Asymptotic methods in resonance analytical dynamics:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2004
|
| Schriftenreihe: | Stability and control
21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 255 S. graph. Darst. |
| ISBN: | 0415310083 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | STABILITY AND CONTROLITHEORY, METHODS AND APPLICATIONS VOLUME 21
ASYMPTOTIC METHODS IN RESONANCE ANALYTICAL DYNAMICS E.A. GREBENIKOV
RUSSIAN ACADEMY OF SCIENCES MOSCOW, RUSSIA YU.A. MITROPOLSKY NATIONAL
ACADEMY OF SCIENCES OF UKRAINE KIEV, UKRAINE YU.A. RYABOV MOSCOW
INSTITUTE OF AUTO AND HIGHWAY CONSTRUCTION MOSCOW, RUSSIA CHAPMAN &
HALL/CRC A CRC PRESS COMPANY BOCA RATON LONDON NEW YORK WASHINGTON, D.C.
CONTENTS INTRODUCTION TO THE SERIES IX PREFACE XI ACKNOWLEDGMENTS XIX 1
PRELIMINARIES 1 1.0 INTRODUCTION 1 1.1 MAIN SYMBOLS 3 1.2 ASYMPTOTIC
SERIES AND THEIR PROPERTIES 5 1.3 POINCARE S THEOREM ON ASYMPTOTIC
APPROXIMATIONS OF SOLUTIONS OF DIFFERENTIAL EQUATIONS 8 1.4 GEOMETRIE
INTERPRETATION OF SOLUTIONS OF OSCILLATING SYSTEMS 12 1.5 ON THE METHOD
OF CHARACTERISTICS FOR QUASI-LINEAR FIRST-ORDER PARTIAL DIFFERENTIAL
EQUATIONS: METHOD OF CHARACTERISTICS 19 1.6 ITERATIVE VARIANT OF THE
POINCARE-LYAPUNOV SMALL PARAMETER METHOD 20 1.6.1 SIMPLE ITERATIONS 21
1.6.2 ITERATIONS WITH QUADRATIC CONVERGENCE 24 1.7 COMMENTS AND
REFERENCES 28 CONTENTS 2 AVERAGING PRINCIPLE FOR MULTIFREQUENCY SYSTEMS
OF DIFFERENTIAL EQUATIONS 29 2.0 INTRODUCTION 29 2.1 MATHEMATICAL
AVERAGING PRINCIPLE 32 2.2 CLASSIFICATION OF SYSTEMS OF DIFFERENTIAL
EQUATIONS WHERE RESONANCES ARE POSSIBLE 38 2.3 THE BASIS OF THE
ASYMPTOTIC THEORY FOR LOCALLY NONRESONANCE SYSTEMS 41 2.4 INITIAL
CONDITIONS FOR COMPARISON EQUATIONS 53 2.5 AVERAGING OPERATOR FOR
TIME-INDEPENDENT DISTURBANCES 57 2.6 ASYMPTOTIC THEORY OF SYSTEMS WITH
THEIR PATHS PASSING THROUGH RESONANCE POINTS 61 2.7 THE ALGORITHM OF
JOINING OF RESONANCE AND NONRESONANCE PATH SECTIONS 66 2.8 PERIODIC AND
QUASI-PERIODIC OSCILLATIONS IN THE VAN DER POL OSCILLATOR SYSTEM 67 2.9
STUDY OF MULTIFREQUENCY SYSTEMS WITH THEIR SOLUTIONS NOT REMAINING CLOSE
TO RESONANCE POINTS 88 2.10 STUDY OF MULTIFREQUENCY SYSTEMS BELONGING TO
CLASS II 99 2.11 MULTIFREQUENCY SYSTEMS WITH THEIR SOLUTIONS NOT LEAVING
THE NEIGHBORHOOD OF A RESORIANCE POINT 106 2.12 COMMENTS AND REFERENCES
112 3 SOME RESONANCE PROBLEMS OF NONLINEAR MECHANICS 115 3.0
INTRODUCTION 115 3.1 NEWTONIAN THREE-BODY PROBLEM 115 3.2 THE PROBLEM OF
JUSTIFICATION OF THE AVERAGING PRINCIPLE IN THE BOUNDED NEWTONIAN
THREE-BODY PROBLEM 125 3.3 CONSTRUCTION OF EXPLICIT SOLUTIONS OF
AVERAGED DIFFERENTIAL EQUATIONS OF THE BOUNDED THREE-BODY PROBLEM IN THE
CASE OF RESONANCE 132 3.4 QUASI-PERIODIC SOLUTIONS OF RESONANCE
HAMILTONIAN SYSTEMS 137 CONTENTS VII 3.5 MOTION OF A GEOSTATIONARY
SATELLITE 147 3.6 AVERAGING METHOD IN THE THEORY OF PARTIAL DIFFERENTIAL
EQUATIONS 155 3.7 ENERGY METHOD OF CONSTRUCTION OF AMPLITUDE-PHASE
EQUATIONS 164 3.8 AVERAGING METHOD AND MAXIMUM PRINCIPLE IN BOUNDARY
VALUE PROBLEMS 170 3.9 COMMENTS AND REFERENCES 180 4 NUMERICAL-ANALYTIC
METHODS 183 4.0 INTRODUCTION 183 4.1 CONSTRUCTION OF LYAPUNOV TRANSFORM
FOR A LINEAR SYSTEM WITH PERIODIC COEFFICIENTS 184 4.1.1 CONSTRUCTION OF
MATRICES L(T) AND W BY MEANS OF SERIES 185 4.1.2 CONSTRUCTION OF
MATRICES L(T) AND W BY MEANS OF ITERATIONS 186 4.1.3 INTERPOLATION
FORMULAE FOR LYAPUNOV TRANSFORM MATRICES 188 4.2 CONSTRUCTION OF GREEN
AND LYAPUNOV MATRICES 191 4.2.1 NONCRITICAL CASE 191 4.2.2 EXAMPLE 193
4.2.3 CRITICAL CASES 195 4.3 DIRECT NUMERICAL-ANALYTIC METHOD OF
CONSTRUCTION OF PERIODIC SOLUTIONS 196 4.4 CONSTRUCTION OF PERIODIC
SOLUTIONS IN HILL S PROBLEM OF LUNAR MOTION 202 4.5 NUMERICAL-ANALYTIC
