The geometry of higher order Lagrange spaces: applications to mechanics and physics
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1997
|
| Series: | Fundamental theories of physics
82 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 332 S. |
| ISBN: | 079234393X |
Staff View
MARC
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| 100 | 1 | |a Miron, Radu |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The geometry of higher order Lagrange spaces |b applications to mechanics and physics |c by Radu Miron |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1997 | |
| 300 | |a XV, 332 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Fundamental theories of physics |v 82 | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Lagrange spaces | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Mechanics, Analytic | |
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Record in the Search Index
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| adam_text | Contents
Preface xi
1 Lagrange Spaces of Order 1 1
1.1 The Manifold Osc M. Sprays 2
1.2 Nonlinear Connections 7
1.3 iV Linear Connections 12
1.4 c? Tensors of Torsion and Curvature 16
1.5 Parallelism. Structure Equations 21
1.6 Lagrange Spaces 24
1.7 Variational Problem 25
1.8 A Noether Theorem 28
1.9 Canonical Nonlinear Connection
of a Lagrange Space 30
1.10 Canonical Metrical Connection 32
1.11 Finsler Spaces 35
1.12 Generalized Lagrange Spaces 37
1.13 Almost Kahlerian Model
of the Space Ln 40
1.14 Problems 42
2 The Geometry
of 2 Osculator Bundle 45
2.1 The Fibre Bundle Osc2M 45
2.2 Vertical Distributions. Liouville Vector Fields 49
2.3 2 Tangent Structure. 2 Sprays 52
2.4 Nonlinear Connections 56
2.5 J Vertical Distributions 60
2.6 The Dual Coefficients of a Nonlinear Connection 62
2.7 Determination of a Nonlinear Connection from a 2 Spray. 68
v
2.8 The Almost Product Structure P.
The Almost rc Contact Structure IF 70
2.9 Problems 74
3 A Linear Connections.
Structure Equations. 75
3.1 The Algebra of (/ Tensor Fields 75
3.2 A^ Linear Connection on Osc2M 78
3.3 The Coefficients of the A^ Linear Connections 81
3.4 d Tensors of Torsion 86
3.5 d Tensors of Curvature 90
3.6 Structure Equations of an A^ Linear Connection 100
3.7 Problems 106
4 Lagrangians of Second Order. Variational Problem.
Nother Type Theorems. 107
4.1 Lagrangians of Second Order.
Zermelo Conditions 108
4.2 Variational Problem 110
1 2 dy
4.3 Operators TV, TV,— H3
at
4.4 Craig Synge Covectors 116
4.5 The Energies £c (L), £C(L) 119
4.6 Nother Theorems 123
4.7 Jacobi Ostrogradski Momenta 126
4.8 Regular Lagrangians.
Canonical Nonlinear Connections 130
4.9 Prolongation to Osc2M of the Rie
mannian Structures 134
4.10 Prolongation to Osc2M of the Finslerian and Lagrangian
Structures 136
4.11 Problems 139
5 Second Order Lagrange Spaces 141
5.1 The Notion of Lagrange Space
of Order 2 141
5.2 Euler Lagrange Equations
of a Lagrange Space L^n 144
5.3 Canonical Nonlinear Connections 146
5.4 Canonical Metrical TV Connections 150
5.5 Problems 152
6 Geometry of the fc Osculator Bundle 153
6.1 The Notion of fc Osculator Bundle 153
6.2 Vertical Distributions.
Liouville Vector Fields 157
6.3 k Tangent Structure; fc Sprays 160
6.4 Nonlinear Connections 163
6.5 J Vertical Distributions 166
6.6 The Dual Coeficients of a Nonlinear Connection TV on
Osc*M 168
6.7 The Determination of a Nonlinear
Connection from a fc Spray.
