Nonlinear dynamics: mathematical models for rigid bodies with a liquid
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
De Gruyter
2015
|
| Series: | De Gruyter Studies in Mathematical Physics
27 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xv, 393 Seiten Illustrationen, Diagrame |
| ISBN: | 9783110316551 9783110555363 9783110316582 |
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MARC
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| 100 | 1 | |a Lukovsʹkij, Ivan Oleksandrovič |e Verfasser |0 (DE-588)1070322725 |4 aut | |
| 245 | 1 | 0 | |a Nonlinear dynamics |b mathematical models for rigid bodies with a liquid |c Ivan A. Lukovsky |
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| 300 | |a xv, 393 Seiten |b Illustrationen, Diagrame | ||
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Record in the Search Index
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| adam_text |
CONTENTS
FOREWORD TO ENGLISH EDITION V
FOREWORD TO RUSSIAN EDITION VII
INTRODUCTION 1
1 GOVERNING EQUATIONS AND BOUNDARY CONDITIONS IN THE
DYNAMICS OF A BOUNDED VOLUME OF LIQUID 17
1.1 CONSERVATION LAWS. GOVERNING EQUATIONS 17
1.2 STRESS TENSORS, STRAIN RATES, AND THEIR LINKS 24
1.3 MATHEMATICAL AND PHYSICAL MODELS 33
1.4 BOUNDARY AND INITIAL CONDITIONS 38
1.5 FORMULATION OF THE MAIN BOUNDARY-VALUE PROBLEM IN A
CURVILINEAR COORDINATE SYSTEM 41
2 DIRECT METHODS IN THE NONLINEAR PROBLEMS OF THE DYNAMICS
OF BODIES CONTAINING LIQUIDS 50
2.1 VARIATIONAL FORMULATION OF THE FREE-SURFACE PROBLEM OF LIQUID
SLOSHING IN AN IMMOBILE BASIN 50
2.2 MULTIMODAL METHOD FOR AN IMMOBILE BASIN 58
2.3 MODAL EQUATIONS FOR NONCYLINDRICAL BASINS 62
2.4 LINEAR MODAL EQUATIONS FOR AN IMMOBILE TANK 67
2.5 BATEMAN-LUKE PRINCIPLE FOR THE NONLINEAR SLOSHING PROBLEM IN A
TANK PERFORMING PRESCRIBED MOTIONS 70
2.6 MULTIMODAL METHOD FOR A TANK PERFORMING PRESCRIBED MOTIONS . . 77
2.7 EVALUATION OF THE STOKES-ZHUKOVSKY POTENTIALS BY THE VARIATIONAL
METHOD 87
2.8 RESULTING HYDRODYNAMIC FORCES AND MOMENTS 88
2.9 NONLINEAR DYNAMIC EQUATIONS OF THE BODY-LIQUID SYSTEM 96
3 HYDRODYNAMIC THEORY OF MOTIONS OF THE SHIPS TRANSPORTING
LIQUIDS 107
3.1 STATEMENT OF THE PROBLEM 108
HTTP://D-NB.INFO/1052322360
XIV
CONTENTS
3.2 BATEMAN-LUKE VARIATIONAL PRINCIPLE FOR FLOATING BODIES
CONTAINING TANKS
FILLED WITH LIQUIDS FL4
3.3 HYDRODYNAMIC FORCES AND MOMENTS ACTING UPON THE FLOATING
RIGID BODY 118
4 NONLINEAR DIFFERENTIAL EQUATIONS OF SPACE MOTIONS OF A RIGID
BODY CONTAINING AN UPRIGHT CYLINDRICAL CAVITY PARTIALLY FILLED
WITH LIQUID 127
4.1 NONLINEAR MODAL EQUATIONS OF LIQUID SLOSHING IN CYLINDRICAL
VESSELS WITH CIRCULAR AND ANNULAR CROSS SECTIONS 127
4.2 NONLINEAR MODAL EQUATIONS FOR "VISCOUS" LIQUID 143
4.3 HYDRODYNAMIC COEFFICIENTS FOR CIRCULAR CYLINDRICAL TANKS WITH
NONFLAT BOTTOMS 150
4.4 HYDRODYNAMIC COEFFICIENTS FOR THE UPRIGHT CYLINDRICAL TANK OF
ELLIPTIC CROSS SECTION 160
4.5 STOKES-ZHUKOVSKY POTENTIALS FOR COAXIAL CYLINDRICAL TANKS 165
