systems 76
2.6 Standard integro differential systems 88
2.7 Comments and references 97
vi CONTENTS
3 Systems with Slow and Fast Variables
3.1 Introductory remarks 99
3.2 Averaging theorems 104
3.3 Investigation of stability with respect to slow variables 126
3.4 Stability of systems with slow and fast variables reduced to standard
form 132
3.5 Estimates of finite stability of systems with slow and fast
variables 141
3.6 Theorems on stability of autonomous multifrequency systems 148
3.7 Comments and references 153
4 Systems with Small Perturbing Forces
4.1 Introductory remarks 155
4.2 Qualitative investigation of systems with small perturbing forces 155
4.3 Perturbed Lyapunov functions and their construction 157
4.4 Boundedness of solutions of nonlinear systems under small
perturbations 164
4.5 Stability theorems 168
4.6 Instability theorem 178
4.7 Limiting cycles and nested attractors of weakly perturbed systems 180
4.8 Comments and references 183
5 Singularly Perturbed Systems
5.1 Introductory remarks 185
5.2 Description of systems 185
5.3 Asymptotic stability conditions 186
5.4 Singularly perturbed Lurie Postnikov systems 190
5.5 Definiteness of the matrix function 194
5.6 Matrix Lyapunov functions 196
5.7 General theorems on stability and instability 198
5.8 Description and decomposition of singularly perturbed large scale
systems 200
5.9 General problem of stability of singularly perturbed large scale
systems 202
5.10 Instability of singularly perturbed large scale systems 224
CONTENTS vii
5.11 Absolute stability of singularly perturbed large scale systems 226
5.12 Comments and references 231
References 235
Index 243
|
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| bvnumber | BV010693779 |
| classification_tum | MAT 345f |
| ctrlnum | (OCoLC)632644966 (DE-599)BVBBV010693779 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010693779 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:57:19Z |
| institution | BVB |
| isbn | 288449023X |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007137576 |
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| physical | XII, 245 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Gordon and Breach |
| record_format | marc |
| series | Stability and control |
| series2 | Stability and control |
| spelling | Martynjuk, Anatolij A. 1941- Verfasser (DE-588)1020347279 aut Stability analysis nonlinear mechanics equations A. A. Martynyuk Amsterdam [u.a] Gordon and Breach 1995 XII, 245 S. txt rdacontent n rdamedia nc rdacarrier Stability and control 2 Stabilität (DE-588)4056693-6 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 s Stabilität (DE-588)4056693-6 s DE-604 Stability and control 2 (DE-604)BV010641392 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007137576&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Martynjuk, Anatolij A. 1941- Stability analysis nonlinear mechanics equations Stability and control Stabilität (DE-588)4056693-6 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| subject_GND | (DE-588)4056693-6 (DE-588)4205536-2 |
| title | Stability analysis nonlinear mechanics equations |
| title_auth | Stability analysis nonlinear mechanics equations |
| title_exact_search | Stability analysis nonlinear mechanics equations |
| title_full | Stability analysis nonlinear mechanics equations A. A. Martynyuk |
| title_fullStr | Stability analysis nonlinear mechanics equations A. A. Martynyuk |
| title_full_unstemmed | Stability analysis nonlinear mechanics equations A. A. Martynyuk |
| title_short | Stability analysis |
| title_sort | stability analysis nonlinear mechanics equations |
| title_sub | nonlinear mechanics equations |
| topic | Stabilität (DE-588)4056693-6 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| topic_facet | Stabilität Nichtlineare Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007137576&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010641392 |
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