Introduction to mechanics and symmetry: a basic exposition of classical mechanical systems
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York ; Berlin [u.a.]
Springer
1994
|
| Series: | Texts in applied mathematics
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 500 S. graph. Darst. |
| ISBN: | 3540972757 0387972757 3540943471 0387943471 |
Staff View
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| 100 | 1 | |a Marsden, Jerrold E. |d 1942-2010 |e Verfasser |0 (DE-588)124171141 |4 aut | |
| 245 | 1 | 0 | |a Introduction to mechanics and symmetry |b a basic exposition of classical mechanical systems |c Jerrold E. Marsden ; Tudor S. Ratiu |
| 264 | 1 | |a New York ; Berlin [u.a.] |b Springer |c 1994 | |
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| 650 | 7 | |a Symmetrie |2 gtt | |
| 650 | 7 | |a Symétrie (Physique) |2 ram | |
| 650 | 4 | |a Mechanics, Analytic | |
| 650 | 4 | |a Symmetry (Physics) | |
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Record in the Search Index
| _version_ | 1804124049094213632 |
|---|---|
| adam_text | JERROL
D E
. MARSDE
N TUDO
R S
. RATI
U
INTRODUCTIO
N T
O
MECHANIC
S AN
D SYMMETR
Y
A BASI
C EXPOSITIO
N OF
CLASSICA
L MECHANICA
L SYSTEM
S
RNVTFTU YY:/- :YY-
WIT
H 43 ILLUSTRATIONS
SPRINGER-VERLAG
NEW YORK BERLIN HEIDELBER
G LONDO
N PARI
S
TOKYO HON
G KON
G BARCELONA BUDAPEST
CONTENT
S
PREFAC
E I
X
1 INTRODUCTIO
N AN
D OVERVIE
W 1
1.1 LAGRANGIA
N AN
D HAMILTONIA
N FORMALISM
S 1
1.2 TH
E RIGID BOD
Y 5
1.3 LIE-POISSON BRACKETS
, POISSON MANIFOLDS, MOMENTU
M MAP
S 8
1.4 INCOMPRESSIBL
E FLUID
S 14
1.5 TH
E MAXWELL-VLASOV SYSTE
M 17
1.6 TH
E MAXWELL AN
D POISSON-VLASOV BRACKET
S 19
1.7 TH
E POISSON-VLASOV T
O FLUI
D MA
P 21
1.8 TH
E MAXWELL-VLASOV BRACKE
T 22
1.9 TH
E HEAVY TO
P 23
1.10 NONLINEA
R STABILIT
Y 25
1.11 BIFURCATION 36
1.12 TH
E POINCARE-MELNIKOV METHO
D AN
D CHAO
S 39
1.13 RESONANCES
, GEOMETRI
C PHASES
, AN
D CONTRO
L 42
2 HAMILTONIA
N SYSTEM
S O
N LINEA
R SYMPIECTI
C SPACE
S 5
3
2.1 INTRODUCTIO
N 53
2.2 SYMPIECTIC FORM
S ON VECTOR SPACES 57
2.3 EXAMPLE
S 58
2.4 CANONICA
L TRANSFORMATION
S OR SYMPIECTIC MAP
S 60
2.5 TH
E ABSTRAC
T HAMILTO
N EQUATION
S 64
2.6 TH
E CLASSICAL HAMILTO
N EQUATION
S 65
XII CONTENTS
2.7 WHE
N AR
E EQUATION
S HAMILTONIAN
? 67
2.8 HAMILTONIA
N FLOWS 70
2.9 POISSON BRACKET
S 72
2.10 A PARTICL
E IN A ROTATIN
G HOO
P 76
2.11 TH
E POINCARE-MELNIKOV METHO
D AN
D CHAO
S 82
3 A
N INTRODUCTIO
N T
O INFINITE-DIMENSIONA
L SYSTEM
S 9
3
3.1 LAGRANGE
S AN
D HAMILTON
S EQUATION
S FOR FIELD THEOR
Y ..