4.6 HYDRODYNAMIC PARAMETERS CONNECTED WITH MOTIONS OF THE RIGID
BODY 173
4.7 SCALAR EQUATIONS IN SOME SPECIAL CASES 177
4.8 NONLINEAR EQUATIONS OF PERTURBED MOTION OF THE BODY CONTAINING
A CYLINDRICAL CAVITY PARTIALLY FILLED WITH LIQUID 194
5 NONLINEAR MODAL EQUATIONS FOR NONCYLINDICAL AXISYMMETRIC
TANKS 199
5.1 NATURAL SLOSHING MODES FOR THE NONTRUNCATED CONICAL TANK 200
5.2 NATURAL SLOSHING MODES FOR TRUNCATED CONICAL TANKS 209
5.3 NONLINEAR MODAL EQUATIONS FOR NONTRUNCATED CONICAL TANKS 222
5.4 NONLINEAR MODAL EQUATIONS FOR TRUNCATED CONICAL TANKS 231
5.5 SPHERICAL VESSEL 236
6 DERIVATION OF THE NONLINEAR EQUATIONS OF SPACE MOTIONS OF THE
BODY*LIQUID SYSTEM BY THE METHOD OF PERTURBATION THEORY 239
6.1 REDUCTION TO A SEQUENCE OF LINEAR BOUNDARY-VALUE PROBLEMS . 239
6.2 VECTOR FORM OF THE NONLINEAR EQUATIONS OF SPACE MOTIONS OF THE
BODY-LIQUID SYSTEM 242
6.3 MAIN BOUNDARY-VALUE PROBLEMS FOR AXIALLY SYMMETRIC CYLINDRICAL
CAVITIES NEAR THE FREE SURFACE 250
6.4 SCALAR FORM OF THE NONLINEAR EQUATIONS AND THEIR HYDRODYNAMIC
COEFFICIENTS IN SPECIAL CASES 255
CONTENTS
XV
6.5 THE CASE OF AN UPRIGHT CYLINDRICAL CAVITY WITH CIRCULAR OR ANNULAR
CROSS SECTION 263
6.6 THE CASE OF CAVITIES OF COMPLEX GEOMETRIC SHAPES 268
7 EQUIVALENT MECHANICAL SYSTEMS IN THE DYNAMICS OF A RIGID
BODY WITH LIQUID 285
7.1 NONLINEAR EQUATIONS OF TRANSLATIONAL MOTION OF A RIGID BODY WITH
A CYLINDRICAL CAVITY PARTIALLY FILLED WITH LIQUID 286
7.2 EQUIVALENT MECHANICAL SYSTEMS FOR A RIGID BODY WITH LIQUID . 296
8 FORCED FINITE-AMPLITUDE LIQUID SLOSHING IN MOVING VESSELS 305
8.1 DYNAMIC STABILITY OF RESONANT LIQUID SLOSHING UNDER HORIZONTAL
HARMONIC EXCITATIONS 305
8.2 STABILITY OF FORCED AND PARAMETRIC SLOSHING IN THE SIMPLEST CASE .
307
8.3 CONSTRUCTION THE PERIODIC SOLUTIONS OF (8.2.1) BY ALTERNATIVE
APPROXIMATE METHODS 316
8.4 PERIODIC BUBNOV-GALERKIN SOLUTION OF (8.1.3) 323
8.5 STABILITY OF PERIODIC SOLUTIONS OF (8.1.3) 326
8.6 FORCED SLOSHING IN A VESSEL UNDER ANGULAR EXCITATIONS 332
8.7 ANALYSIS OF THE RESPONSE CURVES 338
8.8 FORCED LIQUID SLOSHING WITH DAMPING EFFECTS 347
8.9 HYDRODYNAMIC FORCES 357
8.10 TRANSIENT SLOSHING 361
8.11 FORCED LIQUID SLOSHING IN A TAPERED CONICAL TANK 368
BIBLIOGRAPHY 377
INDEX 391 |
| any_adam_object | 1 |
| author | Lukovsʹkij, Ivan Oleksandrovič |
| author_GND | (DE-588)1070322725 |
| author_facet | Lukovsʹkij, Ivan Oleksandrovič |
| author_role | aut |
| author_sort | Lukovsʹkij, Ivan Oleksandrovič |
| author_variant | i o l io iol |
| building | Verbundindex |
| bvnumber | BV042533981 |
| classification_rvk | SK 810 SK 950 UG 3900 |
| classification_tum | MTA 490f MTA 090f |
| ctrlnum | (OCoLC)912470221 (DE-599)DNB1052322360 |
| dewey-full | 531.11 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.11 |
| dewey-search | 531.11 |
| dewey-sort | 3531.11 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV042533981 |
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| indexdate | 2024-08-03T02:21:04Z |
