Regularization in orbital mechanics: theory and practice
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
[2017]
|
| Schriftenreihe: | De Gruyter Studies in Mathematical Physics
volume 42 |
| Schlagworte: | |
| Online-Zugang: | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110558555&searchTitles=true Inhaltsverzeichnis |
| Beschreibung: | XV, 403 Seiten Illustrationen, Diagramme |
| ISBN: | 9783110558555 3110558556 |
Internformat
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| 245 | 1 | 0 | |a Regularization in orbital mechanics |b theory and practice |c Javier Roa |
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| 264 | 1 | |a Berlin |b De Gruyter |c [2017] | |
| 264 | 4 | |c © 2017 | |
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Datensatz im Suchindex
| _version_ | 1804177885871734784 |
|---|---|
| adam_text | CONTENTS
FOREWORD* VII
1 INTRODUCTION. CURRENT CHALLENGES IN SPACE EXPLORATION * 1
1.1 ACCESSIBLE SPACE * 1
1.2 DISTRIBUTED SPACE SYSTEMS * 3
1.3 EFFICIENT ORBIT TRANSFERS * 4
1.3.1 LOW-THRUST MISSIONS * 5
1.3.2 SOLAR SAILING * 6
1.3.3 GRAVITY-ASSIST TRAJECTORIES * 6
1.4 ORBIT PROPAGATION * 7
1.5 THE AIM OF THE PRESENT BOOK * 9
PART I: REGULARIZATION
2 THEORETICAL ASPECTS OF REGULARIZATION * 13
2.1 WHY BOTHER? * 14
2.2 THE SUNDMAN TRANSFORMATION
-----
17
2.2.1 GENERALIZED SUNDMAN TRANSFORMATION * 19
2.2.2 TIME TRANSFORMATIONS IN W-BODY SYSTEMS * 22
2.3 STABILIZATION OF THE EQUATIONS OF MOTION * 24
2.4 LINEARIZATION
-----
27
2.4.1 LEVI-CIVITA VARIABLES * 28
2.4.2 CARTESIAN COORDINATES * 30
2.4.3 UNIVERSAL SOLUTIONS * 31
2.5 SETS OF ORBITAL ELEMENTS * 33
2.6 CANONICAL TRANSFORMATIONS * 37
2.7 GAUGE FREEDOM IN CELESTIAL MECHANICS * 42
2.8 CONCLUSIONS
-----
45
3 THE KUSTAANHEIMO-STIEFEL SPACE AND THE HOPF FI BRAT ION * 47
3.1 THE NEED FOR AN EXTRA DIMENSION: FIBRATIONS OF HYPERSPHERES
3.2 THE KS TRANSFORMATION AS A HOPF MAP * 51
3.2.1 DEFINING THE FIBERS * 52
3.2.2 THE VELOCITY AND THE BILINEAR RELATION * 54
3.2.3 THE TWO-BODY PROBLEM * 55
3.2.4 THE INVERSE MAPPING* 56
3.3 STABILITY IN KS SPACE * 57
3.3.1 A CENTRAL THEOREM * 58
3.3.2
3.3.3
3.3.4
3.3.5
3.4
3.4.1
3.4.2
3.5
3.5.1
3.5.2
3.6
3.6.1
3.6.2
3.7
3.7.1
3.7.2
3.8
4
4.1
4.2
4.2.1
4.2.2
4.2.3
4.3
4.4
4.5
4.6
4.7
5
5.1
5.1.1
5.1.2
5.2
5.3
5.3.1
5.3.2
5.4
5.5
5.6
5.6.1
THE FUNDAMENTAL MANIFOLD F
-----
59
FIXED POINTS, LIM IT CYCLES, AND ATTRACTORS * 59
RELATIVE DYNAMICS AND SYNCHRONISM * 60
STABILITY OF THE FUNDAMENTAL MANIFOLD
-----
61
ORDER AND CHAOS
-----
63
THE ^-S E P A RA TIO N
-----
64
TOPOLOGICAL STABILITY
-----
65
TOPOLOGICAL STABILITY IN N -BODY PROBLEMS
-----
66
THE PYTHAGOREAN THREE-BODY PROBLEM
-----
67
FIELD STARS INTERACTING WITH A STELLAR BINARY * 69
GAUGE-GENERALIZED ELEMENTS IN KS SPACE
-----
72
NATURAL SETS OF ELEMENTS: GEOMETRICAL INTERPRETATION * 72
