Averaging in stability theory: a study of resonance multi-frequency systems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer Acad. Publ.
1993
|
| Schriftenreihe: | Mathematics and its applications / Soviet series
79 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Russ. übers. |
| Beschreibung: | XIII, 279 S. |
| ISBN: | 0792315812 |
Internformat
MARC
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| 100 | 1 | |a Chapaev, Michail M. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Usrednenie v teorii ustojčvosti |
| 245 | 1 | 0 | |a Averaging in stability theory |b a study of resonance multi-frequency systems |c by M. M. Hapaev |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1993 | |
| 300 | |a XIII, 279 S. | ||
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| 500 | |a Aus d. Russ. übers. | ||
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Datensatz im Suchindex
| _version_ | 1804122402695675904 |
|---|---|
| adam_text | Contents
Preface xi
1 Averaging of Ordinary Differential Equations in One
and Multi — Frequency Systems 1
1.1 Introduction 1
1.2 Averaging in Standard Form Systems 3
1.3 Averaging in Systems with Slow and Fast Variables ... 7
1.4 Averaging in Multi Frequency Systems 13
2 Generalization of Lyapunov Second Method and Aver¬
aging in Stability Theory 19
2.1 Introduction 20
2.2 Lyapunov Functions Positive Definite in Subset of
Variables 24
2.3 Equipotential Surfaces of Perturbed Lyapunov Function.
Proximity of Solutions of Complete and Unperturbed
Systems 26
2.4 Perturbed Lyapunov Function in Annular Region. The¬
orem on Stability 29
2.5 Theorem on Attraction of Solutions to Equilibrium Point 36
2.6 Investigation of Stability on Finite Interval 38
2.7 Investigation of Stability in Higher Approximations ... 41
vii
viii
2.8 Theorem on Asymptotic Stability of Perturbed Nonlin¬
ear Systems in Neutral Case 44
2.9 Theorems on Asymptotic Stability of Standard Form
Systems and Systems with Small Perturbations 48
2.10 Theorem on Stability of Systems Splitting without Per¬
turbations 50
2.11 Stability of Systems with Additional Correlations be¬
tween Properties of Mean and Derivative of Lyapunov
Function 53
2.12 Investigation of Stability by Averaging over Explicit
Time Dependence 57
2.13 Investigation of Stability by Averaging along Solutions
of Linear System 62
2.14 Investigation of Stability of Integro Differential Systems 65
2.15 On Numerical Realization of Theorems of Generalized
Lyapunov Second Method 70
2.16 Theorems on Instability 77
2.17 Study of Stability of Perturbed Systems Using Positive
Definite Function which is not Lyapunov Function ... 88
3 Stability of Systems of Ordinary Differential Equations
with Quasi — Periodic Coefficients 102
3.1 Investigation of Stability by Means of Lyapunov Func¬
tion of Linear System 103
3.2 Construction of Perturbed Lyapunov Function for
Higher Order Resonances Ill
4 Stability of Multi Frequency Systems 114
4.1 Statement of the Problem 115
4.2 Stability of Single Frequency Systems of Equations
with Asymptotically Stable Averaged System 117
ix
4.3 Stability of Multi Frequency Systems of Equations with
Asymptotically Stable Averaged System 119
4.4 Stability of Multi Frequency Systems on Finite Time
Interval 129
4.5 Stability of Multi Frequency Problems of Nonlinear
Mechanics 132
5 Stability of Orbits in Three Body Problem 140
5.1 Orbit Stability in Three Body Problem and Description
of the Models 141
5.2 Canonical Variable, Equations and Integrals of Motion
in the Point like Three Body Problem 143
5.3 Resonance Curves and Choice of New Variables 147
5.4 Construction of Perturbed Lyapunov Function and Sta¬
bility of Point Like Model of Three Body Problem . . 148
5.5 Corrections to Force Function in Hydrodynamic Model
of Planets 153
5.6 Theorem on Stability of Planetary Systems 155
5.7 Evolution of Planetary Orbits 160
6 Stability of Systems with Admissible Region of Motion.
Stability of Gyroscope with No Contact Suspension 167
6.1 Estimation of Region of Motion of the System 168
6.2 Stability of Systems with Known Region of Motions . . . 174
6.3 Stability of Multi Frequency Systems with Known Re¬
gion of Motions 176