The Structures F and F 174
6.8 Problems 177
7 Linear Connections on OscfcM 179
7.1 d Tensors Algebra 179
7.2 TV Linear Connection 182
7.3 iV Linear Connections in Adapted
Basis 185
7.4 d Tensors of Torsion 188
7.5 (f Tensors of Curvature 191
7.6 The d Tensors of Curvature in Adapted Basis 193
7.7 The Structure Equations 199
7.8 Problems 202
8 Lagrangians of Order k. Applications to Higher
Order Analytical Mechanics. 203
8.1 Lagrangians of Order k.
Zermello Conditions 203
8.2 Variational Problem 205
8.3 Operators f,I^,...J$, 20S
dt
8.4 Craig Synge Covectors 210
8.5 Energies of Higher Order 212
8.6 Noether Theorems 215
8.7 Jacobi Ostrogradski Momenta 219
8.8 Regular Lagrangians.
Canonical Nonlinear Connection 223
8.9 Problems 226
9 Prolongation of the
Riemannian, Finslerian
and Lagrangian Structures
to the fc Osculator Bundle 227
9.1 Prolongation to Osc^M
of the Riemannian Structures 227
9.2 Prolongation to the Osculator
Bundle of the Finslerian Structures 233
9.3 Prolongation to OsckM of a Lagrangian Structure .... 238
9.4 Remarkable Regular Lagrangians
of Order k 239
9.5 Problems 242
10 Higher Order Lagrange Spaces 243
10.1 The Definition of the Space L{k 244
10.2 Canonical Metrical iV Connections 249
10.3 The Riemannian (k — l)n Contact
Model of the Space L^n 254
10.4 The Gravitational and Electromagnetic Fields in L(k)n . 256
10.5 The Generalized Lagrange Spaces
of Order k 260
10.6 Problems 263
11 Subspaces in Higher Order Lagrange Spaces 265
11.1 Submanifolds in OscfcM 265
11.2 Subspaces in the Lagrange Space
of Order k, LSkHl 268
11.3 Induced Nonlinear Connection 270
11.4 The Relative Covariant Derivative 274
11.5 The Gauss Weingarten Formulae 279
11.6 The Gauss Codazzi Equations 282
11.7 Problems 2S4
12 Gauge Theory in the Higher
Order Lagrange Spaces 285
12.1 Gauge Transformations in Principal Bundles 286
12.2 Gauge ^ Osculator Bundles 287
12.3 The Local Representation of Gauge
Transformations 290
12.4 Gauge d Tensor Fields.
Gauge Nonlinear Connections 295
12.5 Gauge iV Linear Connections
and Gauge h and i a Covariant
Derivatives 299
12.6 Einstein Yang Mills Equations 301
12.7 Gauge Invariance of the Lagrangians
of Order fc 304
References 309
Index 331
|
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| isbn | 079234393X |
| language | English |
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| physical | XV, 332 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Kluwer |
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| series | Fundamental theories of physics |
| series2 | Fundamental theories of physics |
| spelling | Miron, Radu Verfasser aut The geometry of higher order Lagrange spaces applications to mechanics and physics by Radu Miron Dordrecht [u.a.] Kluwer 1997 XV, 332 S. txt rdacontent n rdamedia nc rdacarrier Fundamental theories of physics 82 Mathematische Physik Geometry, Differential Lagrange spaces Mathematical physics Mechanics, Analytic Ordnung n (DE-588)4322729-6 gnd rswk-swf Lagrange-Raum (DE-588)4458304-7 gnd rswk-swf Lagrange-Raum (DE-588)4458304-7 s Ordnung n (DE-588)4322729-6 s DE-604 Fundamental theories of physics 82 (DE-604)BV000012461 82 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007789992&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Miron, Radu The geometry of higher order Lagrange spaces applications to mechanics and physics Fundamental theories of physics Mathematische Physik Geometry, Differential Lagrange spaces Mathematical physics Mechanics, Analytic Ordnung n (DE-588)4322729-6 gnd Lagrange-Raum (DE-588)4458304-7 gnd |
| subject_GND | (DE-588)4322729-6 (DE-588)4458304-7 |
| title | The geometry of higher order Lagrange spaces applications to mechanics and physics |
| title_auth | The geometry of higher order Lagrange spaces applications to mechanics and physics |
| title_exact_search | The geometry of higher order Lagrange spaces applications to mechanics and physics |
| title_full | The geometry of higher order Lagrange spaces applications to mechanics and physics by Radu Miron |
| title_fullStr | The geometry of higher order Lagrange spaces applications to mechanics and physics by Radu Miron |
| title_full_unstemmed | The geometry of higher order Lagrange spaces applications to mechanics and physics by Radu Miron |
| title_short | The geometry of higher order Lagrange spaces |
| title_sort | the geometry of higher order lagrange spaces applications to mechanics and physics |
| title_sub | applications to mechanics and physics |
| topic | Mathematische Physik Geometry, Differential Lagrange spaces Mathematical physics Mechanics, Analytic Ordnung n (DE-588)4322729-6 gnd Lagrange-Raum (DE-588)4458304-7 gnd |
| topic_facet | Mathematische Physik Geometry, Differential Lagrange spaces Mathematical physics Mechanics, Analytic Ordnung n Lagrange-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007789992&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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