GAUGE FREEDOM IN KS SPACE * 78
ORTHOGONAL BASES * 80
BASIS ATTACHED TO THE FIBER
-----
80
CROSS PRODUCT * 81
CONCLUSIONS
-----
82
THE DROMO FORMULATION * 84
HANSEN IDEAL FRAMES
-----
85
DROMO
-----
86
THE ECCENTRICITY VECTOR * 88
THE ORBITAL PLANE
-----
89
EVOLUTION EQUATIONS
-----
90
IMPROVED PERFORMANCE * 92
VARIATIONAL EQUATIONS AND THE NONCANONICITY OF DROMO * 95
GAUGE-GENERALIZED DROMO FORMULATION * 97
SINGULARITIES * 98
CONCLUSIONS
-----
99
DEDICATED FORMULATION: PROPAGATING HYPERBOLIC ORBITS * 101
ORBITAL M OTION
-----
103
THE ECCENTRICITY VECTOR
-----
104
THE HYPERBOLIC ANOMALY * 107
HYPERBOLIC ROTATIONS AND THE LORENTZ GROUP
-----
108
VARIATION OF PARAMETERS * 109
THE NEW INDEPENDENT VARIABLE * 109
EVOLUTION EQUATIONS
-----
113
ORBITAL PLANE DYNAMICS
-----
115
TIME ELEMENT
-----
116
NUMERICAL EVALUATION
-----
119
HYPERBOLIC COMETS
-----
120
5.6.2 GEOCENTRIC FLYBYS * 123
5.7 CONCLUSIONS
------
126
6 EVALUATING THE NUMERICAL PERFORMANCE * 127
6.1 IMPLEMENTATION * 128
6.1.1 FORCE MODELS * 128
6.1.2 FORMULATIONS * 129
6.1.3 NUMERICAL INTEGRATION * 131
6.1.4 VARIATIONAL EQUATIONS * 131
6.2 EVALUATING THE PERFORMANCE * 132
6.2.1 PROBLEM 1
-----
133
6.2.2 PROBLEM 2
-----
137
6.3 CONCLUSIONS * 140
PART II: APPLICATIONS
7 THE THEORY OF ASYNCHRONOUS RELATIVE MOTION * 143
7.1 DEFINITION OF THE PROBLEM
-----
146
7.2 SYNCHRONISM IN RELATIVE MOTION
-----
146
7.2.1 TIME-SYNCHRONOUS APPROACH
-----
148
7.2.2 ASYNCHRONOUS APPROACH
-----
148
7.2.3 A SIMPLE EXAMPLE
-----
153
7.2.4 IMPROVING THE ACCURACY WITH SECOND-ORDER CORRECTIONS OF THE TIME
DELAY
-----
155
7.3 GENERALIZING THE TRANSFORMATION * 157
7.3.1 THE TIME DELAY USING EQUINOCTIAL ORBITAL ELEMENTS
-----
157
7.3.2 CONNECTION WITH THE TIME-SYNCHRONOUS SOLUTION * 161
7.4 THE CIRCULAR CASE * 162
7.4.1 SECOND-ORDER CORRECTION
-----
164
7.5 NUMERICAL EVALUATION
-----
165
7.5.1 KEPLERIAN MOTION * 166
7.5.2 PERTURBED MOTION
-----
167
7.6 CONCLUSIONS
-----
171
8 UNIVERSAL AND REGULAR SOLUTIONS TO RELATIVE MOTION * 172
8.1 RELATIVE MOTION IN DROMO VARIABLES * 174
8.2 RELATIVE MOTION IN SPERLING-BURDET VARIABLES * 177
8.3 RELATIVE MOTION IN KUSTAANHEIMO-STIEFEL VARIABLES------181
8.3.1 SUMMARY
------
183
8.4 ON THE FICTITIOUS TIM E
-----
183
8.5 NUMERICAL EXAMPLES * 184
8.6 GENERIC PROPAGATION OF THE VARIATIONAL EQUATIONS * 189
8.6.1 INITIALIZINGTHE INDEPENDENT VARIABLE * 191
8.6.2 THE TIME ELEMENT * 192
8.7 CONCLUSIONS
-----
194
9 GENERALIZED LOGARITHMIC SPIRALS: A NEW ANALYTIC SOLUTION WITH
CONTINUOUS
THRUST * 195
9.1 THE EQUATIONS OF MOTION. FIRST INTEGRALS * 198
9.1.1 THE EQUATION OF THE ENERGY * 200
9.1.2 THE EQUATION OF THE ANGULAR MOMENTUM * 201
9.1.3 THE FLIGHT DIRECTION ANGLE T J J
-----
202
9.1.4 THE FUNDAMENTAL THEOREM OF CURVES * 203
9.1.5 FAMILIES OF SOLUTIONS * 205
9.1.6 FORM OF THE SOLUTION * 206
9.2 ELLIPTIC SPIRALS (KI 0) * 207