. 93
3.2 EXAMPLES
: HAMILTON
S EQUATION
S 95
3.3 EXAMPLES
: POISSON BRACKET
S AN
D CONSERVED QUANTITIE
S . . . 103
4 INTERLUDE
: MANIFOLDS
, VECTO
R FIELDS
, DIFFERENTIA
L FORM
S 10
9
4.1 MANIFOLDS 109
4.2 DIFFERENTIAL FORM
S 113
4.3 TH
E LIE DERIVATIV
E 120
4.4 STOKES
THEORE
M 124
5 HAMILTONIA
N SYSTEM
S O
N SYMPLECTI
C MANIFOLD
S 13
1
5.1 SYMPLECTIC MANIFOLDS 131
5.2 SYMPLECTI
C TRANSFORMATION
S 134
5.3 COMPLE
X STRUCTURE
S AN
D KAHLE
R MANIFOLDS 135
5.4 HAMILTONIA
N SYSTEM
S 140
5.5 POISSON BRACKET
S ON SYMPLECTIC MANIFOLDS 142
6 COTANGEN
T BUNDLE
S 14
7
6.1 TH
E LINEA
R CAS
E 147
6.2 TH
E NONLINEA
R CASE 149
6.3 COTANGEN
T LIFTS 152
6.4 LIFTS OF ACTION
S 155
6.5 GENERATIN
G FUNCTION
S 156
6.6 FIBE
R TRANSLATION
S AN
D MAGNETI
C TERM
S 158
6.7 A PARTICL
E I
N A MAGNETI
C FIEL
D 160
6.8 LINEARIZATIO
N OF HAMILTONIA
N SYSTEM
S 161
7 LAGRANGIA
N MECHANIC
S 16
7
7.1 TH
E PRINCIPL
E OF CRITICA
L ACTIO
N 167
7.2 TH
E LEGENDRE TRANSFORM 169
7.3 LAGRANGE
S EQUATION
S 171
7.4 HYPERREGULA
R LAGRANGIAN
S AN
D HAMILTONIAN
S 173
7.5 GEODESIES 178
7.6 TH
E KALUZA-KLEI
N APPROAC
H T
O CHARGE
D PARTICLE
S 181
7.7 MOTIO
N IN A POTENTIA
L FIELD 183
7.8 TH
E LAGRANGE-D ALEMBER
T PRINCIPL
E 186
7.9 TH
E HAMILTON-JACOB
I EQUATIO
N 191
7.10 TH
E CLASSICAL LIMIT AN
D TH
E MASLOV INDE
X 197
CONTENTS
YY
YY
8 VARIATIONA
L PRINCIPLES
, CONSTRAINTS
, ROTATIN
G SYSTEM
S 21
1
8.1 A RETUR
N T
O VARIATIONA
L PRINCIPLE
S 211
8.2 TH
E LAGRANG
E MULTIPLIE
R THEORE
M 219
8.3 HOLONOMIC CONSTRAINT
S 221
8.4 CONSTRAINE
D MOTIO
N IN A POTENTIA
L FIELD 223
8.5 DIRA
C CONSTRAINT
S 226
8.6 CENTRIFUGAL AN
D CORIOLIS FORCES 231
8.7 TH
E GEOMETRI
C PHAS
E FOR A PARTICL
E IN A HOO
P 235
8.8 TH
E GENERA
L THEOR
Y OF MOVING SYSTEM
S 238
9 A
N INTRODUCTIO
N T
O LI
E GROUP
S 24
1
9.1 BASIC DEFINITIONS AN
D PROPERTIE
S 243
9.2 SOME CLASSICAL LIE GROUP
S 256
9.3 ACTION
S OF LIE GROUP
S 267
1
0 POISSO
N MANIFOLD
S 28
5
10.1 TH
E DEFINITION OF POISSON MANIFOLDS 285
10.2 EXAMPLE
S 286
10.3 HAMILTONIA
N VECTOR FIELD
S AN
D CASIMI
R FUNCTION
S 291
10.4 EXAMPLE
S 295
10.5 PROPERTIE
S OF HAMILTONIA
N FLOWS 296
10.6 TH
E POISSON TENSOR 298
10.7 QUOTIENT
S OF POISSON MANIFOLDS 308
10.8 TH
E SCHOUTE
N BRACKE
T 311
10.9 GENERALITIE
S ON LIE-POISSON STRUCTURE
S 318
1
1 MOMENTU
M MAP
S 32
3
11.1 CANONICA
L ACTION
S AN
D THEI
R INFINITESIMAL GENERATOR
S . . . 323
11.2 MOMENTU
M MAP
S 325
11.3 A
N ALGEBRAI
C DEFINITION OF TH
E MOMENTU
M MA
P 328
11.4 CONSERVATIO
N OF MOMENTU
M MAP
S 329
11.5 EXAMPLE
S 330
11.6 EQUIVARIANC
E OF MOMENTU
M MAP
S 336
1
2 COMPUTATIO
N AN
D PROPERTIE
S O
F MOMENTU
M MAP
S 33
9
12.1 MOMENTU
M MAP
S ON COTANGEN
T BUNDLE
S 339
12.2 MOMENTU
M MAP
S ON TANGEN
T BUNDLE
S 344
12.3 EXAMPLE
S 345
12.4 EQUIVARIANC
E AN
D INFINITESIMAL EQUIVARIANC
E 351
12.5 EQUIVARIAN
T MOMENTU
M MAP
S AR
E POISSON 357
12.6 MORE EXAMPLE
S 360
12.7 POISSON AUTOMORPHISM
S 365
12.8 MOMENTU
M MAP
S AN
D CASIMI
R FUNCTION
S 366
XIV CONTENTS
1
3 EULER-POINCAR
E AN
D LIE-POISSO
N REDUCTIO
N 36
9
13.1 TH
E LIE-POISSON REDUCTIO
N THEORE
M 369
13.2 PROOF OF TH
