The calculus of variations and functional analysis: with optimal control and applications in mechanics
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific Publ.
2003
|
| Series: | Series on stability, vibration and control of systems
Series A ; 12 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 420 S. graph. Darst. |
| ISBN: | 9812385819 |
Staff View
MARC
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Record in the Search Index
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| adam_text | SERIES ON STABILITY, VIBRATION AND CONTROL OF SYSTEMS ^TEH |GP SERIES A
VOLUME 12 FOUNDER AND EDITOR: ARDESHIR GURAN CO-EDITORS: C. CHRISTOV, M.
CLOUD, F. PICHLER & W. B. ZIMMERMAN THE CALCULUS OF VARIATIONS AND
FUNCTIONAL ANALYSIS WITH OPTIMAL CONTROL AND APPLICATIONS IN MECHANICS
LEONID P. LEBEDEV NATIONAL UNIVERSITY OF COLOMBIA, COLOMBIA & ROSTOV
STATE UNIVERSITY, RUSSIA MICHAEL J. CLOUD LAWRENCE TECHNOLOGICAL
UNIVERSITY, USA *$ WORLD SCIENTIFIC NEW JERSEY * LONDON * SINGAPORE *
SHANGHAI * HONGKONG * TAIPEI * RANGALORE CONTENTS FOREWORD V PREFACE IX
1. BASIC CALCULUS OF VARIATIONS 1 1.1 INTRODUCTION 1 1.2 EULER S
EQUATION FOR THE SIMPLEST PROBLEM 14 1.3 SOME PROPERTIES OF EXTREMALS OF
THE SIMPLEST FUNCTIONAL 19 1.4 RITZ S METHOD 22 1.5 NATURAL BOUNDARY
CONDITIONS 30 1.6 SOME EXTENSIONS TO MORE GENERAL FUNCTIONALS 33 1.7
FUNCTIONALS DEPENDING ON FUNCTIONS IN MANY VARIABLES . 43 1.8 A
FUNCTIONAL WITH INTEGRAND DEPENDING ON PARTIAL DERIVA- TIVES OF HIGHER
ORDER 48 1.9 THE FIRST VARIATION 54 1.10 ISOPERIMETRIC PROBLEMS 66 1.11
GENERAL FORM OF THE FIRST VARIATION 73 1.12 MOVABLE ENDS OF EXTREMALS 78
1.13 WEIERSTRASS-ERDMANN CONDITIONS AND RELATED PROBLEMS . 82 1.14
SUFFICIENT CONDITIONS FOR MINIMUM 88 1.15 EXERCISES 97 2. ELEMENTS OF
OPTIMAL CONTROL THEORY 99 2.1 A VARIATIONAL PROBLEM AS A PROBLEM OF
OPTIMAL CONTROL. 99 2.2 GENERAL PROBLEM OF OPTIMAL CONTROL 101 2.3
SIMPLEST PROBLEM OF OPTIMAL CONTROL 104 XI XII CALCULUS OF VARIATIONS
AND FUNCTIONAL ANALYSIS 2.4 FUNDAMENTAL SOLUTION OF A LINEAR ORDINARY
DIFFERENTIAL EQUATION ILL 2.5 THE SIMPLEST PROBLEM, CONTINUED 112 2.6
PONTRYAGIN S MAXIMUM PRINCIPLE FOR THE SIMPLEST PROBLEM 113 2.7 SOME
MATHEMATICAL PRELIMINARIES 118 2.8 GENERAL TERMINAL CONTROL PROBLEM 131
2.9 PONTRYAGIN S MAXIMUM PRINCIPLE FOR THE TERMINAL OPTI- MAL PROBLEM
137 2.10 GENERALIZATION OF THE TERMINAL CONTROL PROBLEM 140 2.11 SMALL
VARIATIONS OF CONTROL FUNCTION FOR TERMINAL CONTROL PROBLEM 145 2.12 A
DISCRETE VERSION OF SMALL VARIATIONS OF CONTROL FUNCTION FOR GENERALIZED
TERMINAL CONTROL PROBLEM 147 2.13 OPTIMAL TIME CONTROL PROBLEMS 151 2.14
FINAL REMARKS ON CONTROL PROBLEMS 155 2.15 EXERCISES 157 3. FUNCTIONAL
ANALYSIS 159 3.1 A NORMED SPACE AS A METRIC SPACE 160 3.2 DIMENSION OF A
LINEAR SPACE AND SEPARABILITY 165 3.3 CAUCHY SEQUENCES AND BANACH SPACES
169 3.4 THE COMPLETION THEOREM 180 3.5 CONTRACTION MAPPING PRINCIPLE 184
3.6 LP SPACES AND THE LEBESGUE INTEGRAL 192 3.7 SOBOLEV SPACES 199 3.8
COMPACTNESS 205 3.9 INNER PRODUCT SPACES, HILBERT SPACES 215 3.10 SOME
ENERGY SPACES IN MECHANICS 220 3.11 OPERATORS AND FUNCTIONAL 240 3.12
SOME APPROXIMATION THEORY 245 3.13 ORTHOGONAL DECOMPOSITION OF A HILBERT
SPACE AND THE RIESZ REPRESENTATION THEOREM 249 3.14 BASIS, GRAM-SCHMIDT
PROCEDURE, FOURIER SERIES IN HILBERT SPACE 253 3.15 WEAK CONVERGENCE 259
3.16 ADJOINT AND SELF-ADJOINT OPERATORS 267 3.17 COMPACT OPERATORS 273
3.18 CLOSED OPERATORS 281 3.19 INTRODUCTION TO SPECTRAL CONCEPTS 285
CONTENTS XIII 3.20 THE FREDHOLM THEORY IN HUBERT SPACES 290 3.21
EXERCISES 301 4. SOME APPLICATIONS IN MECHANICS 307 4.1 SOME PROBLEMS OF
MECHANICS FROM THE VIEWPOINT OF THE CALCULUS OF VARIATIONS; THE VIRTUAL
WORK PRINCIPLE . . . . 307 4.2 EQUILIBRIUM PROBLEM FOR A CLAMPED
MEMBRANE AND ITS GENERALIZED SOLUTION 313 4.3 EQUILIBRIUM OF A FREE
MEMBRANE 315 4.4 SOME OTHER PROBLEMS OF EQUILIBRIUM OF LINEAR MECHANICS
317 4.5 THE RITZ AND BUBNOV-GALERKIN METHODS 325 4.6 THE
HAMILTON-OSTROGRADSKIJ PRINCIPLE AND THE GENERAL- IZED SETUP OF
DYNAMICAL PROBLEMS OF CLASSICAL MECHANICS 328 4.7 GENERALIZED SETUP OF