9.2.1 THE TRAJECTORY * 208
9.2.2 THE TIME OF FLIG H T
-----
210
9.3 PARABOLIC SPIRALS (K I
= 0) * 211
9.3.1 THE TRAJECTORY * 212
9.3.2 THE TIME OF FLIGHT * 213
9.4 HYPERBOLIC SPIRALS (K I 0) * 213
9.4.1 TYPE I HYPERBOLIC SPIRALS
-----
215
9.4.2 TYPE II HYPERBOLIC SPIRALS * 217
9.4.3 TRANSITION BETWEEN TYPE I AND TYPE II SPIRALS * 220
9.5 SUMMARY * 222
9.6 OSCULATING ELEMENTS * 222
9.7 IN-ORBIT DEPARTURE POINT * 225
9.8 PRACTICAL CONSIDERATIONS * 228
9.9 CONTINUITY OF THE SOLUTION * 229
9.9.1 ELLIPTIC TO PARABOLIC * 230
9.9.2 HYPERBOLIC TO PARABOLIC * 230
9.9.3 ASYMPTOTIC LIMIT FROM TYPE I HYPERBOLIC SPIRALS * 230
9.9.4 ASYMPTOTIC LIM IT FROM TYPE II HYPERBOLIC SPIRALS * 231
9.10 CONCLUSIONS * 231
10 LAMBERT*S PROBLEM WITH GENERALIZED LOGARITHMIC SPIRALS * 233
10.1 INTRODUCTION TO LAMBERT*S PROBLEM * 233
10.2 CONTROLLED GENERALIZED LOGARITHMIC SPIRALS * 235
10.3 THE TWO-POINT BOUNDARY-VALUE PROBLEM * 239
10.3.1 THE MINIMUM-ENERGY SPIRAL * 240
10.3.2 CONJUGATE SPIRALS * 242
10.3.3 FAMILIES OF SOLUTIONS * 242
10.3.4 THE THRUST ACCELERATION * 245
10.3.5 THE AV DUE TO THE THRUST
-----
247
10.3.6 THE LOCUS OF VELOCITIES * 247
10.4 FIXING THE TIME OF FLIGHT * 248
10.5 REPETITIVE TRANSFERS * 250
10.6 EVALUATING THE PERFORMANCE * 252
10.7 ADDITIONAL PROPERTIES * 254
10.8 ADDITIONAL DYNAMICAL CONSTRAINTS * 255
10.8.1 ARRIVAL CONDITIONS * 256
10.8.2 RADIUS
-----
256
10.8.3 ECCENTRICITY * 257
10.8.4 SEMIMAJOR AXIS * 258
10.8.5 PERIAPSIS AND APOAPSIS RADII * 258
10.9 CONCLUSIONS * 259
11 LOW-THRUST TRAJECTORY DESIGN WITH CONTROLLED GENERALIZED LOGARITHMIC
SPIRALS
* 261
11.1 ORBIT TRANSFERS * 262
11.1.1 BITANGENT TRANSFERS * 262
11.1.2 TRANSFERS BETWEEN ARBITRARY ORBITS. INTRODUCING COAST ARCS * 266
11.1.3 EXISTENCE OF SOLUTIONS. THE ADMISSIBLE REGION * 270
11.1.4 CONTROLLING THE TIME OF FLIGHT * 271
11.2 PERIODIC ORBITS * 272
11.2.1 COAXIAL SOLUTIONS * 272
11.2.2 GENERIC PERIODIC ORBITS * 273
11.3 MULTINODE TRANSFERS * 275
11.4 THREE-DIMENSIONAL MOTION * 276
11.4.1 THE THRUST ACCELERATION * 280
11.4.2 MODELING THE OUT-OF-PLANE MOTION * 280
11.4.3 TRANSFERS BETWEEN ARBITRARY ORBITS * 285
11.5 APPLICATIONS
-----
286
11.5.1 SIMPLIFIED MODEL
-----
287
11.5.2 REAL EPHEMERIS * 290
11.6 CONCLUSIONS * 292
12 NONCONSERVATIVE EXTENSION OF KEPLERIAN INTEGRALS AND NEW FAMILIES OF
ORBITS
* 293
12.1 THE ROLE OF FIRST INTEGRALS * 293
12.2 DYNAMICS * 296
12.2.1 SIMILARITY TRANSFORMATION * 297
12.2.2 INTEGRALS OF MOTION AND DYNAMICAL SYMMETRIES * 298
12.2.3 PROPERTIES OF THE SIMILARITY TRANSFORMATION * 301
12.2.4 SOLVABILITY * 302
12.3 CASE Y = 1: CONIC SECTIONS * 303
12.4 CASE Y = 2: GENERALIZED LOGARITHMIC SPIRALS * 304
12.5 CASE Y = 3: GENERALIZED CARDIOIDS
-----
304
12.5.1 ELLIPTIC MOTION
-----
304
12.5.2 PARABOLIC MOTION: THE CARDIOID * 306
12.5.3 HYPERBOLIC MOTION
-----
306
