Methods of accelerated convergence in nonlinear mechanics:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Delhi
Hindustan Publ. Corp.
1976
Berlin [u.a.] Springer |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Russ. übers. |
| Beschreibung: | VIII, 291 S. |
| ISBN: | 3540071067 0387071067 |
Internformat
MARC
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| 240 | 1 | 0 | |a Metod uskorennoj schodimosti v nelinejnoj mechanike |
| 245 | 1 | 0 | |a Methods of accelerated convergence in nonlinear mechanics |c N. N. Bogoljubov, Ju. A. Mitropoliskii and A. M. Samoilenko |
| 264 | 1 | |a Delhi |b Hindustan Publ. Corp. |c 1976 | |
| 264 | 1 | |a Berlin [u.a.] |b Springer | |
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Datensatz im Suchindex
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| adam_text | TABLE OF CONTENTS
Preface to the Russian Edition iii
Preface to the English Edition v
Chapter 0. Introduction 1
Chapter 1. Quasi Periodic Solutions in Problems of Nonlinear Mechanics 5
§ 1. Statement of the Problem. The Existence of an Invariant Manifold 5
§ 2. Auxiliary Theorems 20
§ 3. Lemma on Iterations 27
§ 4. Theorem on Quasi Periodic Solutions 35
§ 5. Parametric Dependence of Quasi Periodic Solutions. Asymptotic
and Convergent Expansions 47
§ 6. Quasi Periodic Solutions in Second Order Systems 54
Chapter 2. General Solutions of Nonlinear Differential Equations in the
Neighbourhood of Quasi Periodic Solutions 60
§ 7. Statement of the Problem 60
§ 8. Some Auxiliary Statements 63
§ 9. Inductive Theorem 68
§ 10. Iteration Process and its Convergence 73
§ 11. Theorem on Reducibility of Nonlinear Equations 81
Chapter 3. A Smoothing Technique 88
§ 12. Loss of Derivatives 88
§ 13. Examples of Smoothing Operators 89
§ 14. The Basic Properties of a Smoothing Operator 92
§ 15. Iteration Process with Smoothing 97
Chapter 4. Trajectories on a Torus 99
§ 16. Behaviour of Trajectories on a Two Dimensional Torus .... 99
§ 17. Behaviour of Trajectories on an m Dimensional Torus 102
§ 18. Inductive Theorem 103
§19. Proof of the Theorem on the Reducibility of Equations on a Torus. 112
viii Table of Contents
Chapter 5. Linear Systems with Quasi Periodic Coefficients 121
§ 20. Reducibility Theorem 121
§21. Solution of the Auxiliary Equation 123
§22. Proof of Reducibility Theorem 128
§23. Construction of a Fundamental Matrix of Solutions .... 136
§ 24. The Measure of Reducible Systems. Statement of the Problem . . 145
§ 25. A Generalized Reducibility Theorem 147
§ 26. Metric Propositions 156
§27. Proof of the Measure Theorem 169
§28. Linear Systems with Smooth Right Hand Sides 181
Chapter 6. Neighbourhood of an Invariant Smooth Toroidal Manifold . 192
§ 29. Behaviour of Integral Curves in the Neighbourhood of Toroidal
Manifolds 192
§ 30. Auxiliary Propositions 196
§ 31. Iteration Theorem 220
§ 32. Reducibility Theorem in the Neighbourhood of a Toroidal
Manifold 226
§ 33. Behaviour under Perturbation of Integral Curves in the Neigh¬
bourhood of an Invariant Manifold 235
Chapter 7. Neighbourhood of a Compact Invariant Manifold of a Non
Autonomous System 243
§ 34. Statement of the Problem and Basic Postulates 243
§ 35. Lemma on the Solutions of an Auxiliary System 246
§ 36. Inductive Theorem 249
§ 37. Neighbourhood of an Invariant Manifold 261
§ 38. Behaviour of Solutions of a System of Two Equations in the
Neighbourhood of Equilibrium Positions 266
Appendices I to XV 269
References 288
|
| any_adam_object | 1 |
| author | Bogoljubov, Nikolaj N. 1940- Mitropolʹskij, Jurij Alekseevič 1917-2008 Samojlenko, Anatolij M. 1938-2020 |
| author_GND | (DE-588)103330097 (DE-588)104890029 (DE-588)108416569 |
