Mechanics and dynamical systems with Mathematica:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2000
|
| Series: | Modeling and simulation in science, engineering and technology
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 417 S. Ill., graph. Darst. |
| ISBN: | 376434007X 081764007X |
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MARC
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Record in the Search Index
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| adam_text |
NICOLA BELLOMO LUIGI PREZIOSI ANTONIO ROMANO MECHANICS AND DYNAMICAL
SYSTEMS WITH MATHEMATICA BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS
PREFACE IX I MATHEMATICAL METHODS FOR DIFFERENTIAL EQUATIONS 1 MODELS
AND DIFFERENTIAL EQUATIONS 1 1.1 INTRODUCTION 1 1.2 MATHEMATICAL MODELS
AND COMPUTATION 2 1.3 EXAMPLES OF MATHEMATICAL MODELS 8 1.4 VALIDATION,
DETERMINISM, AND STOCHASTICITY 16 2 MODELS AND MATHEMATICAL PROBLEMS 19
2.1 INTRODUCTION 19 2.2 CLASSIFICATION OF MODELS 20 2.3 STATEMENT OF
PROBLEMS 26 2.4 SOLUTION OF INITIAL-VALUE PROBLEMS 29 2.5 REPRESENTATION
OF THE DYNAMIC RESPONSE 40 2.6 ON THE SOLUTION OF BOUNDARY-VALUE
PROBLEMS . . . . 46 2.7 PROBLEMS 50 3 STABILITY AND PERTURBATION METHODS
57 3.1 INTRODUCTION 57 3.2 STABILITY DEFINITIONS 63 3.3 LINEAR STABILITY
METHODS 65 3.4 NONLINEAR STABILITY 71 3.5 REGULAR PERTURBATION METHODS
76 3.6 PROBLEMS 87 VI CONTENTS II MATHEMATICAL METHODS OF CLASSICAL
MECHANICS 4 NEWTONIAN DYNAMICS 93 4.1 INTRODUCTION 93 4.2 PRINCIPLES OF
NEWTONIAN MECHANICS 95 4.3 BALANCE LAWS FOR SYSTEMS OF POINT MASSES 102
4.4 ACTIVE AND REACTIVE FORCES 106 4.4.1 CONSTRAINTS AND REACTIVE FORCES
107 4.4.2 ACTIVE FORCES AND FORCE FIELDS 115 4.5 APPLICATIONS 122 4.5.1
DYNAMICS OF SIMPLE PENDULUM 123 4.5.2 PARTICLE SUBJECT TO A CENTRAL
FORCE 125 4.5.3 HEAVY PARTICLE FALLING IN AIR 129 4.5.4 THREE-POINT
MASSES SUBJECT TO ELASTIC FORCES . . . 133 4.6 PROBLEMS 136 5 RIGID BODY
DYNAMICS 139 5.1 INTRODUCTION 139 5.2 RIGID BODY MODELS 140 5.3 ACTIVE
AND REACTIVE FORCES IN RIGID BODY DYNAMICS 148 5.4 CONSTRAINED RIGID
BODY MODELS 152 5.5 ARTICULATED SYSTEMS 162 5.6 APPLICATIONS 165 5.6.1
RIGID BODY MODEL OF A VEHICLE AND PLANE DYNAMICS 166 5.6.2 COMPOUND
PENDULUM 167 5.6.3 UNIFORM ROTATIONS 170 5.6.4 FREE ROTATIONS OF A
GYROSCOPE 171 5.6.5 BALL ON AN INCLINED PLANE 174 5.7 PROBLEMS 178 6
ENERGY METHODS AND LAGRANGIAN MECHANICS 183 6.1 INTRODUCTION 183 6.2
ELEMENTARY AND VIRTUAL WORK 185 6.3 ENERGY THEOREMS 189 6.4 THE METHOD
OF LAGRANGE EQUATIONS 194 6.5 POTENTIAL AND FIRST INTEGRALS 200 6.6
ENERGY METHODS AND STABILITY 207 6.7 APPLICATIONS 211 6.7.1 THREE BODY
ARTICULATED SYSTEM 212 6.7.2 STABILITY OF DUFFING'S MODEL 214 CONTENTS
VI I 6.7.3 FREE ROTATIONS OR POINSOT'S MOTION 217 6.7.4 HEAVY GYROSCOPE
220 6.7.5 THE ROLLING COIN 224 6.8 PROBLEMS 227 III BIFURCATIONS,
CHAOTIC DYNAMICS, STOCHASTIC MODELS, AND DISCRETIZATION OF CONTINUOUS
MODELS 7 DETERMINISTIC AND STOCHASTIC MODELS IN APPLIED SCIENCES 233 7.1
INTRODUCTION 233 7.2 MATHEMATICAL MODELING IN APPLIED SCIENCES 234 7.3
EXAMPLES OF MATHEMATICAL MODELS 239 7.4 FURTHER REMARKS ON MODELING 244
7.5 MATHEMATICAL MODELING AND STOCHASTICITY 246 7.5.1 RANDOM VARIABLES
AND STOCHASTIC CALCULUS . . . 251 7.5.2 MOMENT REPRESENTATION OF THE
DYNAMIC RESPONSE 259 7.5.3 STATISTICAL REPRESENTATION OF LARGE SYSTEMS .
