Celestial dynamics: chaoticity and dynamics of celestial systems
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH
2013
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026057366&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XI, 309 S. Ill., graph. Darst. 240 mm x 170 mm |
| ISBN: | 9783527409778 9783527651856 9783527651863 9783527651870 |
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MARC
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Record in the Search Index
| _version_ | 1819323896779767808 |
|---|---|
| adam_text | Titel: Celestial dynamics
Autor: Dvorak, Rudolf
Jahr: 2013
VII
Contents
Preface XI
1 Introduction: the Challenge of Science 1
2 Hamiltonian Mechanics 7
2.1 Hamilton s Equations from Hamiltonian Principle 10
2.2 Poisson Brackets 11
2.3 Canonical Transformations 13
2.4 Hamilton-Jacobi Theory 19
2.5 Action-Angle Variables 23
3 Numerical and Analytical Tools 27
3.1 Mappings 27
3.1.1 Simple Examples 28
3.1.1.1 Twist Map 28
3.1.1.2 Logistic Map 29
3.1.1.3 Arnold Cat Map 31
3.1.1.4 Standard Map 33
3.1.1.5 TheCircleMap 35
3.1.1.6 The Dissipative Standard Map 37
3.1.2 Hadjidemetriou Mapping 38
3.2 Lie-Series Numerical Integration 41
3.2.1 A Simple Example 43
3.3 Chaos Indicators 48
3.3.1 Lyapunov Characteristic Exponent 48
3.3.2 Fast Lyapunov Indicator 50
3.3.3 Mean Exponential Growth Factor ofNearby Orbits 50
3.3.4 Smaller Alignment Index 51
3.3.5 Spectral Analysis Method 51
3.4 Perturbation Theory 52
3.4.1 Lie-Transformation Method 55
3.4.2 Mapping method 64
4 The Stability Problem 69
4.1 Review on Different Concepts of Stability 69
VIII I Contents
4.2 Integrable Systems 72
4.3 Nearly Integrable Systems 78
4.4 Resonance Dynamics 80
4.5 KAM Theorem 86
4.6 Nekhoroshev Theorem 91
4.7 The Froeschle-Guzzo-Lega Hamiltonian 99
5 The Two-Body Problem 105
5.1 From Newton to Kepler 106
5.2 Unperturbed Kepler Motion 108
5.3 Classification of Orbits: Ellipses, Hyperbolae and Parabolae 110
5.4 Kepler Equation 112
5.5 Complex Description 115
5.5.1 The KS-Transformation 117
5.6 Motion in Space and the Keplerian Elements 118
5.7 Astronomical Determination ofthe Gravitational Constant 120
5.8 Solution ofthe Kepler Equation 120
6 The Restricted Three-Body Problem 123
6.1 Set-Up and Formulation 124
6.2 Equilibria ofthe System 127
6.3 Motion Close to I4 and I5 131
6.4 Motion Close to Li, I2, I3 134
6.5 Potential and the Zero Velocity Curves 136
6.6 Spatial Restricted Three-Body Problem 141
6.7 Tisserand Criterion 144
6.8 Elliptic Restricted Three-Body Problem 145
6.9 Dissipative Restricted Three-Body Problem 146
7 The Sitnikov Problem 149
7.1 Circular Case: the MacMillan Problem 150
7.1.1 Qualitative Estimates 150
7.2 Motion ofthe Planet off the z-Axes 153
7.3 Elliptic Case 157
7.3.1 Numerical Results 158
7.3.1.1 The Unstable Center 164
7.3.2 Analytical Results 165
7.3.2.1 Analytical Solution ofthe Sitnikov Problem 166
7.3.2.2 The Linearized Solution 167
7.3.2.3 Linear Stability 170
7.3.2.4 Nonlinear Solution 172
7.4 The Vrabec Mapping 176
7.5 General Sitnikov Problem 180
7.5.1 Qualitative Estimates 180
7.5.2 Phase Space Structure 182
Contents IIX
8 Planetary Theory 185
8.1 Planetary Perturbation Theory 185
8.1.1 A Simple Example 185
8.1.2 Principlesof Planetary Theory 187
8.1.3 The Integration Constants - the Osculating Elements 190
8.1.4 First-Order Perturbation 191
8.1.5 Second-Order Perturbation 192
8.2 Equations of Motion for n Bodies 194
8.2.1 The Virial Theorem 195
8.2.2 Reduction to Heliocentric Coordinates 196
8.3 Lagrange Equations ofthe Planetary n-Body Problem 198
8.3.1 Legendre Polynomials 198
8.3.2 Delaunay Elements 200
8.4 The Perturbing Function in Elliptic Orbital Elements 203
