Stability and chaos in celestial mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
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| Schriftenreihe: | Springer praxis books in astronomy and planetary sciences
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 250 - 256 |
| Beschreibung: | XV, 261 S. graph. Darst. |
| ISBN: | 9783540851455 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | 3.10.2 GYLDEN S PROBLEM 58 TABLE OF CONTENTS PREFACE XI ACKNOWLEDGMENTS
XIV ORDER AND CHAOS 1 1.1 CONTINUOUS AND DISCRETE SYSTEMS 1 1.2 LINEAR
STABILITY 4 1.3 CONSERVATIVE AND DISSIPATIVE SYSTEMS 6 1.4 THE
ATTRACTORS AND BASINS OF ATTRACTION 7 1.5 THE LOGISTIC MAP 9 1.6 THE
STANDARD MAP 12 1.7 THE DISSIPATIVE STANDARD MAP 15 1.8 HENON S MAPPING
17 NUMERICAL DYNAMICAL METHODS 21 2.1 POINCARE MAP 21 2.2 LYAPUNOV
EXPONENTS 23 2.3 THE ATTRACTOR S DIMENSION 25 2.4 TIME SERIES ANALYSIS
26 2.5 FOURIER ANALYSIS 31 2.6 FREQUENCY ANALYSIS 32 2.7 HENON S METHOD
33 2.8 FAST LYAPUNOV INDICATORS 35 KEPLER S PROBLEM 39 3.1 THE MOTION OF
THE BARYCENTER 40 3.2 THE SOLUTION OF KEPLER S PROBLEM 41 3.3 * AND G
SERIES 44 3.4 ELLIPTIC MOTION 44 3.4.1 MEAN AND ECCENTRIC ANOMALY 46
3.4.2 SOLUTION OF KEPLER S EQUATION 48 3.5 PARABOLIC MOTION 49 3.6
HYPERBOLIC MOTION 50 3.7 CLASSIFICATION OF THE ORBITS 51 3.8 SPACECRAFT
TRANSFERS 53 3.9 DELAUNAY VARIABLES 53 3.10 THE TWO-BODY PROBLEM WITH
VARIABLE MASS 57 3.10.1 THE ROCKET EQUATION 57 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/998588970 DIGITALISIERT DURCH VIII TABLE
OF CONTENTS 4 THE THREE*BODY PROBLEM AND THE LAGRANGIAN SOLUTIONS 63 4.1
THE RESTRICTED THREE-BODY PROBLEM 63 4.1.1 THE PLANAR, CIRCULAR,
RESTRICTED THREE-BODY PROBLEM 63 4.1.2 EXPANSION OF THE PERTURBING
FUNCTION 65 4.1.3 THE PLANAR, ELLIPTIC, RESTRICTED THREE-BODY PROBLEM 67
4.1.4 THE INCLINED, CIRCULAR, RESTRICTED THREE-BODY PROBLEM 67 4.2 THE
CIRCULAR, RESTRICTED LAGRANGIAN SOLUTIONS 68 4.3 THE ELLIPTIC,
RESTRICTED LAGRANGIAN SOLUTIONS 73 4.4 THE ELLIPTIC, UNRESTRICTED
TRIANGULAR SOLUTIONS 76 5 ROTATIONAL DYNAMICS 83 5.1 EULER ANGLES 83 5.2
ANDOYER-DEPRIT VARIABLES 85 5.3 FREE RIGID BODY MOTION 87 5.4 PERTURBED
RIGID BODY MOTION 89 5.5 THE SPIN-ORBIT PROBLEM 91 5.5.1 THE
CONSERVATIVE SPIN-ORBIT PROBLEM 91 5.5.2 THE AVERAGED EQUATION 94 5.5.3
THE DISSIPATIVE SPIN-ORBIT PROBLEM 95 5.5.4 THE DISCRETE SPIN-ORBIT
PROBLEM 96 5.6 MOTION AROUND AN OBLATE PRIMARY 97 5.7 INTERACTION
BETWEEN TWO BODIES OF FINITE DIMENSIONS 98 5.8 THE TETHER SATELLITE 99
5.9 THE DUMBBELL SATELLITE 103 6 PERTURBATION THEORY 107 6.1
NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS 107 6.2 CLASSICAL PERTURBATION
THEORY 108 6.2.1 AN EXAMPLE 110 6.2.2 COMPUTATION OF THE PRECESSION OF
THE PERIHELION 112 6.3 RESONANT PERTURBATION THEORY 112 6.3.1 THREE-BODY
RESONANCE 114 6.4 DEGENERATE PERTURBATION THEORY 115 6.4. TABLE OF
CONTENTS IX 7.2.4 TRAPPING DIOPHANTINE NUMBERS 145 7.2.5
COMPUTER-ASSISTED PROOFS 148 7.3 A SURVEY OF KAM RESULTS IN CELESTIAL
MECHANICS 149 7.3.1 ROTATIONAL TORI IN THE SPIN-ORBIT PROBLEM 149 7.3.2
LIBRATIONAL INVARIANT SURFACES IN THE SPIN-ORBIT PROBLEM ... 150 7.3.3
THE SPATIAL PLANETARY THREE-BODY PROBLEM 152 7.3.4 THE CIRCULAR, PLANAR,
RESTRICTED THREE-BODY PROBLEM 153 7.4 GREENE S METHOD FOR THE BREAKDOWN
THRESHOLD 156 7.5 LOW-DIMENSIONAL TORI 160 7.6 A DISSIPATIVE KAM THEOREM
162 7.7 CONVERSE KAM 165 7.7.1 CONJUGATE POINTS CRITERION 168 7.7.2
CONE-CROSSING CRITERION 169 7.7.3 TANGENT ORBIT INDICATOR 170 7.8
CANTORI 173 8 LONG-TIME STABILITY 177 8.1 ARNOLD S DIFFUSION 177 8.2
NEKHOROSHEV S THEOREM 178 8.3 NEKHOROSHEV S ESTIMATES AROUND ELLIPTIC
