Tensor analysis and nonlinear tensor functions:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Dordrecht
Kluwer Academic Publishers
2002
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Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XVIII, 662 S. graph. Darst. |
ISBN: | 140201015X |
Internformat
MARC
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Datensatz im Suchindex
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adam_text | TENSOR ANALYSIS AND NONLINEAR TENSOR FUNCTIONS BY YU. I. DIMITRIENKO
BAUMAN MOSCOW STATE TECHNICAL UNIVERSITY, MOSCOW, RUSSIA KLUWER ACADEMIC
PUBLISHERS DORDRECHT / BOSTON / LONDON TABLE OF CONTENTS PREFACE VII
SOURCES OF TENSOR CALCULUS IX INTRODUCTION XV CHAPTER 1. TENSOR ALGEBRA
1 1.1. LOCAL BASIS VECTORS. JACOBIAN AND METRIC MATRICES 1 1.2. VECTOR
PRODUCT 12 1.3. GEOMETRIC DEFINITION OF A TENSOR AND ALGEBRAIC OPERA-
TIONS ON TENSORS 17 1.4. ALGEBRA OF TENSOR FIELDS 34 1.5. EIGENVALUES OF
A TENSOR 40 1.6. SYMMETRIC, SKEW-SYMMETRIC AND ORTHOGONAL TENSORS 43
1.7. PHYSICAL COMPONENTS OF TENSORS 50 1.8. TENSORS OF HIGHER ORDERS 53
1.9. PSEUDOTENSORS 59 CHAPTER 2. TENSORS IN LINEAR SPACES 65 2.1. LINEAR
N-DIMENSIONAL SPACE 65 2.2. MATRICES OF THE NTH ORDER 74 2.3. LINEAR
TRANSFORMATIONS OF N-DIMENSIONAL SPACES 85 2.4. DUAL SPACE 93 2.5.
ALGEBRA OF TENSORS IN N-DIMENSIONAL LINEAR SPACES 98 2.6. OUTER FORMS
116 CHAPTER 3. GROUPS OF TRANSFORMATIONS 129 3.1. LINEAR TRANSFORMATIONS
OF COORDINATES 129 3.2. TRANSFORMATION GROUPS IN THREE-DIMENSIONAL
EUCLIDEAN SPACE 142 3.3. SYMMETRY OF FINITE BODIES 146 3.4. MATRIX
REPRESENTATION OF TRANSFORMATION GROUPS 164 CHAPTER 4. INDIFFERENT
TENSORS AND INVARI- ANTS 169 4.1. INDIFFERENT TENSORS 169 4.2. A NUMBER
OF INDEPENDENT COMPONENTS FOR INDIFFERENT TENSORS 180 4.3. SYMMETRIC
INDIFFERENT TENSORS 192 4.4. SCALAR INVARIANTS * * 202 4.5. INVARIANTS
OF SYMMETRIC SECOND-ORDER TENSORS 212 CHAPTER 5. TENSOR FUNCTIONS 227
5.1. LINEAR TENSOR FUNCTIONS 227 5.2. SCALAR FUNCTIONS OF A TENSOR
ARGUMENT 253 5.3. POTENTIAL TENSOR FUNCTIONS 265 5.4. QUASILINEAR TENSOR
FUNCTIONS 274 5.5. SPECTRAL RESOLUTIONS OF SECOND-ORDER TENSORS 283 5.6.
SPECTRAL RESOLUTIONS OF QUASILINEAR TENSOR FUNCTIONS 298 5.7.
NONPOTENTIAL TENSOR FUNCTIONS 310 5.8. DIFFERENTIATION OF A TENSOR
FUNCTION WITH RESPECT TO A TENSOR ARGUMENT 325 VI TABLE OF CONTENTS 5.9.
SCALAR FUNCTIONS OF SEVERAL TENSOR ARGUMENTS 328 5.10. TENSOR FUNCTIONS
OF SEVERAL TENSOR ARGUMENTS 342 CHAPTER 6. TENSOR ANALYSIS 347 6.1.
COVARIANT DIFFERENTIATION 347 6.2. DIFFERENTIATION OF SECOND-ORDER
TENSORS 357 6.3. PROPERTIES OF COVARIANT DERIVATIVES 361 6.4. COVARIANT
DERIVATIVES OF THE SECOND ORDER 367 6.5. DIFFERENTIATION IN ORTHOGONAL
CURVILINEAR COORDINATES 372 CHAPTER 7. GEOMETRY OF CURVES AND SUR- FACES
385 7.1. CURVES IN THREE-DIMENSIONAL EUCLIDEAN SPACE 385 7.2. SURFACES
IN THREE-DIMENSIONAL EUCLIDEAN SPACE 394 7.3. CURVES ON A SURFACE 413
7.4. GEOMETRY IN A VICINITY OF A SURFACE 426 7.5. PLANAR SURFACES IN K 3
432 CHAPTER 8. TENSORS IN RIEMANNIAN SPACES AND AFFINELY CONNECTED
SPACES 437 8.1. RIEMANNIAN SPACES 437 8.2. AFFINELY CONNECTED SPACES 448
8.3. RIEMANNIAN AFFINELY CONNECTED SPACES 456 8.4. THE
RIEMANN-CHRISTOFFEL TENSOR 462 CHAPTER 9. INTEGRATION OF TENSORS 475
9.1. CURVILINEAR INTEGRALS OF TENSORS 475 9.2. SURFACE INTEGRALS OF
TENSORS 483 9.3. VOLUME INTEGRALS OF TENSORS 488 CHAPTER 10. TENSORS IN
CONTINUUM MECHAN- ICS 493 10.1. DEFORMATION THEORY 493 10.2. VELOCITY
CHARACTERISTICS OF CONTINUUM MOTION 508 10.3. CO-ROTATIONAL DERIVATIVES
516 10.4. MASS, MOMENTUM AND ANGULAR MOMENTUM BALANCE LAWS 524 10.5.