8.5 Explicit First-Order Planetary Theory for the Osculating Elements 207
8.5.1 Perturbation ofthe Mean Longitude 209
8.6 Small Divisors 211
8.7 Long-Term Evolution of Our Planetary System 213
9 Resonances 215
9.1 Mean Motion Resonances in Our Planetary System 215
9.1.1 The 13 : 8 Resonance between Venus and Earth 215
9.1.2 The 1 : 1 Mean Motion Resonance: Trojan Asteroids 218
9.2 Method of Laplace-Lagrange 223
9.3 Secular Resonances 231
9.3.1 Asteroids with Small Inclinations and Eccentricities 231
9.3.2 Comets and Asteroids with Large Inclinations and Eccentricities: the
Kozai Resonance 236
9.4 Three-Body Resonances 239
9.4.1 Asteroids in Three-Body Resonances 239
9.4.2 Three Massive Celestial Bodies in Three-Body Resonances 240
9.4.3 Application to the Galilean Satellites 245
10 Lunar Theory 249
10.1 Hill s Lunar Theory 250
10.1.1 Periodic Motion 255
10.2 Classical Lunar Theory 261
10.2.1 Secular Part: Motion ofthe Nodes and the Perihelion 263
10.3 Principal Inequalities 264
10.3.1 The Variation 265
10.3.2 The Evection 267
10.3.3 Annual Equation, Parallactic Inequality and Principal Perturbation in
Latitude 268
X | Contents
11 Concluding Remarks 271
Appendix A Important Persons in the Field 277
Appendix B Formulae 281
B.l Hansen Coefficients 281
B.2 Laplace Coefficients 283
B.3 Bessel Functions 284
B.4 Expansions in the Two-Body Problem 289
Acknowledgement 293
References 295
Index 305
|
| any_adam_object | 1 |
| author | Dvorak, Rudolf 1946- Lhotka, Christoph 1978- |
| author_GND | (DE-588)110054652 (DE-588)1034830996 |
| author_facet | Dvorak, Rudolf 1946- Lhotka, Christoph 1978- |
| author_role | aut aut |
| author_sort | Dvorak, Rudolf 1946- |
| author_variant | r d rd c l cl |
| building | Verbundindex |
| bvnumber | BV041080567 |
| classification_rvk | US 1200 |
| ctrlnum | (OCoLC)845210917 (DE-599)DNB1025271955 |
| 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 |
| format | Book |
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| id | DE-604.BV041080567 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:30:19Z |
| institution | BVB |
| isbn | 9783527409778 9783527651856 9783527651863 9783527651870 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026057366 |
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| owner_facet | DE-19 DE-BY-UBM DE-703 DE-83 |
| physical | XI, 309 S. Ill., graph. Darst. 240 mm x 170 mm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Wiley-VCH |
| record_format | marc |
| spellingShingle | Dvorak, Rudolf 1946- Lhotka, Christoph 1978- Celestial dynamics chaoticity and dynamics of celestial systems Himmelsmechanik (DE-588)4127484-2 gnd |
| subject_GND | (DE-588)4127484-2 (DE-588)4123623-3 |
| title | Celestial dynamics chaoticity and dynamics of celestial systems |
| title_auth | Celestial dynamics chaoticity and dynamics of celestial systems |
| title_exact_search | Celestial dynamics chaoticity and dynamics of celestial systems |
| title_full | Celestial dynamics chaoticity and dynamics of celestial systems Rudolf Dvorak and Christoph Lhotka |
| title_fullStr | Celestial dynamics chaoticity and dynamics of celestial systems Rudolf Dvorak and Christoph Lhotka |
| title_full_unstemmed | Celestial dynamics chaoticity and dynamics of celestial systems Rudolf Dvorak and Christoph Lhotka |
| title_short | Celestial dynamics |
| title_sort | celestial dynamics chaoticity and dynamics of celestial systems |
| title_sub | chaoticity and dynamics of celestial systems |
| topic | Himmelsmechanik (DE-588)4127484-2 gnd |
| topic_facet | Himmelsmechanik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026057366&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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