The three-body problem:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam u.a.
Elsevier
1990
|
| Series: | Studies in astronautics
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 576 S. graph. Darst. |
| ISBN: | 0444874402 044441813X |
Staff View
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| 245 | 1 | 0 | |a The three-body problem |c Christian Marchal |
| 246 | 1 | 3 | |a The three body problem |
| 264 | 1 | |a Amsterdam u.a. |b Elsevier |c 1990 | |
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Record in the Search Index
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| adam_text | IMAGE 1
STUDIES IN ASTRONAUTICS 4
THE THREE-BODY
PROBLEM
CHRISTIAN MARCH AL OFFICE NATIONAL D ETUDES ET DE
RECHERCHESAEROSPATIALES, CHAETILLON, FRANCE
AMSTERDAM - OXFORD - NEW YORK -TOKYO 1990
IMAGE 2
X
CONTENTS
FOREWORD DEDICATION ACKNOWLEDGMENTS SHORT TABLE OF
CONTENTS
CONTENTS
1.SUMMARIES (ENGLISH, FRENCH, RUSSIAN, GERMAN, SPANISH, JAPANESE,
CHINESE, ARABIC) 2 .HISTORY
3.THE LAW OF UNIVERSAL ATTRACTION 4.EXACT FORMULATIONS OF THE THREE-BODY
PROBLEM 4.1.THE CLASSICAL FORMULATION 4.2.THE LAGRANGIAN FORMULATION
4.3.THE JACOBI FORMULATION 4.4.THE HAMILTON AND DELAUNAY FORMULATION
5.THE INVARIANTS IN THE THREE-BODY PROBLEM
5.1.THE TEN CLASSICAL INTEGRALS AND THE LAGRANGE-JACOBI IDENTITY
5.1.1.THE INTEGRAL OF THE CENTER OF MASS 5.1.2.THE INTEGRAL OF ANGULAR
MOMENTUM
5.1.3.THE INTEGRAL OF THE ENERGY 5.1.4.THE LAGRANGE-JACOBI IDENTITY
5.2.THE UNSUCCESSFUL RESEARCHES OF NEW INTEGRALS 5.3.THE SCALE
TRANSFORMATION, THE VARIATIONAL THREE-
BODY PROBLEM AND THE ELEVENTH LOCAL INTEGRAL 5.4.THE INTEGRAL
INVARIANTS 6.EXISTENCE AND UNIQUENESS OF SOLUTIONS. BINARY AND TRIPLE
COLLISIONS. REGULARIZATIONS OF SINGULARITIES 7.FINAL SIMPLIFICATIONS,
THE ELIMINATION OF NODES, THE ELIMINATION OF TIME.
8.SIMPLE SOLUTIONS OF THE THREE-BODY PROBLEM
8.1.THE LAGRANGIAN AND EULERIAN SOLUTIONS. THE CENTRAL CONFIGURATIONS
IMAGE 3
XI
8.2.STABILITY OF EULERIAN AND LAGRANGIAN MOTIONS 44
8.2.1.FIRST-ORDER ANALYSIS 46
8.2.2.COMPLETE ANALYSIS OF STABILITY 50
8.3.THE EULERIAN AND LAGRANGIAN MOTIONS IN NATURE AND IN ASTRONAUTICS 51
8.4.OTHER EXACT SOLUTIONS OF THE THREE-BODY PROBLEM 53
8.4.1.THE ISOCELES SOLUTIONS 53
8.4.2.THE Z-AXIS HILL SOLUTIONS 54
8.5.OTHER SIMPLE SOLUTIONS OF THE THREE-BODY PROBLEM 54
9.THE RESTRICTED THREE-BODY PROBLEM 58
9.1.THE CIRCULAR RESTRICTED THREE-BODY PROBLEM 59