CONSTRUCTION OF MATHIEU FUNCTIONS 206 4.5.1 ALGORITHM CONSTRUCTION 206
4.5.2 COMPUTATIONAL LAYOUT 209 4.5.3 QUICK-BASIC PROGRAM 212 4.5.4
COMMENTS ON THE PROGRAM 219 4.6 ALGORITHM FOR CONSTRUCTION OF SOLUTIONS
OF THE PLANE BOUNDED THREE-BODY PROBLEM 220 4.6.1 INITIAL DIFFERENTIAL
EQUATIONS OF THE PROBLEM 220 4.6.2 BASIC EQUATIONS FOR THE COEFFICIENTS
OF THE SOUGHT SOLUTION 222 4.6.3 CONSTRUCTION OF A SOLUTION BY THE
METHOD OF SIMPLE ITERATIONS 224 VIII CONTENTS 4.6.4 CONSTRUCTION OF A
SOLUTION BY THE METHOD OF ITERATIONS WITH QUADRATIC CONVERGENCE 228 4.7
NUMERICAL-ANALYTIC IMPLEMENTATION OF KRYLOV-BOGOLYUBOV TRANSFORM 236 4.8
COMMENTS AND REFERENCES 241 REFERENCES 243 INDEX * 253
|
| any_adam_object | 1 |
| author | Grebenikov, Evgenij A. Mitropolʹskij, Jurij Alekseevič 1917-2008 Rjabov, Jurij A. |
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| author_role | aut aut aut |
| author_sort | Grebenikov, Evgenij A. |
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| 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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| isbn | 0415310083 |
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| series | Stability and control |
| series2 | Stability and control: theory, methods and applications; 21 |
| spelling | Grebenikov, Evgenij A. Verfasser aut Asymptotic methods in resonance analytical dynamics E. A. Grebenikov ; Yu. A. Mitropolsky ; Yu. A. Ryabov Boca Raton [u.a.] Chapman & Hall/CRC 2004 XIX, 255 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Stability and control: theory, methods and applications; 21 Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Nichtlineare Mechanik (DE-588)4042095-4 gnd rswk-swf Gleichung (DE-588)4021246-4 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Asymptotik (DE-588)4126634-1 s Nichtlineare Mechanik (DE-588)4042095-4 s Gleichung (DE-588)4021246-4 s Mitropolʹskij, Jurij Alekseevič 1917-2008 Verfasser (DE-588)104890029 aut Rjabov, Jurij A. Verfasser aut Stability and control theorie, methods and applications 21 (DE-604)BV010641392 21 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019983068&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grebenikov, Evgenij A. Mitropolʹskij, Jurij Alekseevič 1917-2008 Rjabov, Jurij A. Asymptotic methods in resonance analytical dynamics Stability and control Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd Gleichung (DE-588)4021246-4 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4128130-5 (DE-588)4042095-4 (DE-588)4021246-4 (DE-588)4126634-1 |
| title | Asymptotic methods in resonance analytical dynamics |
| title_auth | Asymptotic methods in resonance analytical dynamics |
| title_exact_search | Asymptotic methods in resonance analytical dynamics |
| title_full | Asymptotic methods in resonance analytical dynamics E. A. Grebenikov ; Yu. A. Mitropolsky ; Yu. A. Ryabov |
| title_fullStr | Asymptotic methods in resonance analytical dynamics E. A. Grebenikov ; Yu. A. Mitropolsky ; Yu. A. Ryabov |
| title_full_unstemmed | Asymptotic methods in resonance analytical dynamics E. A. Grebenikov ; Yu. A. Mitropolsky ; Yu. A. Ryabov |
| title_short | Asymptotic methods in resonance analytical dynamics |
| title_sort | asymptotic methods in resonance analytical dynamics |
| topic | Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd Gleichung (DE-588)4021246-4 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Differentialgleichung Numerisches Verfahren Nichtlineare Mechanik Gleichung Asymptotik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019983068&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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