6.4 Stability of Gyroscope with No Contact Suspension . . 180
7 Averaging and Stability in Systems of Equations with
Delay 187
7.1 Averaging in Systems with Delay 188
7.2 Stability of Systems with Deviating Argument 192
X
7.3 Stability in Multi Frequency Systems with Delay . . . 197
7.4 Effect of Variable Tide Delay on the Evolution of Orbital
Elements of a Tide Forming Body 204
8 Stability of Partial Differential Equations 210
8.1 Statement of the Problem 210
8.2 Theorem on Stability 216
8.3 Theorem on Stability over Finite Interval 223
8.4 Theorem on Instability 226
8.5 Stability of Some Hyperbolic Systems 228
8.6 Stability of Nonlinear Evolutionary Differential Equation
with Perturbation 234
9 Stability of Stable System Influenced by Small Random
Perturbations 246
9.1 Construction of Perturbations of Lyapunov Functions
under Small Random Perturbations 247
9.2 Averaging in Some Stochastic Systems 256
Bibliography 263
Index 275
|
| any_adam_object | 1 |
| author | Chapaev, Michail M. |
| author_facet | Chapaev, Michail M. |
| author_role | aut |
| author_sort | Chapaev, Michail M. |
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| building | Verbundindex |
| bvnumber | BV008038426 |
| classification_rvk | SK 520 |
| ctrlnum | (OCoLC)246570378 (DE-599)BVBBV008038426 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV008038426 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:13:19Z |
| institution | BVB |
| isbn | 0792315812 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005288590 |
| oclc_num | 246570378 |
| open_access_boolean | |
| owner | DE-12 DE-703 DE-83 DE-188 |
| owner_facet | DE-12 DE-703 DE-83 DE-188 |
| physical | XIII, 279 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spelling | Chapaev, Michail M. Verfasser aut Usrednenie v teorii ustojčvosti Averaging in stability theory a study of resonance multi-frequency systems by M. M. Hapaev Dordrecht u.a. Kluwer Acad. Publ. 1993 XIII, 279 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 79 Aus d. Russ. übers. Stabilität (DE-588)4056693-6 gnd rswk-swf Mittelungsverfahren (DE-588)4126019-3 gnd rswk-swf Ljapunov-Funktion (DE-588)4274502-0 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s DE-604 Stabilität (DE-588)4056693-6 s Ljapunov-Funktion (DE-588)4274502-0 s Mittelungsverfahren (DE-588)4126019-3 s DE-188 Soviet series Mathematics and its applications 79 (DE-604)BV004708148 79 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005288590&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chapaev, Michail M. Averaging in stability theory a study of resonance multi-frequency systems Stabilität (DE-588)4056693-6 gnd Mittelungsverfahren (DE-588)4126019-3 gnd Ljapunov-Funktion (DE-588)4274502-0 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| subject_GND | (DE-588)4056693-6 (DE-588)4126019-3 (DE-588)4274502-0 (DE-588)4167992-1 |
| title | Averaging in stability theory a study of resonance multi-frequency systems |
| title_alt | Usrednenie v teorii ustojčvosti |
| title_auth | Averaging in stability theory a study of resonance multi-frequency systems |
| title_exact_search | Averaging in stability theory a study of resonance multi-frequency systems |
| title_full | Averaging in stability theory a study of resonance multi-frequency systems by M. M. Hapaev |
| title_fullStr | Averaging in stability theory a study of resonance multi-frequency systems by M. M. Hapaev |
| title_full_unstemmed | Averaging in stability theory a study of resonance multi-frequency systems by M. M. Hapaev |
| title_short | Averaging in stability theory |
| title_sort | averaging in stability theory a study of resonance multi frequency systems |
| title_sub | a study of resonance multi-frequency systems |
| topic | Stabilität (DE-588)4056693-6 gnd Mittelungsverfahren (DE-588)4126019-3 gnd Ljapunov-Funktion (DE-588)4274502-0 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| topic_facet | Stabilität Mittelungsverfahren Ljapunov-Funktion Ljapunov-Stabilitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005288590&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004708148 |
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