Exterior differential systems and the calculus of variations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston ; Basel ; Stuttgart
Birkhäuser
1983
|
| Schriftenreihe: | Progress in mathematics
25 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 335 Seiten Diagramme |
| ISBN: | 3764331038 |
Internformat
MARC
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| 245 | 1 | 0 | |a Exterior differential systems and the calculus of variations |c Phillip A. Griffiths |
| 264 | 1 | |a Boston ; Basel ; Stuttgart |b Birkhäuser |c 1983 | |
| 300 | |a 335 Seiten |b Diagramme | ||
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Datensatz im Suchindex
| _version_ | 1804114703516958720 |
|---|---|
| adam_text | TABLE OF CONTENTS
INTRODUCTION 1
0. PRELIMINARIES 15
a) Notations from Manifold Theory
b) The Language of Jet Manifolds
c) Frame Manifolds
d) Differential Ideals
e) Exterior Differential Systems
1. EULER-LAGRANGE EQUATIONS FOR DIFFERENTIAL SYSTEMS WITH ONE
INDEPENDENT VARIABLE 32
a) Setting up the Problem; Classical Examples
b) Variational Equations for Integral Manifolds of
Differential Systems
c) Differential Systems in Good Form; the Derived Flag,
Cauchy Characteristics, and Prolongation of Exterior
Differential Systems
d) Derivation of the Euler-Lag range Equations; Examples
e) The Euler-Lagrange Differential System; Non-Degenerate
Variational Problems; Examples
II. FIRST INTEGRALS OF THE EULER-LAGRANGE SYSTEM; NOETHER S
THEOREM AND EXAMPLES 107
a) First Integrals and Noether s Theorem; Some Classical
Examples; Variational Problems Algebraically Integrable
by Quadratures
b) Investigation of the Euler-Lagrange System for Some
Differential-Geometric Variational Problems:
i) / K2 ds for Plane Curves; ii) Affine Arclength;
Mi) / K2 ds for Space Curves; and iv) Delauney
Problem.
III. EULER EQUATIONS FOR VARIATIONAL PROBLEMS IN HOMOGENEOUS
SPACES 161
a) Derivation of the Equations: i) Motivation;
ii) Review of the Classical Case; iii) the General
Euler Equations
b) Examples: i) the Euler Equations Associated to / K2/2 ds
for Curves in En; ii) Some Problems as in i) but for
Curves in Sn; iii) Euler Equations Associated to Non-
degenerate Ruled Surfaces
IV. ENDPOINT CONDITIONS; JACOBI EQUATIONS AND THE 2 VARIATION;
CONJUGATE POINTS; FIELDS AND THE HAMILTON-JACOBI EQUATION;
THE LAGRANGE PROBLEM 199
a) Endpoint Conditions; Well-Posed Variational Problems;
Examples
b) Jacobi Vector Fields and Conjugate Points; Examples
c) Geometry of the Reduced Momentum Space; the 2nc
Variation; the Index Form and Sufficient Conditions
for a Local Minimum
d) Fields and the Hami1ton-Jacobi Equation; Further
Sufficient Conditions for a Local Minimum
e) Mixed Endpoint Conditions and the Classical Problem
of Lagrange; i) Well-Posed Mixed Variational
Problems; ii) The Lagrange Problem; iii) The
Classical Approach to the Lagrange Problem;
iv) Some Related Examples
APPENDIX: MISCELLANEOUS REMARKS AND EXAMPLES 310
a) Problems with Integral Constraints; Examples
b) Classical Problems Expressed in Moving Frames
INDEX 329
BIBLIOGRAPHY 332
|
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| author_GND | (DE-588)131881434 |
| author_facet | Griffiths, Phillip 1938- |
| author_role | aut |
| author_sort | Griffiths, Phillip 1938- |
| author_variant | p g pg |
| building | Verbundindex |
| bvnumber | BV000240648 |
| classification_rvk | SK 370 SK 540 SK 660 SK 780 |
| classification_tum | MAT 535f MAT 498f |
| ctrlnum | (OCoLC)230639778 (DE-599)BVBBV000240648 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000240648 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:10:56Z |
| institution | BVB |
| isbn | 3764331038 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000144566 |
| oclc_num | 230639778 |
| open_access_boolean | |
| owner | DE-12 DE-20 DE-91G DE-BY-TUM DE-703 DE-384 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-706 DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-188 |
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| physical | 335 Seiten Diagramme |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Griffiths, Phillip 1938- Verfasser (DE-588)131881434 aut Exterior differential systems and the calculus of variations Phillip A. Griffiths Boston ; Basel ; Stuttgart Birkhäuser 1983 335 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 25 Äußeres Differentialsystem (DE-588)4141545-0 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Äußeres Differentialsystem (DE-588)4141545-0 s Erscheint auch als Online-Ausgabe 978-1-4615-8166-6 Progress in mathematics 25 (DE-604)BV000004120 25 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000144566&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Griffiths, Phillip 1938- Exterior differential systems and the calculus of variations Progress in mathematics Äußeres Differentialsystem (DE-588)4141545-0 gnd Variationsrechnung (DE-588)4062355-5 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4141545-0 (DE-588)4062355-5 (DE-588)4012248-7 |
| title | Exterior differential systems and the calculus of variations |
| title_auth | Exterior differential systems and the calculus of variations |
| title_exact_search | Exterior differential systems and the calculus of variations |
| title_full | Exterior differential systems and the calculus of variations Phillip A. Griffiths |
| title_fullStr | Exterior differential systems and the calculus of variations Phillip A. Griffiths |
| title_full_unstemmed | Exterior differential systems and the calculus of variations Phillip A. Griffiths |
| title_short | Exterior differential systems and the calculus of variations |
| title_sort | exterior differential systems and the calculus of variations |
| topic | Äußeres Differentialsystem (DE-588)4141545-0 gnd Variationsrechnung (DE-588)4062355-5 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Äußeres Differentialsystem Variationsrechnung Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000144566&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT griffithsphillip exteriordifferentialsystemsandthecalculusofvariations |