E LIE-POISSON REDUCTIO
N THEORE
M FOR GL{N) . . 372
13.3 PROO
F OF TH
E LIE-POISSON REDUCTIO
N THEORE
M FOR DIFF
VO
I(-M) 373
13.4 PROOF OF TH
E LIE-POISSON REDUCTIO
N THEORE
M FOR DIFF
CA
N(F
) 375
13.5 LIE-POISSON REDUCTIO
N USING MOMENTU
M FUNCTION
S 377
13.6 REDUCTIO
N AN
D RECONSTRUCTIO
N OF DYNAMIC
S 379
13.7 TH
E LINEARIZED LIE-POISSON BRACKE
T 383
13.8 TH
E EULER-POINCAR
E EQUATION
S 388
13.9 TH
E REDUCE
D EULER-LAGRANG
E EQUATION
S 396
1
4 COADJOIN
T ORBIT
S 39
9
14.1 EXAMPLE
S OF COADJOINT ORBIT
S 400
14.2 TANGEN
T VECTORS T
O COADJOINT ORBIT
S 406
14.3 EXAMPLE
S OF TANGEN
T VECTORS 407
14.4 TH
E SYMPLECTI
C STRUCTUR
E ON COADJOINT ORBIT
S 408
14.5 EXAMPLE
S OF SYMPLECTIC STRUCTURE
S ON ORBIT
S 412
14.6 TH
E ORBI
T BRACKE
T VI
A RESTRICTIO
N 413
14.7 TH
E SPECIAL LINEA
R GROU
P ON TH
E PLAN
E 420
14.8 TH
E EUCLIDEA
N GROU
P OF TH
E PLAN
E 421
14.9 TH
E EUCLIDEA
N GROU
P OF THREE-SPAC
E 424
1
5 TH
E FRE
E RIGI
D BOD
Y 43
1
15.1 MATERIAL
, SPATIAL
, AN
D BOD
Y COORDINATE
S 431
15.2 TH
E LAGRANGIA
N OF TH
E FREE RIGID BOD
Y 432
15.3 TH
E LAGRANGIA
N AN
D HAMILTONIA
N FOR TH
E RIGID BOD
Y IN
BOD
Y REPRESENTATIO
N 434
15.4 KINEMATIC
S ON LIE GROUP
S 438
15.5 POINSOT
S THEORE
M 439
15.6 EULE
R ANGLES 440
15.7 TH
E HAMILTONIA
N OF TH
E FREE RIGID BOD
Y IN TH
E MATERIA
L
DESCRIPTIO
N VI
A EULE
R ANGLES 442
15.8 TH
E ANALYTICA
L SOLUTION OF TH
E FREE RIGID BOD
Y PROBLE
M . . 444
15.9 RIGID BOD
Y STABILIT
Y 449
15.10HEAVY TO
P STABILIT
Y 453
15.11THE RIGID BOD
Y AN
D TH
E PENDULU
M 458
REFERENCE
S 46
5
INDE
X 49
3
|
| any_adam_object | 1 |
| author | Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S. |
| author_GND | (DE-588)124171141 |
| author_facet | Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S. |
| author_role | aut aut |
| author_sort | Marsden, Jerrold E. 1942-2010 |
| author_variant | j e m je jem t s r ts tsr |
| building | Verbundindex |
| bvnumber | BV009701207 |
| callnumber-first | Q - Science |
| callnumber-label | QA808 |
| callnumber-raw | QA808 |
| callnumber-search | QA808 |
| callnumber-sort | QA 3808 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 350 UF 1000 |
| classification_tum | PHY 012f PHY 200f |
| ctrlnum | (OCoLC)30073716 (DE-599)BVBBV009701207 |
| dewey-full | 531 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531 |
| dewey-search | 531 |
| dewey-sort | 3531 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV009701207 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:39:29Z |
| institution | BVB |
| isbn | 3540972757 0387972757 3540943471 0387943471 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006417410 |
| oclc_num | 30073716 |
| open_access_boolean | |
| owner | DE-20 DE-29T DE-91G DE-BY-TUM DE-703 DE-19 DE-BY-UBM DE-634 DE-188 DE-11 |
| owner_facet | DE-20 DE-29T DE-91G DE-BY-TUM DE-703 DE-19 DE-BY-UBM DE-634 DE-188 DE-11 |