9.2.THE HILL PROBLEM 63
9.2.1.THE BROWN SERIES 64
9.2.2.THE LUNAR MOTION WITHIN 1000 KM 66
9.3.THE ELLIPTIC, PARABOLIC AND HYPERBOLIC RESTRICTED THREE-BODY
PROBLEMS 68
9.4.THE COPENHAGEN PROBLEM AND THE COMPUTATIONS OF MICHEL HENON 71
10.THE GENERAL THREE-BODY PROBLEM. QUANTITATIVE ANALYSIS 79 10.1.THE
ANALYTICAL METHODS 79
10.2.AN EXAMPLE OF THE VON ZEIPEL METHOD. INTEGRATION OF THE THREE-BODY
PROBLEM TO THE FIRST ORDER 81
10.2.1.PRINCIPLE OF THE METHOD OF VON ZEIPEL 83
10.2.2.APPLICATION OF THE METHOD OF VON ZEIPEL TO THE THREE-BODY PROBLEM
84
10.2.3.FIRST-ORDER INTEGRATION OF THE THREE-BODY PROBLEM 87
10.2.4.A CONCRETE PICTURE OF THE WIDE PERTURBATIONS OF THE THREE-BODY
PROBLEM 93
10.2.5 .GENERAL CONSIDERATIONS ON THE FIRST-ORDER INTEGRATION 96
10.3.INTEGRATION OF THE THREE-BODY PROBLEM TO THE SECOND ORDER 98
10.4.THE NUMERICAL METHODS 99
10.4.1.A THREE-BODY MOTION OF THE EXCHANGE TYPE 101
10.4.2.AN OSCILLATORY MOTION OF THE SECOND KIND 103
10.4.3.STUDIES OF GRAVITATIONAL SCATTERING 106
10.5.PERIODIC ORBITS AND NUMERICAL METHODS 118
10.5.1.COMPUTATION OF PERIODIC ORBITS. THE METHOD OF ANALYTIC
CONTINUATION. THE UTMOST REDUCTION OF THE THREE-BODY PROBLEM AND THE
ELIMINATION OF
IMAGE 4
XLL
TRIVIAL SIDE-EFFECTS
10.5.2.THE METHOD OF ANALYTIC CONTINUATION FOR THREE GIVEN MASSES
10.5.3.THE METHOD OF ANALYTIC CONTINUATION AND THE MODIFICATION OF
MASSES 10.6. PER IODIC ORBITS AND SYMMETRY PROPERTIES
10.6.1.THE FOUR TYPES OF SPACE-TIME SYMMETRIES 10.6.2.FAMILIES OF
SYMMETRIC PERIODIC ORBITS 10.7.THE VICINITY AND THE STABILITY OF
PERIODIC ORBITS 10.7.1.DEFINITION AND GENERALITIES
10.7.2.THE EVOLUTION OF IGNORABLE PARAMETERS. THE
ORBITAL STABILITY. THE IN PLANE STABILITY 10.7.3.THE FIRST-ORDER
ANALYSIS
10.7.4.SIMPLE CASES OF THE FIRST-ORDER ANALYSIS 10.7.4.1.RECTILINEAR
PERIODIC ORBITS 10.7.4.2.PLANE PERIODIC ORBITS 10.7.4.3.SYMMETRIC
PERIODIC ORBITS 10.7.4.4.CIRCULAR RESTRICTED CASE AND HILL CASE
10.7.5.FIRST-ORDER STABILITY, THE GENERAL DIS
CUSSION
10.7.6.ON THE EVOLUTION OF FIRST-ORDER STABILITY ALONG THE FAMILIES OF
PERIODIC ORBITS 10.7.7.ELEMENTS OF THE ALL-ORDER STABILITY ANALYSIS. THE
NEAR-RESONANCE THEOREM
10.7.7.1.ANALYTIC AUTONOMOUS DIFFERENTIAL SYSTEMS.
THE VICINITY OF A POINT OF EQUILIBRIUM 10.7 . 7 . 2 . ANALYTIC
DIFFERENTIAL SYSTEMS. THE VICINITY OF A PERIODIC SOLUTION
10.7.7.3.MOT IONS IN THE CENTRAL SUBSET. MOTIONS IN THE CRITICAL CASE.