DYNAMIC PROBLEMS FOR A MEMBRANE 330 4.8 OTHER DYNAMIC PROBLEMS OF LINEAR
MECHANICS 345 4.9 THE FOURIER METHOD 346 4.10 AN EIGENFREQUENCY BOUNDARY
VALUE PROBLEM ARISING IN LINEAR MECHANICS 348 4.11 THE SPECTRAL THEOREM
352 4.12 THE FOURIER METHOD, CONTINUED 358 4.13 EQUILIBRIUM OF A VON
KAERMAEN PLATE 363 4.14 A UNILATERAL PROBLEM 373 4.15 EXERCISES 380
APPENDIX A HINTS FOR SELECTED EXERCISES 383 REFERENCES 415 INDEX 417
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| any_adam_object | 1 |
| author | Lebedev, Leonid P. 1946- Cloud, Michael J. 1960- |
| author_GND | (DE-588)124355560 (DE-588)120264242 |
| author_facet | Lebedev, Leonid P. 1946- Cloud, Michael J. 1960- |
| author_role | aut aut |
| author_sort | Lebedev, Leonid P. 1946- |
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| building | Verbundindex |
| bvnumber | BV020003725 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)249914099 (DE-599)BVBBV020003725 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV020003725 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:10:35Z |
| institution | BVB |
| isbn | 9812385819 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013325406 |
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| physical | XIII, 420 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | World Scientific Publ. |
| record_format | marc |
| series | Series on stability, vibration and control of systems |
| series2 | Series on stability, vibration and control of systems : Series A |
| spelling | Lebedev, Leonid P. 1946- Verfasser (DE-588)124355560 aut The calculus of variations and functional analysis with optimal control and applications in mechanics Leonid P. Lebedev ; Michael J. Cloud Singapore [u.a.] World Scientific Publ. 2003 XIII, 420 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on stability, vibration and control of systems : Series A 12 Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 s Funktionalanalysis (DE-588)4018916-8 s DE-604 Variationsrechnung (DE-588)4062355-5 s Cloud, Michael J. 1960- Verfasser (DE-588)120264242 aut Series on stability, vibration and control of systems Series A ; 12 (DE-604)BV013189168 12 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013325406&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lebedev, Leonid P. 1946- Cloud, Michael J. 1960- The calculus of variations and functional analysis with optimal control and applications in mechanics Series on stability, vibration and control of systems Funktionalanalysis (DE-588)4018916-8 gnd Variationsrechnung (DE-588)4062355-5 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4062355-5 (DE-588)4121428-6 |
| title | The calculus of variations and functional analysis with optimal control and applications in mechanics |
| title_auth | The calculus of variations and functional analysis with optimal control and applications in mechanics |
| title_exact_search | The calculus of variations and functional analysis with optimal control and applications in mechanics |
| title_full | The calculus of variations and functional analysis with optimal control and applications in mechanics Leonid P. Lebedev ; Michael J. Cloud |
| title_fullStr | The calculus of variations and functional analysis with optimal control and applications in mechanics Leonid P. Lebedev ; Michael J. Cloud |
| title_full_unstemmed | The calculus of variations and functional analysis with optimal control and applications in mechanics Leonid P. Lebedev ; Michael J. Cloud |
| title_short | The calculus of variations and functional analysis |
| title_sort | the calculus of variations and functional analysis with optimal control and applications in mechanics |
| title_sub | with optimal control and applications in mechanics |
| topic | Funktionalanalysis (DE-588)4018916-8 gnd Variationsrechnung (DE-588)4062355-5 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Funktionalanalysis Variationsrechnung Optimale Kontrolle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013325406&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013189168 |
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