Integrable systems in celestial mechanics
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| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Boston u. a.
Birkhäuser
2008
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| Schriftenreihe: | Progress in mathematical physics
51 |
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| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Integrable systems in celestial mechanics |c Diarmuid Ó Mathúna |
| 264 | 1 | |a Boston u. a. |b Birkhäuser |c 2008 | |
| 300 | |a X, 234 S. |b graph. Darst. | ||
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| 650 | 0 | 7 | |a Himmelsmechanik |0 (DE-588)4127484-2 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1819660689703174144 |
|---|---|
| adam_text | Titel: Integrable systems in celestial mechanics
Autor: Ó Mathúna, Diarmuid
Jahr: 2008
Contents
Preface............................................................ ix
0 General Introduction............................................... 1
1 Lagrangian Mechanics..............................................21
1 Lagrangian Systems............................................... 21
2 Ignorable Coordinates............................................. 22
3 Separable Systems................................................. 24
4 Liouville Systems.................................................. 26
2 The Kepler Problem................................................29
1 Features of the Ellipse: Geometry and Analysis..................... 29
2 The Two-Body Problem............................................ 33
3 The Kepler Problem: Vectorial Treatment.......................... 35
4 The Kepler Problem: Lagrangian Analysis.......................... 41
3 The Euler Problem I — Planar Case................................. 49
1 The Gravitational Field of Two Fixed Centers: Planar Case.......... 49
2 The Lagrangian in Liouville Form: The Energy Integral.............. 51
3 The First Integrals in Liouville Coordinates ........................ 53
4 The First Integrals in Spheroidal Coordinates ...................... 54
5 Reduction of the Equations: The Regularizing Variable............. 56
6 Some Particular Cases............................................. 58
7 Analysis of the Generic Equation .................................. 62
8 The Equation for S = cosa: Specification of A...................... 65
9 The Equation for R................................................ 77
10 The Time-Angle Relation .......................................... 88
11 The Complementary Range........................................ 93
12 The Singular Case: C = 0........................................... 98
13 Summary of the Orbit Solutions ................................... 105
4 The Euler Problem II — Three-dimensional Case ....................113
1 The Gravitational Field of Two Fixed Centers: General Case ........ 113
2 The Ignorable Coordinate: Liouville s Form and the Energy Integral. 115
viii Contents
3 The First Integrals in Liouville Coordinates ........................ 118
4 The First Integrals in Spheroidal Coordinates...................... 119
5 Reduction of Equations: The Regularization........................ 120
6 Normalization of the Quarries..................................... 121
7 The cr-equation in the Case ß = 0.................................. 123
8 The R-equation.................................................... 125
9 The Integration of the Third (Longitude) Coordinate ............... 133
10 The Time-Angle Relation .......................................... 142
5 The Earth Satellite — General Analysis..............................143
1 The Geopotential and the Density Distribution..................... 143
2 The Vinti Potential ................................................ 147
3 The Vinti Dynamical Problem...................................... 150
4 The Integration of the Lagrangian Equations....................... 153
5 Reduction of the Equations; Regularization; Normalization......... 155
6 The a -Equation: Definition of A ................................... 157
7 The R-Equation.................................................... 159
8 The Integration of the cp-Coordinate............................... 172
9 The Time-Angle Relation .......................................... 182
6 The Earth Satellite — Some Special Orbits...........................193
1 Orbits in the Near Equatorial Band................................. 193
2 The Equatorial Orbit............................................... 196
3 The Polar Orbit.................................................... 199
4 The Critical Inclination.......................................... 205
Appendix: Calculation and Exhibition of Orbits;
The Time-Angle Relation...........................................211
1 Orbits in Chapter 3................................................ 213
2 Orbits in Chapters 5 and 6......................................... 214
3 The Time-Angle Relation .......................................... 215
4 Orbits Derived from Given Initial Conditions in Chapter 3.......... 216
References............................................................227
Index.................................................................231
|
| any_adam_object | 1 |
| author | Ó Mathúna, Diarmuid |
| author_facet | Ó Mathúna, Diarmuid |
| author_role | aut |
| author_sort | Ó Mathúna, Diarmuid |
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| bvnumber | BV035055387 |
| callnumber-first | Q - Science |
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| callnumber-subject | QB - Astronomy |
| classification_rvk | SK 950 US 1200 |
| ctrlnum | (OCoLC)72655605 (DE-599)BVBBV035055387 |
| dewey-full | 521 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 521 - Celestial mechanics |
| dewey-raw | 521 |
| dewey-search | 521 |
| dewey-sort | 3521 |
| dewey-tens | 520 - Astronomy and allied sciences |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV035055387 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T21:12:37Z |
| institution | BVB |
| isbn | 9780817645953 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016723984 |
| oclc_num | 72655605 |
| open_access_boolean | |
| owner | DE-384 |
| owner_facet | DE-384 |
| physical | X, 234 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematical physics |
| series2 | Progress in mathematical physics |
| spellingShingle | Ó Mathúna, Diarmuid Integrable systems in celestial mechanics Progress in mathematical physics Celestial mechanics Two-body problem Integrables System (DE-588)4114032-1 gnd Himmelsmechanik (DE-588)4127484-2 gnd |
| subject_GND | (DE-588)4114032-1 (DE-588)4127484-2 |
| title | Integrable systems in celestial mechanics |
| title_auth | Integrable systems in celestial mechanics |
| title_exact_search | Integrable systems in celestial mechanics |
| title_full | Integrable systems in celestial mechanics Diarmuid Ó Mathúna |
| title_fullStr | Integrable systems in celestial mechanics Diarmuid Ó Mathúna |
| title_full_unstemmed | Integrable systems in celestial mechanics Diarmuid Ó Mathúna |
| title_short | Integrable systems in celestial mechanics |
| title_sort | integrable systems in celestial mechanics |
| topic | Celestial mechanics Two-body problem Integrables System (DE-588)4114032-1 gnd Himmelsmechanik (DE-588)4127484-2 gnd |
| topic_facet | Celestial mechanics Two-body problem Integrables System Himmelsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016723984&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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