THERMODYNAMIC LAWS 538 10.6. THE DEFORMATION COMPATIBILITY EQUATION 546
10.7. THE COMPLETE SYSTEM OF CONTINUUM MECHANICS LAWS 553 CHAPTER 11.
TENSOR FUNCTIONS IN CONTINUUM MECHANICS 555 11.1. ENERGETIC AND
QUASIENERGETIC COUPLES OF TENSORS 555 11.2. GENERAL PRINCIPLES FOR
TENSOR FUNCTIONS IN CONTINUUM MECHANICS 572 11.3. THE MATERIAL
INDIFFERENCE PRINCIPLE 582 11.4. THE MATERIAL SYMMETRY PRINCIPLE 600
11.5. TENSOR FUNCTIONS FOR NONLINEAR ELASTIC CONTINUA 618 11.6. TENSOR
FUNCTIONS FOR NONLINEAR HYPOELASTIC CONTINUA 646 REFERENCES 653 SUBJECT
INDEX 655
|
any_adam_object | 1 |
author | Dimitrienko, Yu. I. 1962- |
author_GND | (DE-588)1067771077 |
author_facet | Dimitrienko, Yu. I. 1962- |
author_role | aut |
author_sort | Dimitrienko, Yu. I. 1962- |
author_variant | y i d yi yid |
building | Verbundindex |
bvnumber | BV019851630 |
callnumber-first | Q - Science |
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dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 515 - Analysis |
dewey-raw | 515/.63 |
dewey-search | 515/.63 |
dewey-sort | 3515 263 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Book |
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id | DE-604.BV019851630 |
illustrated | Illustrated |
indexdate | 2024-07-09T20:07:35Z |
institution | BVB |
isbn | 140201015X |
language | English |
lccn | 2002040550 |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013176320 |
oclc_num | 494393335 |
open_access_boolean | |
owner | DE-91G DE-BY-TUM DE-634 DE-11 DE-188 |
owner_facet | DE-91G DE-BY-TUM DE-634 DE-11 DE-188 |
physical | XVIII, 662 S. graph. Darst. |
publishDate | 2002 |
publishDateSearch | 2002 |
publishDateSort | 2002 |
publisher | Kluwer Academic Publishers |
record_format | marc |
spelling | Dimitrienko, Yu. I. 1962- Verfasser (DE-588)1067771077 aut Tensor analysis and nonlinear tensor functions by Yu. I. Dimitrienko Dordrecht Kluwer Academic Publishers 2002 XVIII, 662 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Calcul tensoriel ram Calculus of tensors Tensorfunktion (DE-588)4135267-1 gnd rswk-swf Tensoranalysis (DE-588)4204323-2 gnd rswk-swf Tensoranalysis (DE-588)4204323-2 s Tensorfunktion (DE-588)4135267-1 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013176320&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Dimitrienko, Yu. I. 1962- Tensor analysis and nonlinear tensor functions Calcul tensoriel ram Calculus of tensors Tensorfunktion (DE-588)4135267-1 gnd Tensoranalysis (DE-588)4204323-2 gnd |
subject_GND | (DE-588)4135267-1 (DE-588)4204323-2 |
title | Tensor analysis and nonlinear tensor functions |
title_auth | Tensor analysis and nonlinear tensor functions |
title_exact_search | Tensor analysis and nonlinear tensor functions |
title_full | Tensor analysis and nonlinear tensor functions by Yu. I. Dimitrienko |
title_fullStr | Tensor analysis and nonlinear tensor functions by Yu. I. Dimitrienko |
title_full_unstemmed | Tensor analysis and nonlinear tensor functions by Yu. I. Dimitrienko |
title_short | Tensor analysis and nonlinear tensor functions |
title_sort | tensor analysis and nonlinear tensor functions |
topic | Calcul tensoriel ram Calculus of tensors Tensorfunktion (DE-588)4135267-1 gnd Tensoranalysis (DE-588)4204323-2 gnd |
topic_facet | Calcul tensoriel Calculus of tensors Tensorfunktion Tensoranalysis |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013176320&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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