12.6 CASE Y = 4: GENERALIZED SINUSOIDAL SPIRALS * 310
12.6.1 ELLIPTIC MOTION * 311
12.6.2 PARABOLIC MOTION: SINUSOIDAL SPIRAL (OFF-CENTER CIRCLE) * 313
12.6.3 HYPERBOLIC MOTION * 314
12.7 SUMMARY* 316
12.8 UNIFIED SOLUTION IN WEIERSTRASSIAN FORMALISM * 316
12.9 PHYSICAL DISCUSSION OF THE SOLUTIONS * 318
12.9.1 CONNECTION WITH SCHWARZSCHILD GEODESICS * 318
12.9.2 NEWTON*S THEOREM OF REVOLVING ORBITS------320
12.9.3 GEOMETRIEALAND PHYSICAL RELATIONS
---
321
12.10 CONCLUSIONS
-----
322
13 CONCLUSIONS
* 324
PART III: APPENDICES
A HYPERCOMPLEX NUMBERS * 329
A .L COMPLEX AND HYPERBOLIC NUMBERS
------
330
A.1.1 THE MODULUS
------
331
A .L.2 THE GEOMETRY OF TWO-DIMENSIONAL HYPERCOMPLEX NUMBERS * 332
A .L.3 ANGLES AND ROTATIONS
------
332
A.2 QUATERNIONS * 333
A.2.1 ROTATIONS IN E 3
------
334
A.2.2 QUATERNION DYNAMICS * 334
B FORMULATIONS IN PERFORM * 336
C STUMPFF FUNCTIONS * 339
D INVERSE TRANSFORMATIONS * 343
D.L INVERSE TRANSFORMATIONS IN EQUINOCTIAL VARIABLES * 343
D.1.1 ASYNCHRONOUS CASE * 343
D .L.2 SYNCHRONOUS CASE * 344
D.2 CARTESIAN TO DROMO * 345
D. 3 LINEAR FORM OF THE HOPF FIBRATION
-----
346
E ELLIPTIC INTEGRALS AND ELLIPTIC FUNCTIONS * 348
E. L PROPERTIES AND PRACTICAL RELATIONS * 349
E.1.1 RECIPROCAL-MODULUS TRANSFORMATION * 349
E .L.2 IMAGINARY-ARGUMENT TRANSFORMATION * 350
E .L.3 IMAGINARY-MODULUS TRANSFORMATION * 350
E.2 IMPLEMENTATION * 350
E.2.1 INTRINSIC FUNCTIONS * 350
E.2.2 APPROXIMATION
-----
352
E.3 JACOBI ELLIPTIC FUNCTIONS * 352
E. 4 WEIERSTRASS ELLIPTIC FUNCTIONS * 354
F CONTROLLED GENERALIZED LOGARITHMIC SPIRALS * 356
F. L ELLIPTIC SPIRALS------357
F.1.1 THE TIME OF FLIG H T
-----
359
F.2 PARABOLIC SPIRALS
-----
359
F.2.1 THE TIME OF FLIGHT * 360
F.3 HYPERBOLIC SPIRALS * 361
F.3.1 HYPERBOLIC SPIRALS OF TYPE I
-----
361
F.3.2 HYPERBOLIC SPIRALS OF TYPE II
-----
362
F.3.3 LIMIT CASE K 2 = 2(1 - $)
-----
364
F.4 OSCULATING ELEMENTS * 365
G DYNAMICS IN SEIFFERT*S SPHERICAL SPIRALS * 366
6.1 DYNAMICS
-----
366
6.1.1 THE ACCELERATED TWO-BODY PROBLEM * 368
6.1.2 INTEGRALS OF MOTION * 370
6.1.3 THE OSCULATING ORB IT
-----
371
6.2 THE GEOMETRY OF SEIFFERT*S SPHERICAL SPIRALS * 372
6.3 GROUNDTRACKS
-----
374
6.4 RELATIVE MOTION BETWEEN SEIFFERT*S SPIRALS * 376
6.5 THE SIGNIFICANCE OF SEIFFERT*S SPIRALS * 377
LIST OF FIGURES
-----
379
BIBLIOGRAPHY * 383
INDEX * 399
|
| any_adam_object | 1 |
| author | Roa, Javier |
| author_facet | Roa, Javier |
| author_role | aut |
| author_sort | Roa, Javier |
| author_variant | j r jr |
| building | Verbundindex |
| bvnumber | BV044532970 |
| classification_rvk | US 1200 |
| ctrlnum | (OCoLC)1011409116 (DE-599)DNB1135494916 |
| dewey-full | 530 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530 |
| dewey-search | 530 |