EQUILIBRIA 182 8.4 EFFECTIVE ESTIMATES IN THE THREE-BODY PROBLEM 183
8.4.1 EXPONENTIAL STABILITY OF A THREE-BODY PROBLEM 183 8.5 EFFECTIVE
STABILITY OF THE LAGRANGIAN POINTS 187 9 DETERMINATION OF PERIODIC
ORBITS 191 9.1 EXISTENCE OF PERIODIC ORBITS 191 9.1.1 EXISTENCE OF
PERIODIC ORBITS (CONSERVATIVE SETTING) 191 9.1.2 COMPUTATION OF THE
LIBRATION IN LONGITUDE 193 9.1.3 EXISTENCE OF PERIODIC ORBITS
(DISSIPATIVE SETTING) 194 9.1.4 NORMAL FORM AROUND A PERIODIC ORBIT 196
9.2 THE LINDSTEDT-POINCARE TECHNIQUE 198 9.3 THE KBM METHOD 199 9. X
TABLE OF CONTENTS 10.3 THE BIRKHOFF REGULARIZATION 222 10.3.1 THE B 3
REGULARIZATION 225 A BASICS OF HAMILTONIAN DYNAMICS 227 A.I THE
HAMILTONIAN SETTING 227 A.2 CANONICAL TRANSFORMATIONS 229 A.3 INTEGRABLE
SYSTEMS 232 A.4 ACTION-ANGLE VARIABLES 233 * THE SPHERE OF INFLUENCE 237
C EXPANSION OF THE PERTURBING FUNCTION 239 D FLOQUET THEORY AND LYAPUNOV
EXPONENTS 241 E THE PLANETARY PROBLEM 243 F YOSHIDA S SYMPLECTIC
INTEGRATOR 245 G ASTRONOMICAL DATA 247 REFERENCES 250 INDEX 257
|
| any_adam_object | 1 |
| author | Celletti, Alessandra |
| author_facet | Celletti, Alessandra |
| author_role | aut |
| author_sort | Celletti, Alessandra |
| author_variant | a c ac |
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| bvnumber | BV025591297 |
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| ctrlnum | (OCoLC)698795890 (DE-599)BVBBV025591297 |
| 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 Geographie |
| format | Book |
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| institution | BVB |
| isbn | 9783540851455 |
| language | English |
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| physical | XV, 261 S. graph. Darst. |
| publishDate | 2010 |
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| publisher | Springer |
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| spelling | Celletti, Alessandra Verfasser aut Stability and chaos in celestial mechanics Alessandra Celletti Berlin [u.a.] Springer 2010 XV, 261 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer praxis books in astronomy and planetary sciences Literaturverz. S. 250 - 256 Chaostheorie (DE-588)4009754-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Himmelsmechanik (DE-588)4127484-2 gnd rswk-swf Himmelsmechanik (DE-588)4127484-2 s Dynamisches System (DE-588)4013396-5 s Chaostheorie (DE-588)4009754-7 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020187666&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Celletti, Alessandra Stability and chaos in celestial mechanics Chaostheorie (DE-588)4009754-7 gnd Dynamisches System (DE-588)4013396-5 gnd Himmelsmechanik (DE-588)4127484-2 gnd |
| subject_GND | (DE-588)4009754-7 (DE-588)4013396-5 (DE-588)4127484-2 |
| title | Stability and chaos in celestial mechanics |
| title_auth | Stability and chaos in celestial mechanics |
| title_exact_search | Stability and chaos in celestial mechanics |
| title_full | Stability and chaos in celestial mechanics Alessandra Celletti |
| title_fullStr | Stability and chaos in celestial mechanics Alessandra Celletti |
| title_full_unstemmed | Stability and chaos in celestial mechanics Alessandra Celletti |
| title_short | Stability and chaos in celestial mechanics |
| title_sort | stability and chaos in celestial mechanics |
| topic | Chaostheorie (DE-588)4009754-7 gnd Dynamisches System (DE-588)4013396-5 gnd Himmelsmechanik (DE-588)4127484-2 gnd |
| topic_facet | Chaostheorie Dynamisches System Himmelsmechanik |
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