. . 261 7.6 PROBLEMS 263 8 CHAOTIC DYNAMICS, STABILITY, AND BIFURCATIONS
267 8LL INTRODUCTION 267 8.2 STABILITY DIAGRAMS 268 8.3 STABILITY
DIAGRAMS AND POTENTIAL ENERGY 275 8.4 LIMIT CYCLES 282 8.5 HOPF
BIFURCATION 287 8.6 CHAOTIC MOTIONS 292 8.7 APPLICATIONS 294 8.7.1 RING
ON A ROTATING WIRE 294 8.7.2 METALLIC METER 298 8.7.3 LINE GALLOPING
MODEL 301 8.7.4 FLUTTER INSTABILITY MODEL 304 8.7.5 MODELS PRESENTING
TRANSITION TO CHAOS 306 8.8 PROBLEMS 309 9 DISCRETE MODELS OF CONTINUOUS
SYSTEMS 313 9.1 INTRODUCTION 313 9.2 DIFFUSION MODELS 317 9.3
MATHEMATICAL MODELS OF TRAFFIC FLOW 321 9.4 MATHEMATICAL STATEMENT OF
PROBLEMS 326 VLLL CONTENTS 9.5 DISCRETIZATION OF CONTINUOUS MODELS 329
9.6 PROBLEMS 336 APPENDIX I. NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL
EQUATIONS 341 1 INTRODUCTION 341 2 NUMERICAL METHODS FOR INITIAL-VALUE
PROBLEMS 342 3 NUMERICAL METHODS FOR BOUNDARY-VALUE PROBLEMS 349
APPENDIX II. KINEMATICS, APPLIED FORCES, MOMENTUM AND MECHANICAL ENERGY
357 1 INTRODUCTION 357 2 SYSTEMS OF APPLIED FORCES 358 3 FUNDAMENTAL OF
KINEMATICS 361 4 CENTER OF MASS 363 5 TENSOR OF INERTIA 365 6 LINEAR
MOMENTUM 369 7 ANGULAR MOMENTUM 370 8 KINETIC ENERGY 372 APPENDIX III.
SCIENTIFIC PROGRAMS 377 1 INTRODUCTION TO PROGRAMMING 377 2 SCIENTIFIC
PROGRAMS 382 REFERENCES SUBJECT INDEX 409 411 |
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| id | DE-604.BV012832818 |
| illustrated | Illustrated |
| indexdate | 2024-09-10T00:55:22Z |
| institution | BVB |
| isbn | 376434007X 081764007X |
| language | English |
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| physical | XIII, 417 S. Ill., graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | Birkhäuser |
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| series2 | Modeling and simulation in science, engineering and technology |
| spelling | Bellomo, Nicola 1943- Verfasser (DE-588)11304206X aut Mechanics and dynamical systems with Mathematica Nicola Bellomo ; Luigi Preziosi ; Antonio Romano Boston [u.a.] Birkhäuser 2000 XIII, 417 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Modeling and simulation in science, engineering and technology Mathematica (Computer file) Mécanique analytique Mechanics, Analytic Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 s Mathematica Programm (DE-588)4268208-3 s DE-604 Mechanik (DE-588)4038168-7 s Preziosi, Luigi Verfasser aut Romano, Antonio Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008731291&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bellomo, Nicola 1943- Preziosi, Luigi Romano, Antonio Mechanics and dynamical systems with Mathematica Mathematica (Computer file) Mécanique analytique Mechanics, Analytic Mathematica Programm (DE-588)4268208-3 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4268208-3 (DE-588)4185100-6 (DE-588)4038168-7 |
| title | Mechanics and dynamical systems with Mathematica |
| title_auth | Mechanics and dynamical systems with Mathematica |
| title_exact_search | Mechanics and dynamical systems with Mathematica |
| title_full | Mechanics and dynamical systems with Mathematica Nicola Bellomo ; Luigi Preziosi ; Antonio Romano |
| title_fullStr | Mechanics and dynamical systems with Mathematica Nicola Bellomo ; Luigi Preziosi ; Antonio Romano |
| title_full_unstemmed | Mechanics and dynamical systems with Mathematica Nicola Bellomo ; Luigi Preziosi ; Antonio Romano |
| title_short | Mechanics and dynamical systems with Mathematica |
| title_sort | mechanics and dynamical systems with mathematica |
| topic | Mathematica (Computer file) Mécanique analytique Mechanics, Analytic Mathematica Programm (DE-588)4268208-3 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Mathematica (Computer file) Mécanique analytique Mechanics, Analytic Mathematica Programm Theoretische Mechanik Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008731291&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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