THE CRITICAL HAMILTONIAN CASE
10.7.7.4.CRITICAL HAMILTONIAN CASE. THE N TH -ORDER
STUDY. THE QUASI-INTEGRALS. GENERALIZATION OF BIRKHOFF DIFFERENTIAL
ROTATIONS 10.7.7.5.THE SIX MAIN TYPES OF STABILITY AND
INSTABILITY
10.7.7.6.A LOWER BOUND OF M FOR A POWER-M INSTA BILITY 10.7.8.TWO
CONJECTURES ON THE STABILITY OR INSTA BILITY OF PERIODIC SOLUTIONS OF
ANALYTIC
HAMILTONIAN SYSTEMS
123
127
134 136 136 141
146 146
149 150 158
158 161 164 166
169
171
174
174
184
194
206
213
216
217
IMAGE 5
10.7.9.ON THE CASES WITH MULTIPLE FLOQUET MULTIPLIERS
OR MULTIPLE EIGENVALUES 221
10.7.10.EXAMPLE . THE ALL-ORDER STABILITY OF LAGRANGIAN MOTIONS 222
10.7.10.1 .THE FIRST ORDER STUDY 224
10.7.10.2.THE SECOND SIMPLIFICATION 225
10.7.10.3.THE QUASI-INTEGRALS I N 227
10.7.10.4.EX TENSION TO THE CIRCULAR LAGRANGIAN MOTIONS OF THE GENERAL
THREE-BODY PRO BLEM 231
10.7.10.5.THE SECOND-ORDER STUDY 237
10.7.10.6.THE THIRD-ORDER STUDY 245
10.8.THE SERIES OF SOME SIMPLE SOLUTIONS OF THE THREEBODY PROBLEM 248
10.8.1.THE PSEUDO-CIRCULAR ORBITS 249
10.8.2.A FAMILY OF PERIODIC ORBITS WITH THE LARGEST
NUMBER OF SYMMETRIES 251
10.8.3.THE HALO ORBITS ABOUT THE COLLINEAR LAGRANGIAN POINTS 257
10.9.EXAMPLES OF NUMERICAL INTEGRATIONS 277
10.9.1.RESEARCHES BY CONTINUITY
THE RETROGRADE PSEUDO-CIRCULAR ORBITS OF THE THREE-BODY PROBLEM WITH
THREE EQUAL MASSES 277
10.9.2.A NUMERICAL EXPERIMENT. THE PYTHAGOREAN PRO BLEM 284
10.9.3.THE METHOD OF NUMERICAL EXPLORATION. ENCOUN TERS OF SATELLITES
291
11.THE GENERAL THREE-BODY PROBLEM. QUALITATIVE ANALYSIS
AND QUALITATIVE METHODS 301
11.1.THE PROTOTYPE OF QUALITATIVE METHODS 301
11.2.THE TRIVIAL TRANSFORMATIONS AND THE CORRESPONDING SYMMETRIES AMONG
N-BODY ORBITS 302
11.2.1.THE SPACE-TIME SYMMETRIES 305
11.2.2.THE SPACE SYMMETRIES 309
11.2.3.THE REMAINING SYMMETRIES 310
11 . 2.4.MULTI-SYMMETRIES 311
11.3.OTHER EARLY QUALITATIVE RESEARCHES 311
11.3.1.THE EULERIAN AND LAGRANGIAN SOLUTIONS. THE CENTRAL CONFIGURATIONS
311
11.3.2.THE RESEARCH OF NEW INTEGRALS OF MOTION 316
11.4.PERIODIC ORBITS. THE METHOD OF POINCARE 317
IMAGE 6
11.4.1.THE THREE FIRST SPECIES OF POINCARE PERIODIC
ORBITS 317
11.4.2.THE POINCARE CONJECTURE 321
5.UNSYMMETRICAL PERIODIC ORBITS. THE BROWN CONJEC TURE 322
6.THE HILL STABILITY AND ITS GENERALIZATION 323
11.6.1.THE GENERALIZED SEMI-MAJOR AXIS , THE GENE RALIZED SEMI-LATUS
RECTUM , THE MEAN QUADRA TIC DISTANCE , THE MEAN HARMONIC DISTANCE
AND THE SUNDMAN FUNCTION 326
11.6.2.THE CLASSICAL RELATIONS AND THE NEW NOTATION 327 11 .
