An introduction to modern variational techniques in mechanics and engineering:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser [u.a.]
2004
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 346 S. graph. Darst. |
| ISBN: | 9781461264675 0817633995 3764333995 |
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Record in the Search Index
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| adam_text | IMAGE 1
B.D. VUJANOVIC
T.M. ATANACKOVIC
AN INTRODUCTION TO MODERN VANATIONAL TECHNIQUES IN MECHANICS AND
ENGINEERING
BIRKHAEUSER BOSTON * BASEL * BERLIN
IMAGE 2
CONTENTS
PREFACE IX
I DIFFERENTIAL VARIATIONAL PRINCIPLES OF MECHANICS
1 THE ELEMENTS OF ANALYTICAL MECHANICS EXPRESSED USING THE
LAGRANGE-D ALEMBERT DIFFERENTIAL VARIATIONAL PRINCIPLE 3 1.1
INTRODUCTION 3
1.2 DIFFERENTIAL EQUATIONS OF MOTION IN CARTESIAN COORDINATES . 3 1.2.1
FREE DYNAMICAL SYSTEMS 3
1.2.2 CONSTRAINED MOTION. LAGRANGIAN EQUATIONS WITH MULTIPLIERS 4
1.3 AN INVARIANT FORM OF DYNAMICS, THE LAGRANGE-D ALEMBERT DIFFERENTIAL
VARIATIONAL PRINCIPLE FOR HOLONOMIC DYNAMICAL SYSTEMS 9
1.3.1 THE PRINCIPLE 9
1.3.2 GENERALIZED COORDINATES AND THEIR VARIATIONS . . .. 11 1.3.3 THE
LAGRANGE-D ALEMBERT VARIATIONAL PRINCIPLE EXPRESSED IN TERMS OF
GENERALIZED COORDINATES, CENTRAL LAGRANGIAN EQUATIONS 13
1.4 EULER-LAGRANGIAN EQUATIONS 16
1.4.1 THE STRUCTURE OF THE KINETIC ENERGY. EXPLICIT FORM OF
EULER-LAGRANGIAN EQUATIONS 18
1.4.2 TWO IMPORTANT CONSERVATION LAWS OF THE EULER-LAGRANGIAN EQUATIONS:
MOMENTUM AND JACOBI CONSERVATION LAWS 22
1.4.3 ON THE DISTURBED MOTION AND GEOMETRIE STABILITY OF THE SCLERONOMIC
POTENTIAL DYNAMICAL SYSTEMS . . 28 1.5 A BRIEF OUTLINE OF THE
NONHOLONOMIC DYNAMICAL SYSTEMS . 33 1.6 SOME OTHER FORMS OF THE
EQUATIONS OF MOTION 44
1.6.1 THE GIBBS-APPELL EQUATIONS: HOLONOMIC DYNAMICAL SYSTEMS 44
1.6.2 THE GIBBS-APPELL EQUATIONS: NONHOLONOMIC DYNAMICAL SYSTEMS 49
1.6.3 KANE S EQUATIONS 52
1.7 NIELSEN AND MANGERONE-DELEANU DIFFERENTIAL EQUATIONS . .. 55 1.8
HAMILTON S CANONICAL DIFFERENTIAL EQUATIONS OF MOTION . .. 59
IMAGE 3
VI CONTENTS
1.9 CANONICAL TRANSFORMATIONS 64
1.10 POISSON BRACKETS, THE CONDITIONS OF CANONICITY OF A GIVEN
TRANSFORMATION 69
2 THE HAMILTON-JACOBI METHOD OF INTEGRATION OF CANONICAL EQUATIONS 73
2.1 INTRODUCTION 73
2.2 THE HAMILTON-JACOBI PARTIAL DIFFERENTIAL EQUATION 73
2.3 SOME APPLICATIONS OF THE HAMILTON-JACOBI METHOD 77
2.3.1 LINEARLY DAMPED OSCILLATOR 77
2.3.2 SIMPLE HARMONIE OSCILLATOR 78
2.3.3 THE CASE WHEN A PARTICULAR SOLUTION OF THE RICCATI EQUATION IS
AVAILABLE 80
2.4 THE OSCILLATORY MOTION WITH TWO DEGREES OF FREEDOM . .. 84 2.5
APPLICATION OF THE HAMILTON-JACOBI METHOD TO THE STUDY OF RHEOLINEAR
OSCILLATIONS 96
2.6 A CONJUGATE APPROACH TO HAMILTON-JACOBI THEORY. THE CASE OF
RHEOLINEAR SYSTEMS 111
2.7 QUADRATIC CONSERVATION LAWS OF RHEOLINEAR DYNAMICAL SYSTEMS WITH TWO
DEGREES OF FREEDOM 116
2.7.1 AN ALTERNATIVE FORM OF THE QUADRATIC CONSERVATION LAW 122