| institution | BVB |
| isbn | 9783110316551 9783110555363 9783110316582 |
| language | English |
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| physical | xv, 393 Seiten Illustrationen, Diagrame |
| publishDate | 2015 |
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| publisher | De Gruyter |
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| series | De Gruyter Studies in Mathematical Physics |
| series2 | De Gruyter Studies in Mathematical Physics |
| spelling | Lukovsʹkij, Ivan Oleksandrovič Verfasser (DE-588)1070322725 aut Nonlinear dynamics mathematical models for rigid bodies with a liquid Ivan A. Lukovsky Berlin De Gruyter 2015 xv, 393 Seiten Illustrationen, Diagrame txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematical Physics 27 Hier auch später erschienene, unveränderte Nachdrucke Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Fluid-Struktur-Wechselwirkung (DE-588)4314754-9 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 s Fluid-Struktur-Wechselwirkung (DE-588)4314754-9 s DE-604 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-038973-9 Erscheint auch als Online-Ausgabe, PDF 978-3-11-031657-5 De Gruyter Studies in Mathematical Physics 27 (DE-604)BV040141722 27 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4691884&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027968146&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lukovsʹkij, Ivan Oleksandrovič Nonlinear dynamics mathematical models for rigid bodies with a liquid De Gruyter Studies in Mathematical Physics Nichtlineare Dynamik (DE-588)4126141-0 gnd Fluid-Struktur-Wechselwirkung (DE-588)4314754-9 gnd |
| subject_GND | (DE-588)4126141-0 (DE-588)4314754-9 |
| title | Nonlinear dynamics mathematical models for rigid bodies with a liquid |
| title_auth | Nonlinear dynamics mathematical models for rigid bodies with a liquid |
| title_exact_search | Nonlinear dynamics mathematical models for rigid bodies with a liquid |
| title_full | Nonlinear dynamics mathematical models for rigid bodies with a liquid Ivan A. Lukovsky |
| title_fullStr | Nonlinear dynamics mathematical models for rigid bodies with a liquid Ivan A. Lukovsky |
| title_full_unstemmed | Nonlinear dynamics mathematical models for rigid bodies with a liquid Ivan A. Lukovsky |
| title_short | Nonlinear dynamics |
| title_sort | nonlinear dynamics mathematical models for rigid bodies with a liquid |
| title_sub | mathematical models for rigid bodies with a liquid |
| topic | Nichtlineare Dynamik (DE-588)4126141-0 gnd Fluid-Struktur-Wechselwirkung (DE-588)4314754-9 gnd |
| topic_facet | Nichtlineare Dynamik Fluid-Struktur-Wechselwirkung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4691884&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027968146&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV040141722 |
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