Foundations of differential geodesy:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1994
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 373 S. graph. Darst. |
| ISBN: | 3540583041 0387583041 |
Staff View
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| 245 | 1 | 0 | |a Foundations of differential geodesy |c Joseph Zund |
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Record in the Search Index
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| adam_text | Contents
Chapter I Role of Coordinates in Geodesy
and Geometry 1
1 Coordinates in Geodesy and Geometry 1
2 Marussi-Hotine Approach to Geodesy 5
3 Classical Formulations of the Tensor Calculus 15
4 Abstract Notion of a Tensor 26
5 Preview of the Leg Calculus 39
Problems for Chapter I 41
Chapter II Ricci Calculus 45
1 Introduction 45
2 3-Leg Algebra 46
3 Congruences 50
4 Geometry of Congruences 51
5 Ricci Coefficients 53
6 Calculation of Ricci Coefficients 56
7 Commutativity of Leg Derivatives 57
8 Lie Bracket 60
9 Jacobi and Schouten Identities 61
10 Interpretation of Ricci Coefficients 63
11 Miscellaneous Leg Representations 65
12 Lame Equations 67
Problems for Chapter II 70
Chapter III Cartan Calculus 73
1 Introduction 73
2 Exterior Product 74
3 Exterior Differentiation 78
4 Basic Properties of the Exterior Product
and Differentiation 81
5 Cartan’s Viewpoint 83
XIV
6 Structural Equations of Cartan 86
7 Commutators and Schouten Identities 92
8 Cartan Calculus and the Classical Tensor
Calculus 93
9 Coordinates in the Cartan and Ricci Calculus 97
10 Conclusions and Summary 99
Problems for Chapter III 100
Chapter IV General Leg Calculus 105
1 Introduction 105
2 Fundamental Idea of the Leg Calculus 106
3 Identification of the Ricci Coefficients 110
4 Permutation Algorithm 111
5 Interpretation of the Leg Coefficients 113
6 Basic Equations in the Leg Calculus 114
7 Commutators and Lie Brackets 116
8 Laplacian of a Scalar Function 121
9 Lame Equations and Identities 123
10 Coordinates in the Leg Calculus 126
11 Reconstruction Theorem and General
Viewpoint 132
Problems for Chapter IV 136
Chapter V Gaussian Differential Geometry 139
1 Introduction 139
2 The Framework of Gaussian Differential
Geometry 141
3 Gauss Operator and First Basic Form 148
4 Second Basic Form 153
5 Third and Fourth Basic Forms 159
6 Congruence and Surface Eigenstructure
Theorems 161
7 Two Digressions 169
8 Basic Equations of the Surface Leg Calculus 172
9 Frenet Equations 175
10 Meusnier and Bonnet Formulas 178
XV
11 Geodesic Curvature and Torsion in an Arbitrary
Direction, and Euler’s Formula 180
12 Euler’s Osculating Paraboloid and Dupin’s
Indicatrix of Curvature 183
13 Triply-Orthogonal Systems and Dupin’s
Theorem 186
Problems for Chapter V 192
Chapter VI Basic Equations for Differential
Geodesy 197
1 Introduction 197
2 Newtonian Gravitation and the Geopotential
Field 197
3 Marussi Ansatz and the Hotine 3-Leg 200
4 Hotine Leg Calculus and N-Integrability
Conditions 203
5 Marussi Tensor 206
6 Bruns Curvature Equation 211
7 Bruns Equation and Hotine’s Theorem 213
8 n-Integrability Conditions 216
9 The Hotine-Marussi Equations 218
10 3-Dimensional Laplacian of Local Gravity 219
11 2-Dimensional Laplacian of Local Gravity 221
Problems for Chapter VI 223
Chapter VII The Fundamental Theorem of Differential
Geodesy 227
1 Introduction 227
2 Basic Assumptions 227
3 The Fundamental Theorem of Differential
Geodesy 229
4 Discussion 231
5 Extension Problem 232
6 Two Subsidiary Problems 237
7 The Congruence-Forming Property 238
