Symmetry in mechanics: a gentle, modern introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2001
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 183 - 187, Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 193 S. graph. Darst. |
| ISBN: | 3764341459 0817641459 9780817641450 |
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MARC
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Record in the Search Index
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| adam_text | IMAGE 1
STEPHANIE FRANK SINGER
SYMMETRY IN MECHANICS
A GENTLE, MODERN INTRODUCTION
BIRKHAEUSER
BOSTON * BASEL * BERLIN
IMAGE 2
CONTENTS
PREFACE IX
0 PRELIMINARIES 1
0.1 NOTATION AND CONVENTIONS 1
0.2 PHYSICS AND MATH BACKGROUND 2
1 THE TWO-BODY PROBLEM 5
1.1 FIRST SIMPLIFICATION 7
1.2 SECOND SIMPLIFICATION 12
1.3 RECOVERING KEPLER S LAWS 14
2 PHASE SPACES ARE SYMPLECTIC MANIFOLDS 19
2.1 THE PLANE AND THE AREA FORM 20
2.2 VECTORS, COVECTORS AND ANTISYMMETRIC BILINEAR FORMS . . .. 24 2.3
VECTOR FIELDS AND DIFFERENTIAL FORMS 29
2.4 THE CYLINDER AND JACOBIAN MATRICES 34
2.5 MORE EXAMPLES OF PHASE SPACES 39
2.6 PULLBACK CALCULATIONS 41
3 DIFFERENTIAL GEOMETRY 47
3.1 MANIFOLDS 48
IMAGE 3
VI
CONTENTS
3.2 DIFFERENTIABLE FUNCTIONS 55
3.3 VECTOR FIELDS AND FORMS ON MANIFOLDS 58
4 TOTAL ENERGY FUNCTIONS ARE HAMILTONIAN FUNCTIONS 65
4.1 TOTAL ENERGY AND EQUATIONS OF MOTION 66
4.2 PARTICLES ON THE LINE 69
4.3 MAGNETISM IN THREE-SPACE 71
4.4 ENERGY CONSERVATION AND APPLICATIONS 72
4.5 AN EXAMPLE FROM THE TWO-BODY PROBLEM 81
5 SYMMETRIES ARE LIE GROUP ACTIONS 83
5.1 FROM SYMMETRIES TO GROUPS 84
5.2 MATRIX LIE GROUPS 86
5.3 ABSTRACT LIE GROUPS (OPTIONAL) 90
5.4 GROUP ACTIONS 91
5.5 ORBITS OF GROUP ACTIONS 95
5.6 SYMMETRIES OF HAMILTONIAN SYSTEMS 96
6 INFINITESIMAL SYMMETRIES ARE LIE ALGEBRAS 101
6.1 MATRIX LIE ALGEBRAS 102
6.2 VECTOR FIELDS ASSOCIATED TO LIE ALGEBRA ELEMENTS 107
6.3 ABSTRACT LIE ALGEBRAS (OPTIONAL) 111
7 CONSERVED QUANTITIES ARE MOMENTUM MAPS 113
7.1 DEFINITION OF MOMENTUM MAP 114
7.2 EXAMPLES FROM THE TWO-BODY PROBLEM 117
7.3 MOMENTUM MAPS FROM GROUP ACTIONS (OPTIONAL) 119
8 REDUCTION AND THE TWO-BODY PROBLEM 123
8.1 FIRST REDUCTION 124
8.2 SECOND REDUCTION 129
8.3 RECOVERING KEPLER S LAWS 133
8.4 ZERO ANGULAR MOMENTUM 134
8.5 SYMPLECTIC GEOMETRY 137
8.6 CONCLUDING REMARKS 138
IMAGE 4
CONTENTS VII
RECOMMENDED READING 141
SOLUTIONS 147
REFERENCES 183
INDEX 189
|
| any_adam_object | 1 |
| author | Singer, Stephanie Frank 1964- |
| author_GND | (DE-588)122914686 |
| author_facet | Singer, Stephanie Frank 1964- |
| author_role | aut |
| author_sort | Singer, Stephanie Frank 1964- |
| author_variant | s f s sf sfs |
| building | Verbundindex |
| bvnumber | BV013769143 |
| classification_rvk | UF 1000 SK 950 |
| ctrlnum | (OCoLC)54049299 (DE-599)BVBBV013769143 |
| 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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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:51:38Z |
| institution | BVB |
| isbn | 3764341459 0817641459 9780817641450 |
| language | English |
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| physical | XII, 193 S. graph. Darst. |
| publishDate | 2001 |
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| spelling | Singer, Stephanie Frank 1964- Verfasser (DE-588)122914686 aut Symmetry in mechanics a gentle, modern introduction Stephanie Frank Singer Boston [u.a.] Birkhäuser 2001 XII, 193 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 183 - 187, Hier auch später erschienene, unveränderte Nachdrucke Geometría Diferencial Mecánica Analítica Symmetrie (DE-588)4058724-1 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 s Symmetrie (DE-588)4058724-1 s DE-604 Differentialgeometrie (DE-588)4012248-7 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009411654&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Singer, Stephanie Frank 1964- Symmetry in mechanics a gentle, modern introduction Geometría Diferencial Mecánica Analítica Symmetrie (DE-588)4058724-1 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4058724-1 (DE-588)4185100-6 (DE-588)4012248-7 |
| title | Symmetry in mechanics a gentle, modern introduction |
| title_auth | Symmetry in mechanics a gentle, modern introduction |
| title_exact_search | Symmetry in mechanics a gentle, modern introduction |
| title_full | Symmetry in mechanics a gentle, modern introduction Stephanie Frank Singer |
| title_fullStr | Symmetry in mechanics a gentle, modern introduction Stephanie Frank Singer |
| title_full_unstemmed | Symmetry in mechanics a gentle, modern introduction Stephanie Frank Singer |
| title_short | Symmetry in mechanics |
| title_sort | symmetry in mechanics a gentle modern introduction |
| title_sub | a gentle, modern introduction |
| topic | Geometría Diferencial Mecánica Analítica Symmetrie (DE-588)4058724-1 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Geometría Diferencial Mecánica Analítica Symmetrie Theoretische Mechanik Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009411654&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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