Stability of critical equilibrium states:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Manchester u.a.
Manchester Univ. Press
1991
|
| Series: | Nonlinear science
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | X, 207 S. graph. Darst. |
| ISBN: | 0719027055 |
Staff View
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| 100 | 1 | |a Chazin, Leonid G. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Ustojčivost' kritičeskich položenij ravnovesija |
| 245 | 1 | 0 | |a Stability of critical equilibrium states |c L. G. Khazin and E. E. Shnol |
| 264 | 1 | |a Manchester u.a. |b Manchester Univ. Press |c 1991 | |
| 300 | |a X, 207 S. |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | Contents
Preface viii
Preface to the English edition xi
Some standard notation and assumptions xii
Introduction 1
Notes on Introduction 7
1 Acquaintance with the subject (some remarkable critical
cases) 8
§1.1 Choice of appropriate variables 8
§1.2 Principal critical cases 13
§1.3 The Kamenkov problem (two pairs of pure imaginary
eigenvalues without resonance between frequencies) 17
§1.4 Problems with two degrees of freedom at resonance
between the frequencies of small oscillations 19
§1.5 The Lyapunov problem (two zero eigenvalues and cell {°o)) 25
Remarks and bibliographical notes on Chapter 1 27
Notes on Chapter 1 29
2 Statement of questions and summary of results 30
§2.1 Classification of critical cases 30
§2.2 List of all critical cases up to level of degeneracy 3 35
§2.3 Criteria of stability for cases of co dimension 3 38
§2.4 Standard theorems 42
§2.5 Indices of stability and instability for critical cases having
level of degeneracy not above 3 49
§2.6 Critical cases in the problem of stability of periodic
solutions for general systems of differential equations 50
Remarks and bibliographical notes on Chapter 2 54
Notes on Chapter 2 55
vi Contents
3 Tools of investigation 57
§3.1 Lyapunov functions and Chetayev functions 57
§3.2 Reduction to normal form 63
§3.3 Normalisation and the separation of movements 70
§3.4 Homogeneous systems 75
Remarks and bibliographical notes on Chapter 3 86
Notes on Chapter 3 88
4 Problems corresponding to levels of degeneracy 1 and 2 90
§4.1 Standard elements of the proofs of Theorems S£ and NS£ 90
§4.2 One zero eigenvalue 98
§4.3 A pair of pure imaginary eigenvalues 105
§4.4 Two pairs of pure imaginary eigenvalues (the Kamenkov
problem) 108
§4.5 Two zero eigenvalues 111
§4.6 One zero and a pair of pure imaginary eigenvalues together 115
Remarks and bibliographical notes on Chapter 4 118
Notes on Chapter 4 118
5 Selected problems of high co dimension 120
§5.1 Resonance 1:2 in general systems of differential equations 120
§5.2 Two zero eigenvalues under additional degeneracy
(the Lyapunov problem) 125
§5.3 n pairs of pure imaginary eigenvalues 134
§5.4 Multiple frequencies (resonance 1:1) 142
§5.5 Criterion of stability for case 10: one zero and a pair of
imaginary eigenvalues at additional degeneracy 149
Remarks and bibliographical notes on Chapter 5 152
Notes on Chapter 5 152
6 Hamiltonian systems 154
§6.0 Introductory information 154
§6.1 Statement of questions and summary of results 165
§6.2 Stability of equilibrium states in Hamiltonian systems 171
§6.3 Instability in the presence of one resonance of the
third order 176
§6.4 Stability at one resonance of the fourth order 182
Remarks and bibliographical notes on Chapter 6 188
Notes on Chapter 6 189
Supplement 1 On theorems about instability of equilibrium states 191
Supplement 2 Normalisation and separation of movements 195
Contents vii
Bibliography 201
List of theorems (in the basic text) 206
Index 208
|
| any_adam_object | 1 |
| author | Chazin, Leonid G. Šnol', Ėmmanuil Ė |
| author_facet | Chazin, Leonid G. Šnol', Ėmmanuil Ė |
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| author_sort | Chazin, Leonid G. |
| author_variant | l g c lg lgc ė ė š ėė ėėš |
| building | Verbundindex |
| bvnumber | BV004734504 |
| classification_rvk | SK 520 |
| classification_tum | MAT 345f |
| ctrlnum | (OCoLC)246786053 (DE-599)BVBBV004734504 |
| discipline | Mathematik |
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| id | DE-604.BV004734504 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:16:54Z |
| institution | BVB |
| isbn | 0719027055 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002912676 |
| oclc_num | 246786053 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-91 DE-BY-TUM |
| owner_facet | DE-12 DE-384 DE-91 DE-BY-TUM |
| physical | X, 207 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Manchester Univ. Press |
| record_format | marc |
| series2 | Nonlinear science |
| spelling | Chazin, Leonid G. Verfasser aut Ustojčivost' kritičeskich položenij ravnovesija Stability of critical equilibrium states L. G. Khazin and E. E. Shnol Manchester u.a. Manchester Univ. Press 1991 X, 207 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonlinear science Aus d. Russ. übers. Mechanik - Nichtlineare Analysis Stabilität - Gleichgewicht - Nichtlineare gewöhnliche Differentialgleichung Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Ungleichgewicht (DE-588)4121816-4 gnd rswk-swf Gleichgewicht (DE-588)4121372-5 gnd rswk-swf Nichtlineare Approximation (DE-588)4127922-0 gnd rswk-swf Gleichgewicht (DE-588)4121372-5 s Ungleichgewicht (DE-588)4121816-4 s Nichtlineare Approximation (DE-588)4127922-0 s DE-604 Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s Šnol', Ėmmanuil Ė Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002912676&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chazin, Leonid G. Šnol', Ėmmanuil Ė Stability of critical equilibrium states Mechanik - Nichtlineare Analysis Stabilität - Gleichgewicht - Nichtlineare gewöhnliche Differentialgleichung Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Ungleichgewicht (DE-588)4121816-4 gnd Gleichgewicht (DE-588)4121372-5 gnd Nichtlineare Approximation (DE-588)4127922-0 gnd |
| subject_GND | (DE-588)4167992-1 (DE-588)4121816-4 (DE-588)4121372-5 (DE-588)4127922-0 |
| title | Stability of critical equilibrium states |
| title_alt | Ustojčivost' kritičeskich položenij ravnovesija |
| title_auth | Stability of critical equilibrium states |
| title_exact_search | Stability of critical equilibrium states |
| title_full | Stability of critical equilibrium states L. G. Khazin and E. E. Shnol |
| title_fullStr | Stability of critical equilibrium states L. G. Khazin and E. E. Shnol |
| title_full_unstemmed | Stability of critical equilibrium states L. G. Khazin and E. E. Shnol |
| title_short | Stability of critical equilibrium states |
| title_sort | stability of critical equilibrium states |
| topic | Mechanik - Nichtlineare Analysis Stabilität - Gleichgewicht - Nichtlineare gewöhnliche Differentialgleichung Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Ungleichgewicht (DE-588)4121816-4 gnd Gleichgewicht (DE-588)4121372-5 gnd Nichtlineare Approximation (DE-588)4127922-0 gnd |
| topic_facet | Mechanik - Nichtlineare Analysis Stabilität - Gleichgewicht - Nichtlineare gewöhnliche Differentialgleichung Ljapunov-Stabilitätstheorie Ungleichgewicht Gleichgewicht Nichtlineare Approximation |
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