2.7.2 SOME EXAMPLES 124
3 TRANSFORMATION PROPERTIES OF LAGRANGE-D ALEMBERT VARIATIONAL
PRINCIPLE: CONSERVATION LAWS OF NONCONSERVATIVE DYNAMICAL SYSTEMS 131
3.1 INTRODUCTION 131
3.2 SIMULTANEOUS AND NONSIMULTANEOUS VIRTUAL DISPLACEMENTS (VARIATIONS),
INFINITESIMAL TRANSFORMATIONS 132
3.3 A TRANSFORMATION OF THE LAGRANGE-D ALEMBERT PRINCIPLE . . 135 3.4
THE CONDITIONS FOR THE EXISTENCE OF A CONSERVED QUANTITY OF THE GIVEN
DYNAMICAL SYSTEM 136
3.5 THE GENERALIZED KILLING EQUATIONS 138
3.6 THE BASIC NOETHER IDENTITY AND INTEGRATING FACTORS OF EQUATIONS OF
MOTION 141
3.7 QUADRATIC CONSERVATION LAWS OF EULER S EQUATION 142
3.8 QUADRATIC CONSERVATION LAWS OF THE SCLERONOMIC DUFFING OSCILLATOR
146
3.9 CONSERVATION LAWS OF THE ARBITRARY DEGREE OF A PURELY DISSIPATIVE
DYNAMICAL SYSTEM 149
3.10 POLYNOMIAL CONSERVATION LAWS OF THE GENERALIZED EMDEN-FOWLER
EQUATION 152
IMAGE 4
CONTENTS VII
4 A FIELD METHOD SUITABLE FOR APPLICATION IN CONSERVATIVE AND
NONCONSERVATIVE MECHANICS 159
4.1 INTRODUCTION 159
4.2 THE FIELD CONCEPT AND ITS PARTIAL DIFFERENTIAL EQUATION . . 160
4.2.1 THE BUENDLE OF CONSERVATION LAWS 161
4.2.2 THE INITIAL VALUE PROBLEMS 161
4.3 A NON-HAMILTONIAN RHEONOMIC SYSTEM 164
4.4 SOME EXAMPLES WITH MANY-DEGREES-OF-FREEDOM DYNAMICAL SYSTEMS 166
4.4.1 PROJECTILE MOTION WITH LINEAR AIR RESISTANCE . . .. 166 4.4.2
APPLICATION OF THE FIELD METHOD TO NONHOLONOMIC DYNAMICAL SYSTEMS 170
4.5 NONLINEAR ANALYSIS 173
4.6 CONSERVATION LAWS AND REDUCTION TO QUADRATURES OF THE GENERALIZED
TIME-DEPENDENT DUFFING EQUATION 179
4.6.1 THE CASE OF ARBITRARY Q S (P = 0) 185
4.6.2 THE CASE Q 3 = 0 ISS = 0) 186
4.6.3 REDUCTION TO QUADRATURES BY MEANS OF THE HAMILTONJACOBI METHOD 187
4.6.4 THE CASE WHEN A PARTICULAR SOLUTION OF THE RICCATI EQUATION IS
AVAILABLE 192
II THE HAMILTONIAN INTEGRAL VARIATIONAL PRINCIPLE
5 THE HAMILTONIAN VARIATIONAL PRINCIPLE AND ITS APPLICATIONS 197
5.1 INTRODUCTION 197
5.2 THE SIMPLEST FORM OF THE HAMILTONIAN VARIATIONAL PRINCIPLE 198 5.3
THE HAMILTONIAN PRINCIPLE FOR NONCONSERVATIVE FORCE FIELD 205 5.4 THE
FUNCTIONAL CONTAINING THE HIGHER ORDER DERIVATIVES . . 206 5.5 THE
FUNCTIONAL DEPENDING UPON SEVERAL INDEPENDENT
VARIABLES 207
6 VARIABLE END POINTS, NATURAL BOUNDARY CONDITIONS, BOLZA PROBLEMS 215
6.1 INTRODUCTION 215
6.2 TIME INTERVAL (IO,II) SPECIFIED, GI (IO) ,9I (*I) FREE 215
6.3 THE PROBLEM OF BOLZA 221
6.4 UNSPECIFIED INITIAL AND TERMINAL TIME, VARIABLE END POINTS 226 6.5
JACOBI S FORM OF THE VARIATIONAL PRINCIPLE DESCRIBING THE PATHS OF
CONSERVATIVE DYNAMICAL SYSTEMS 232
6.6 PIECEWISE CONTINUOUS EXTREMAIS. THE WEIERSTRASS-ERDMANN CORNER
CONDITIONS 236
IMAGE 5
VIII CONTENTS
7 CONSTRAINED PROBLEMS 241
7.1 INTRODUCTION 241
7.2 ISOPERIMETRIC CONSTRAINTS 241
7.3 ALGEBRAIC (HOLONOMIC) CONSTRAINTS 246
7.4 DIFFERENTIAL EQUATIONS CONSTRAINTS 248
7.5 THE SIMPLEST FORM OF HAMILTON S VARIATIONAL PRINCIPLE AS A PROBLEM
OF OPTIMAL CONTROL THEORY 250
7.6 CONTINUOUS OPTIMAL CONTROL PROBLEMS 252