6.3.HILL-TYPE STABILITY IN THE GENERAL THREEBODY PROBLEM 329
11.6.4.SCALE EFFECTS 338
11 . 6 . 5.HILL-TYPE STABILITY FOR SYSTEMS WITH POSITIVE
OR ZERO ENERGY INTEGRAL 339
7.FINAL EVOLUTIONS AND TESTS OF ESCAPE 341
11.7.1.THE NEW NOTATIONS AND THE N-BODY PROBLEM 341
11.7.2.THE CLASSICAL RESULTS AND THE NEW NOTATIONS 344
11.7.3.IMPROVEMENTS - (THREE AND N-BODY MOTIONS) 347
11.7.3. 1 . LIMITATIONS ON THE CONFIGURATION, THE
SCALE, THE ORIENTATION 347
11.7.3.2.ON THE EVOLUTION OF THE SEMI-MOMENT OF INERTIA I AND THE MEAN
QUADRATIC DIS TANCE P 349
11.7.3.3.ON THE EVOLUTION OF THE POTENTIAL U AND
THE MEAN HARMONIC DISTANCE V 358
11.7.3.4.A PSYCHOLOGICAL IMPROVEMENT, THE USE OF
* AND * INSTEAD OF P AND V 361
11.7.4.THE PRINCIPLE OF THE TESTS OF ESCAPE 369
11.7.5.EXAMPLE OF THE CONSTRUCTION OF A TEST OF
ESCAPE FOR THE N-BODY PROBLEM 371
11.7.5.1.SIMPLIFICATION OF THE PROBLEM 372
11.7.5.2.RESEARCH OF LONG-TERM VALID RESULTS 373
11.7.5.3.IMPROVEMENT OF THE EFFICIENCY OF THE TEST. EXTENSION TO THE
GENERAL N-BODY PROBLEM 377
11.7.6.FINAL EVOLUTION : THE SINGULARITIES 383
11.7.6.1.THE TWO TYPES OF SINGULARITY OF THE N-BODY PROBLEM 384
11.7.6.2.IMPOSSIBILITY OF THE INFINITE EXPANSION
IMAGE 7
XV
IN A BOUNDED INTERVAL OF TIME FOR THREEBODY MOTIONS 385
11 . 7 .6.3 . ANALYSIS OF A COLLISION 387
11.7.6.4.COLLISIONS AND CENTRAL CONFIGURATIONS 390 11.7.6.5.ON THE
REGULARIZATION OF SINGULARITIES 396 11.7.7.FINAL EVOLUTIONS. THE CHAZY
CLASSIFICATION OF
THREE-BODY MOTIONS 398
11 . 7 . 7 . 1 . RELATIONS AMONG THE LENGTHS X. THE LIMITS OF THE
VECTORS R- /T 401
*
11.7.7.2.THE HYPERBOLIC FINAL EVOLUTION 403
11.7.7.3.THE HYPERBOLIC-PARABOLIC AND THE HYPERBO LIC-ELLIPTIC FINAL
EVOLUTIONS 404
11.7.7.4.THE TRI-PARABOLIC FINAL EVOLUTION 406
11.7.7.5.THE PARABOLIC-ELLIPTIC FINAL EVOLUTION 408 11.7.7.6.THE BOUNDED
EVOLUTION, THE TWO OSCILLATO RY EVOLUTIONS AND THE COLLISIONS OF STARS
410
11 .7.8.SITNIKOV MOTIONS AND OSCILLATORY EVOLUTIONS OF THE FIRST KIND
419
11.7 .9. GENERAL TABLE OF FINAL EVOLUTIONS 424
11 .7 . 10.PROGRESS IN THE TESTS OF ESCAPE 428
11 . 7 . 10.1.CLASSIFICATION OF TESTS 429
11 . 7 . 10 . 2 . THE ERGODIC THEOREM. THE DIFFICULTY OF A TEST OF
BOUNDED MOTIONS 432
11.7.10.3.A TEST OF ESCAPE VALID EVEN FOR VERY SMALL MUTUAL DISTANCES
436
11.7.10.4.AN APPLICATION OF THE VERY EFFICIENT TEST. ANALYSIS IN THE (P
, P ) HALF-PLANE 454 11.7.10.5.A SURVEY OF RECENT PROGRESS IN TESTS OF
ESCAPE. ANALYSIS OF TRIPLE CLOSE APPRO
ACHES 483
11.8.N-BODY MOTIONS AND COMPLETE COLLAPSES. AN EXTENSION OF THE SUNDMAN
THREE-BODY RESULT 489
11 .9. ORIGINAL AND FINAL EVOLUTIONS 493
11 . 9 . 1 . GENERAL THREE-BODY SYSTEMS OF POSITIVE ENERGY AND NON-ZERO
ANGULAR MOMENTUM 494
11.9.2.GENERAL THREE-BODY SYSTEMS OF POSITIVE ENERGY AND ZERO ANGULAR
MOMENTUM 495
11.9.3.GENERAL THREE-BODY SYSTEMS OF ZERO ENERGY AND NON-ZERO ANGULAR
MOMENTUM 496
11.9.4.GENERAL THREE-BODY SYSTEMS OF ZERO ENERGY AND