| dewey-sort | 3530 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV044532970 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:55:11Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110558555 3110558556 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029932209 |
| oclc_num | 1011409116 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM |
| owner_facet | DE-19 DE-BY-UBM |
| physical | XV, 403 Seiten Illustrationen, Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter Studies in Mathematical Physics |
| series2 | De Gruyter Studies in Mathematical Physics |
| spelling | Roa, Javier Verfasser aut Regularization in orbital mechanics theory and practice Javier Roa 201710 Berlin De Gruyter [2017] © 2017 XV, 403 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematical Physics volume 42 Himmelsmechanik (DE-588)4127484-2 gnd rswk-swf Regularisierungsverfahren (DE-588)4846428-4 gnd rswk-swf Umlaufbahn (DE-588)4238276-2 gnd rswk-swf Umlaufbahn Raumfahrt Himmelsmechanik Umlaufbahn (DE-588)4238276-2 s Himmelsmechanik (DE-588)4127484-2 s Regularisierungsverfahren (DE-588)4846428-4 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-055912-5 Erscheint auch als Online-Ausgabe, ePub 978-3-11-055862-3 De Gruyter Studies in Mathematical Physics volume 42 (DE-604)BV040141722 42 X:MVB http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110558555&searchTitles=true DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029932209&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roa, Javier Regularization in orbital mechanics theory and practice De Gruyter Studies in Mathematical Physics Himmelsmechanik (DE-588)4127484-2 gnd Regularisierungsverfahren (DE-588)4846428-4 gnd Umlaufbahn (DE-588)4238276-2 gnd |
| subject_GND | (DE-588)4127484-2 (DE-588)4846428-4 (DE-588)4238276-2 |
| title | Regularization in orbital mechanics theory and practice |
| title_auth | Regularization in orbital mechanics theory and practice |
| title_exact_search | Regularization in orbital mechanics theory and practice |
| title_full | Regularization in orbital mechanics theory and practice Javier Roa |
| title_fullStr | Regularization in orbital mechanics theory and practice Javier Roa |
| title_full_unstemmed | Regularization in orbital mechanics theory and practice Javier Roa |
| title_short | Regularization in orbital mechanics |
| title_sort | regularization in orbital mechanics theory and practice |
| title_sub | theory and practice |
| topic | Himmelsmechanik (DE-588)4127484-2 gnd Regularisierungsverfahren (DE-588)4846428-4 gnd Umlaufbahn (DE-588)4238276-2 gnd |
| topic_facet | Himmelsmechanik Regularisierungsverfahren Umlaufbahn |
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| volume_link | (DE-604)BV040141722 |
| work_keys_str_mv | AT roajavier regularizationinorbitalmechanicstheoryandpractice AT walterdegruytergmbhcokg regularizationinorbitalmechanicstheoryandpractice |