| author_facet | Bogoljubov, Nikolaj N. 1940- Mitropolʹskij, Jurij Alekseevič 1917-2008 Samojlenko, Anatolij M. 1938-2020 |
| author_role | aut aut aut |
| author_sort | Bogoljubov, Nikolaj N. 1940- |
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| bvnumber | BV001966413 |
| classification_rvk | SK 910 UF 1000 |
| ctrlnum | (OCoLC)251422802 (DE-599)BVBBV001966413 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV001966413 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:38:03Z |
| institution | BVB |
| isbn | 3540071067 0387071067 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001282407 |
| oclc_num | 251422802 |
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| owner | DE-91G DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-20 DE-19 DE-BY-UBM DE-706 DE-188 |
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| physical | VIII, 291 S. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
| publishDateSort | 1976 |
| publisher | Hindustan Publ. Corp. Springer |
| record_format | marc |
| spelling | Bogoljubov, Nikolaj N. 1940- Verfasser (DE-588)103330097 aut Metod uskorennoj schodimosti v nelinejnoj mechanike Methods of accelerated convergence in nonlinear mechanics N. N. Bogoljubov, Ju. A. Mitropoliskii and A. M. Samoilenko Delhi Hindustan Publ. Corp. 1976 Berlin [u.a.] Springer VIII, 291 S. txt rdacontent n rdamedia nc rdacarrier Aus d. Russ. übers. Näherungsverfahren (DE-588)4206467-3 gnd rswk-swf Konvergenzbeschleunigung (DE-588)4202431-6 gnd rswk-swf Nichtlineare Mechanik (DE-588)4042095-4 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Nichtlineare Mechanik (DE-588)4042095-4 s Mathematische Methode (DE-588)4155620-3 s DE-604 Näherungsverfahren (DE-588)4206467-3 s Konvergenzbeschleunigung (DE-588)4202431-6 s Mitropolʹskij, Jurij Alekseevič 1917-2008 Verfasser (DE-588)104890029 aut Samojlenko, Anatolij M. 1938-2020 Verfasser (DE-588)108416569 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001282407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bogoljubov, Nikolaj N. 1940- Mitropolʹskij, Jurij Alekseevič 1917-2008 Samojlenko, Anatolij M. 1938-2020 Methods of accelerated convergence in nonlinear mechanics Näherungsverfahren (DE-588)4206467-3 gnd Konvergenzbeschleunigung (DE-588)4202431-6 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4206467-3 (DE-588)4202431-6 (DE-588)4042095-4 (DE-588)4155620-3 |
| title | Methods of accelerated convergence in nonlinear mechanics |
| title_alt | Metod uskorennoj schodimosti v nelinejnoj mechanike |
| title_auth | Methods of accelerated convergence in nonlinear mechanics |
| title_exact_search | Methods of accelerated convergence in nonlinear mechanics |
| title_full | Methods of accelerated convergence in nonlinear mechanics N. N. Bogoljubov, Ju. A. Mitropoliskii and A. M. Samoilenko |
| title_fullStr | Methods of accelerated convergence in nonlinear mechanics N. N. Bogoljubov, Ju. A. Mitropoliskii and A. M. Samoilenko |
| title_full_unstemmed | Methods of accelerated convergence in nonlinear mechanics N. N. Bogoljubov, Ju. A. Mitropoliskii and A. M. Samoilenko |
| title_short | Methods of accelerated convergence in nonlinear mechanics |
| title_sort | methods of accelerated convergence in nonlinear mechanics |
| topic | Näherungsverfahren (DE-588)4206467-3 gnd Konvergenzbeschleunigung (DE-588)4202431-6 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Näherungsverfahren Konvergenzbeschleunigung Nichtlineare Mechanik Mathematische Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001282407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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