7.7 OPTIMAL CONTROL PROBLEMS WITH UNSPECIFIED TERMINAL TIME 257
8 VARIATIONAL PRINCIPLES FOR ELASTIC RODS AND COLUMNS 263
8.1 INTRODUCTION 263
8.2 THE COLUMN WITH CONCENTRATED FORCE AT THE END 264
8.3 ROD WITH COMPRESSIBLE AXIS AND THE INFLUENCE OF SHEAR STRESSES ON
THE DEFORMATION 270
8.4 ROTATING ROD 272
8.4.1 BERNOULLI-EULER THEORY 272
8.4.2 ROTATING ROD WITH SHEAR AND COMPRESSIBILITY: A DIRECTOR THEORY 277
8.5 ROD LOADED BY A FORCE AND A TORQUE 282
8.6 OPTIMAL SHAPE OF A SIMPLY SUPPORTED ROD (LAGRANGE S PROBLEM) 289
8.7 OPTIMAL SHAPE OF A ROD LOADED BY DISTRIBUTED FOLLOWER FORCE 293
8.8 OPTIMAL SHAPE OF THE ROTATING ROD 303
8.9 OPTIMAL SHAPE OF A ROD LOADED BY A FORCE AND A TORQUE . 321 8.10
VARIATIONAL PRINCIPLE FOR SMALL DEFORMATION IMPOSED ON LARGE DEFORMATION
OF A ROD 327
BIBLIOGRAPHY 333
INDEX 343
|
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| spelling | Vujanovic, Bozidar D. Verfasser aut An introduction to modern variational techniques in mechanics and engineering B. D. Vujanovic ; T. M. Atanackovic Boston [u.a.] Birkhäuser [u.a.] 2004 X, 346 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mechanics, Analytic Variational principles Mechanik (DE-588)4038168-7 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Mechanik (DE-588)4038168-7 s Variationsrechnung (DE-588)4062355-5 s DE-604 Atanackovic, Teodor M. 1945- Verfasser (DE-588)122214765 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010547327&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vujanovic, Bozidar D. Atanackovic, Teodor M. 1945- An introduction to modern variational techniques in mechanics and engineering Mechanics, Analytic Variational principles Mechanik (DE-588)4038168-7 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4038168-7 (DE-588)4062355-5 |
| title | An introduction to modern variational techniques in mechanics and engineering |
| title_auth | An introduction to modern variational techniques in mechanics and engineering |
| title_exact_search | An introduction to modern variational techniques in mechanics and engineering |
| title_full | An introduction to modern variational techniques in mechanics and engineering B. D. Vujanovic ; T. M. Atanackovic |
| title_fullStr | An introduction to modern variational techniques in mechanics and engineering B. D. Vujanovic ; T. M. Atanackovic |
| title_full_unstemmed | An introduction to modern variational techniques in mechanics and engineering B. D. Vujanovic ; T. M. Atanackovic |
| title_short | An introduction to modern variational techniques in mechanics and engineering |
| title_sort | an introduction to modern variational techniques in mechanics and engineering |
| topic | Mechanics, Analytic Variational principles Mechanik (DE-588)4038168-7 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Mechanics, Analytic Variational principles Mechanik Variationsrechnung |
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