IMAGE 8
ZERO ANGULAR MOMENTUM
11.9.5.GENERAL THREE-BODY SYSTEMS OF NEGATIVE ENERGY AND NON-ZERO
ANGULAR MOMENTUM 11 . 9 . 6 . REMAINING CASES. RESTRICTED CASES 11.10.ON
THE KOLMOGOROV-ARNOLD-MOSER THEOREM 11.11.THE ARNOLD DIFFUSION
CONJECTURE.
THE TEMPORARY CHAOTIC MOTIONS. THE TEMPORARY CAPTURE 11.12.AN
APPLICATION OF QUALITATIVE METHODS. THE CONTRO VERSY BETWEEN MRS
KAZIMIRCHAK-POLONSKAYA AND MR R.
DVORAK
11.13.THE LAGRANGIAN AND THE QUALITATIVE METHODS 12.MAIN CONJECTURES AND
FURTHER INVESTIGATIONS CONCLUSIONS APPENDICES
REFERENCES BIBLIOGRAPHY SUBJECT INDEX AUTHOR INDEX
497
499 506 507
509
513 517 519 5 23 5 27
5 47
563
566
570
|
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| id | DE-604.BV004732243 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:16:51Z |
| institution | BVB |
| isbn | 0444874402 044441813X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002910783 |
| oclc_num | 21760060 |
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| owner_facet | DE-384 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-703 DE-355 DE-BY-UBR DE-83 DE-188 |
| physical | XVI, 576 S. graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Elsevier |
| record_format | marc |
| series | Studies in astronautics |
| series2 | Studies in astronautics |
| spelling | Marchal, Christian Verfasser aut The three-body problem Christian Marchal The three body problem Amsterdam u.a. Elsevier 1990 XVI, 576 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in astronautics 4 Mecanica Celeste larpcal Celestial mechanics Three-body problem Dreikörperproblem (DE-588)4012974-3 gnd rswk-swf Dreikörperproblem (DE-588)4012974-3 s DE-604 Studies in astronautics 4 (DE-604)BV001896624 4 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002910783&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marchal, Christian The three-body problem Studies in astronautics Mecanica Celeste larpcal Celestial mechanics Three-body problem Dreikörperproblem (DE-588)4012974-3 gnd |
| subject_GND | (DE-588)4012974-3 |
| title | The three-body problem |
| title_alt | The three body problem |
| title_auth | The three-body problem |
| title_exact_search | The three-body problem |
| title_full | The three-body problem Christian Marchal |
| title_fullStr | The three-body problem Christian Marchal |
| title_full_unstemmed | The three-body problem Christian Marchal |
| title_short | The three-body problem |
| title_sort | the three body problem |
| topic | Mecanica Celeste larpcal Celestial mechanics Three-body problem Dreikörperproblem (DE-588)4012974-3 gnd |
| topic_facet | Mecanica Celeste Celestial mechanics Three-body problem Dreikörperproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002910783&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001896624 |
| work_keys_str_mv | AT marchalchristian thethreebodyproblem |