| physical | XIV, 500 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spelling | Marsden, Jerrold E. 1942-2010 Verfasser (DE-588)124171141 aut Introduction to mechanics and symmetry a basic exposition of classical mechanical systems Jerrold E. Marsden ; Tudor S. Ratiu New York ; Berlin [u.a.] Springer 1994 XIV, 500 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 17 Mechanica gtt Mécanique analytique ram Symmetrie gtt Symétrie (Physique) ram Mechanics, Analytic Symmetry (Physics) Mechanik (DE-588)4038168-7 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 gnd rswk-swf Symmetrie (DE-588)4058724-1 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 s Symmetrie (DE-588)4058724-1 s DE-604 Mechanik (DE-588)4038168-7 s Hamiltonsches System (DE-588)4139943-2 s 1\p DE-604 Ratiu, Tudor S. Verfasser aut Texts in applied mathematics 17 (DE-604)BV002476038 17 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006417410&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S. Introduction to mechanics and symmetry a basic exposition of classical mechanical systems Texts in applied mathematics Mechanica gtt Mécanique analytique ram Symmetrie gtt Symétrie (Physique) ram Mechanics, Analytic Symmetry (Physics) Mechanik (DE-588)4038168-7 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Symmetrie (DE-588)4058724-1 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4038168-7 (DE-588)4185100-6 (DE-588)4058724-1 (DE-588)4139943-2 |
| title | Introduction to mechanics and symmetry a basic exposition of classical mechanical systems |
| title_auth | Introduction to mechanics and symmetry a basic exposition of classical mechanical systems |
| title_exact_search | Introduction to mechanics and symmetry a basic exposition of classical mechanical systems |
| title_full | Introduction to mechanics and symmetry a basic exposition of classical mechanical systems Jerrold E. Marsden ; Tudor S. Ratiu |
| title_fullStr | Introduction to mechanics and symmetry a basic exposition of classical mechanical systems Jerrold E. Marsden ; Tudor S. Ratiu |
| title_full_unstemmed | Introduction to mechanics and symmetry a basic exposition of classical mechanical systems Jerrold E. Marsden ; Tudor S. Ratiu |
| title_short | Introduction to mechanics and symmetry |
| title_sort | introduction to mechanics and symmetry a basic exposition of classical mechanical systems |
| title_sub | a basic exposition of classical mechanical systems |
| topic | Mechanica gtt Mécanique analytique ram Symmetrie gtt Symétrie (Physique) ram Mechanics, Analytic Symmetry (Physics) Mechanik (DE-588)4038168-7 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Symmetrie (DE-588)4058724-1 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Mechanica Mécanique analytique Symmetrie Symétrie (Physique) Mechanics, Analytic Symmetry (Physics) Mechanik Theoretische Mechanik Hamiltonsches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006417410&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
| work_keys_str_mv | AT marsdenjerrolde introductiontomechanicsandsymmetryabasicexpositionofclassicalmechanicalsystems AT ratiutudors introductiontomechanicsandsymmetryabasicexpositionofclassicalmechanicalsystems |