8 The Surface-Forming Property 244
9 Conclusions 250
XVI
Problems for Chapter VII 252
Chapter VIII Algebraic Theory of the Marussi
Tensor 255
1 Introduction 255
2 Eigenstructure of Symmetric Tensors 256
3 Eigenstructure of the Marussi Tensor 261
4 The Singularity Condition 264
5 Conclusions 268
Problems for Chapter VIII 269
Chapter IX Conformal Differential Geodesy 273
1 Introduction 273
2 Fundamental Notions of Conformal Geometry 274
3 Conformal Structural Equations 278
4 Conformal Ricci Coefficients 283
5 Conformal Surface Theory 285
6 Conformal Curve Theory 290
7 Generalized Conformal Transformations 295
8 Conclusions 300
Problems for Chapter IX 302
Chapter X Coordinates in Differential Geodesy 303
1 Introduction 303
2 Marussi Hypothesis and Hotine Problem 304
3 Hotine’s Hierarchy of Local Coordinate Systems 308
4 The Marussi-Hotine Approach: A Critique 319
5 Generalized Marussi-Hotine Approach:
A Proposal 322
6 Conclusion 338
Problems for Chapter X 339
Bibliography 345
Index 363
|
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| spelling | Zund, Joseph Verfasser aut Foundations of differential geodesy Joseph Zund Berlin u.a. Springer 1994 XVI, 373 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Coordination ram Coordonnées (Mathématiques) Espaces généralisés Espaces généralisés ram Géodésie Géodésie - Mathématiques Géodésie - Mathématiques ram Géodésie ram Mathematik Coordinates Generalized spaces Geodesy Geodesy Mathematics Mathematische Geodäsie (DE-588)4275272-3 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Geodäsie (DE-588)4020202-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Geodäsie (DE-588)4020202-1 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Mathematische Geodäsie (DE-588)4275272-3 s HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006504609&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zund, Joseph Foundations of differential geodesy Coordination ram Coordonnées (Mathématiques) Espaces généralisés Espaces généralisés ram Géodésie Géodésie - Mathématiques Géodésie - Mathématiques ram Géodésie ram Mathematik Coordinates Generalized spaces Geodesy Geodesy Mathematics Mathematische Geodäsie (DE-588)4275272-3 gnd Differentialgeometrie (DE-588)4012248-7 gnd Geodäsie (DE-588)4020202-1 gnd |
| subject_GND | (DE-588)4275272-3 (DE-588)4012248-7 (DE-588)4020202-1 (DE-588)4151278-9 |
| title | Foundations of differential geodesy |
| title_auth | Foundations of differential geodesy |
| title_exact_search | Foundations of differential geodesy |
| title_full | Foundations of differential geodesy Joseph Zund |
| title_fullStr | Foundations of differential geodesy Joseph Zund |
| title_full_unstemmed | Foundations of differential geodesy Joseph Zund |
| title_short | Foundations of differential geodesy |
| title_sort | foundations of differential geodesy |
| topic | Coordination ram Coordonnées (Mathématiques) Espaces généralisés Espaces généralisés ram Géodésie Géodésie - Mathématiques Géodésie - Mathématiques ram Géodésie ram Mathematik Coordinates Generalized spaces Geodesy Geodesy Mathematics Mathematische Geodäsie (DE-588)4275272-3 gnd Differentialgeometrie (DE-588)4012248-7 gnd Geodäsie (DE-588)4020202-1 gnd |
| topic_facet | Coordination Coordonnées (Mathématiques) Espaces généralisés Géodésie Géodésie - Mathématiques Mathematik Coordinates Generalized spaces Geodesy Geodesy Mathematics Mathematische Geodäsie Differentialgeometrie Geodäsie Einführung |
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