Dynamics and mission design near libration points: 4 Advanced methods for triangular points
Gespeichert in:
Format: | Buch |
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Sprache: | English |
Veröffentlicht: |
Singapore [u.a.]
World Scientific
2001
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Schriftenreihe: | World Scientific monograph series in mathematics
5 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | X, 262 S. graph. Darst. |
ISBN: | 9810242107 |
Internformat
MARC
LEADER | 00000nam a2200000 cc4500 | ||
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035 | |a (DE-599)BVBBV014085761 | ||
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245 | 1 | 0 | |a Dynamics and mission design near libration points |n 4 |p Advanced methods for triangular points |c G. Gómez ... |
264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2001 | |
300 | |a X, 262 S. |b graph. Darst. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 1 | |a World Scientific monograph series in mathematics |v 5 | |
490 | 0 | |a World Scientific monograph series in mathematics |v ... | |
650 | 7 | |a Estabilidade |2 larpcal | |
650 | 7 | |a Mécanique céleste |2 ram | |
650 | 7 | |a Métodos de perturbação (sistemas dinâmicos) |2 larpcal | |
650 | 7 | |a Problemas de n-corpos |2 larpcal | |
650 | 7 | |a Sistemas dinâmicos |2 larpcal | |
650 | 7 | |a Sistemas hamiltonianos |2 larpcal | |
650 | 4 | |a Lagrangian points | |
650 | 4 | |a Three-body problem | |
700 | 1 | |a Gómez, Gérard |e Sonstige |4 oth | |
773 | 0 | 8 | |w (DE-604)BV014085215 |g 4 |
830 | 0 | |a World Scientific monograph series in mathematics |v 5 |w (DE-604)BV013389881 |9 5 | |
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999 | |a oai:aleph.bib-bvb.de:BVB01-009648864 |
Datensatz im Suchindex
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adam_text | Contents
Preface v
Introduction 1
0.1 Detailed Objectives 1
0.2 Known Results About the Stability of £4,5 1
0.2.1 For the Circular RTBP 1
0.2.2 For the Elliptic RTBP 3
0.2.3 The Bicircular Problem 3
0.2.4 Intermediate Models 4
0.3 Main Difficulties of the Problem 5
Chapter 1 Global Stability Zones Around the Triangular Libration
Points 7
1.1 Equations of Motion 7
1.2 Results for the Restricted Circular Problem 9
1.3 Simulations for the Bicircular Problem 17
1.4 Results for the Simulations Using the JPL Model 38
1.5 Discussion and Tentative Explanations 44
Chapter 2 The Normal Form Around L5 in the Three dimensional
RTBP 47
2.1 Checks of the Normal Form 50
Chapter 3 Normal Form of the Bicircular Model and Related Topics 53
3.1 The Equations of the Bicircular Problem 53
3.2 Expansion of the Hamiltonian 55
3.2.1 Expansions of the Potentials and Recurrences 57
3.3 Cancelling the Terms of Order One 60
3.3.1 Cancelling Order 1 Using the Lie Transformation 61
3.3.2 Cancelling Order 1 by Computing the Periodic Orbit 63
vii
viii Contents
3.3.3 Test of the Results 64
3.4 Normal Form to Order Two 65
3.4.1 Diagonalization of H2(x, y,0) Using Floquet Theorem 66
3.4.2 Practical Implementation of Proposition 3.1 73
3.4.2.1 Case of the Hamiltonian Expanded in Complex Variables 74
3 4.2.2 Case of the Hamiltonian Expanded in Real Variables . 75
3.4.3 Applying the Obtained Change of Variables 78
3.4.4 Second Expansion of the Hamiltonian 79
3.5 Normal Form of Terms of Order Higher than Two 81
3.5.1 The Method 82
3.5.1.1 Selecting ck 84
3.5.2 Implementation 84
3.5.2.1 The Algebraic Manipulator 84
3.5.2.2 The Main Algorithm 85
3.5.3 Results 85
3.5.4 The Change of Variables 86
3.5.5 Going Back to Real Coordinates 86
3.5.5.1 The Hamiltonian 87
3.5.5.2 The Change of Variables 88
3.5.6 Checks of the Software 89
3.6 A Test Concerning the Normal Form Around the Small Periodic Orbit
Near L5 in the Bicircular Problem 89
3.7 On the Computation of Unstable Two dimensional Tori 92
3.7.1 The Equations and the Algorithm 92
3.7.2 Truncated Power Series Results 95
3.7.3 Discussion 99
3.8 Big Tori and Stability Zones 100
3.8.1 An Autonomous Intermediate Vector Field and its Vertical Peri¬
odic Orbits 100
3.8.2 Simulations Around the Periodic Orbits. Region of Stability . . 101
3.8.3 Frequency Analysis 101
Chapter 4 The Quasi periodic Model 111
4.1 The Lagrangian and the Hamiltonian 113
4.2 Some Useful Expansions 115
4.3 The Fourier Analysis 118
Chapter 5 Nominal Paths and Stability Properties 133
5.1 Introduction 133
5.2 Idea of the Resolution Method 134
5.3 The Algebraic Manipulator 136
5.3.1 High Level Routines 136
5.3.1.1 Input/output Routines 136
Contents ix
5.3.1.2 Evaluation of the Function 136
5.3.1.3 Evaluation of the Jacobian Matrix 136
5.3.1.4 The Newton Method 136
5.4 Results with the Algebraic Manipulator 137
5.5 Numerical Refinement 138
5.5.1 The Program 139
5.5.2 Nominal Paths 140
5.6 The Neighbourhood of the Almost Planar Nominal Paths 159
Chapter 6 Transfer to Orbits in a Vicinity of the Lagrangian Pointsl63
6.1 Computations of the Transfer Orbits 165
6.1.1 Looking for Arrival Conditions at the QPO 165
6.1.1.1 Case of the Target Orbits of Section 5.5.2 166
6.1.1.2 Case of the Target Orbits of Section 1.4 166
6.1.2 Computing the Successive Swingbys 168
6.1.3 Departure from the GTO. Change of Inclination 171
6.1.4 Global Optimization of the Transfer 173
6.2 Summary of the Results 174
6.2.1 On the Magnitudes 174
6.2.2 On the Shapes of the Transfer Orbits 194
6.2.2.1 Looking at the Orbits in the Sidereal Frame 194
6.2.2.2 Looking at the Orbits in the Synodic Frame 194
Appendix A Global Stability Zones Around the Triangular Libration
Points in the Elliptic RTBP 213
Appendix B Fourier Analysis 227
B.I Introduction 227
B.2 The Method 228
B.2.1 The DFT of Simple Inputs 228
B.2.2 Several Filterings 232
B.2.3 Determination of the Frequencies: First Approximation 234
B.2.4 An Alternative Method to Compute the Coefficients 234
B.2.5 The Effect of Errors on the Frequencies 235
B.2.6 Determination of the Frequencies: Improvement 236
B.3 An Application to the Analysis of Orbits of the Restricted Problem . . 237
Appendix C Geometrical Bounds for the Dynamics: Codimension 1
Manifolds 241
C.I The Center, Center stable and Center unstable Manifolds 241
C.2 On the Analytic Computation of Invariant Manifolds 242
C.3 The Center stable and Center unstable Manifolds for L3 in the RTBP . 243
x Contents
Appendix D Conclusions 249
D.I Summary of Achievements 249
D.2 On the Methodology 252
D.3 On the Application of the Results to the Design of Spacecraft Missions . 253
D.4 Outlook 253
Bibliography 255
Updates with Respect to the Work Done for the European Space Agency 257
|
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institution | BVB |
isbn | 9810242107 |
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spelling | Dynamics and mission design near libration points 4 Advanced methods for triangular points G. Gómez ... Singapore [u.a.] World Scientific 2001 X, 262 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier World Scientific monograph series in mathematics 5 World Scientific monograph series in mathematics ... Estabilidade larpcal Mécanique céleste ram Métodos de perturbação (sistemas dinâmicos) larpcal Problemas de n-corpos larpcal Sistemas dinâmicos larpcal Sistemas hamiltonianos larpcal Lagrangian points Three-body problem Gómez, Gérard Sonstige oth (DE-604)BV014085215 4 World Scientific monograph series in mathematics 5 (DE-604)BV013389881 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009648864&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Dynamics and mission design near libration points World Scientific monograph series in mathematics Estabilidade larpcal Mécanique céleste ram Métodos de perturbação (sistemas dinâmicos) larpcal Problemas de n-corpos larpcal Sistemas dinâmicos larpcal Sistemas hamiltonianos larpcal Lagrangian points Three-body problem |
title | Dynamics and mission design near libration points |
title_auth | Dynamics and mission design near libration points |
title_exact_search | Dynamics and mission design near libration points |
title_full | Dynamics and mission design near libration points 4 Advanced methods for triangular points G. Gómez ... |
title_fullStr | Dynamics and mission design near libration points 4 Advanced methods for triangular points G. Gómez ... |
title_full_unstemmed | Dynamics and mission design near libration points 4 Advanced methods for triangular points G. Gómez ... |
title_short | Dynamics and mission design near libration points |
title_sort | dynamics and mission design near libration points advanced methods for triangular points |
topic | Estabilidade larpcal Mécanique céleste ram Métodos de perturbação (sistemas dinâmicos) larpcal Problemas de n-corpos larpcal Sistemas dinâmicos larpcal Sistemas hamiltonianos larpcal Lagrangian points Three-body problem |
topic_facet | Estabilidade Mécanique céleste Métodos de perturbação (sistemas dinâmicos) Problemas de n-corpos Sistemas dinâmicos Sistemas hamiltonianos Lagrangian points Three-body problem |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009648864&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV014085215 (DE-604)BV013389881 |
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