Orbits: 2nd order singularity-free solutions
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2013
|
| Edition: | 2.ed. |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XXIII, 426 S. graph. Darst. |
| ISBN: | 3642327923 9783642327926 |
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Record in the Search Index
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| adam_text |
CONTENTS
1 INTRODUCTION 1
2 COORDINATE AND TIME SYSTEMS 5
2.1 GEOCENTRIC EARTH-FIXED COORDINATE SYSTEMS 5
2.2 COORDINATE SYSTEM TRANSFORMATIONS 8
2.3 LOCAL COORDINATE SYSTEM 10
2.4 EARTH-CENTRED INERTIAL COORDINATE SYSTEM 12
2.4.1 PRECESSION 13
2.4.2 NUTATION 13
2.4.3 EARTH ROTATION 15
2.4.4 POLAR MOTION 15
2.5 IAU 2000 FRAMEWORK 16
2.6 GEOCENTRIC ECLIPTIC INERTIAL COORDINATE SYSTEM 20
2.7 SATELLITE FIXED COORDINATE SYSTEM 21
2.8 TIME SYSTEMS 24
3 KEPLERIAN ORBITS 27
3.1 KEPLERIAN MOTION 27
3.2 SATELLITE MOTION IN THE ORBITAL PLANE 30
3.3 THE KEPLERIAN EQUATION 33
3.4 STATE VECTOR OF THE SATELLITE 36
4 PERTURBATIONS ON THE ORBITS 39
4.1 PERTURBED EQUATION OF SATELLITE MOTION 39
4.1.1 LAGRANGIAN PERTURBED EQUATION OF SATELLITE MOTION 40
4.1.2 GAUSSIAN PERTURBED EQUATION OF SATELLITE MOTION 43
4.2 PERTURBATION FORCES OF SATELLITE MOTION 46
4.2.1 PERTURBATION OF THE EARTH'S GRAVITATIONAL FIELD 46
4.2.2 PERTURBATION OF THE SUN AND THE MOON AS WELL AS
PLANETS 51
4.2.3 EARTH TIDE AND OCEAN TIDE PERTURBATIONS 52
4.2.4 SOLAR RADIATION PRESSURE 58
XVII
HTTP://D-NB.INFO/1024510069
XVIII CONTENTS
4.2.5 ATMOSPHERIC DRAG 63
4.2.6 ADDITIONAL PERTURBATIONS 66
4.2.7 ORDER ESTIMATIONS OF PERTURBATIONS 68
5 SOLUTIONS OF C
2
O PERTURBATION 69
5.1 C
2
O
PERTURBED EQUATIONS OF MOTION 69
5.2 SOLUTIONS OF
C
2
O
PERTURBED ORBIT 72
5.3 PROPERTIES OF THE SOLUTIONS OF C
2
O PERTURBATIONS 82
5.4 ORBIT CORRECTION 83
6 SOLUTIONS OF GEOPOTENTIAL PERTURBATIONS 87
6.1 INTRODUCTION 87
6.2 PRINCIPLE OF THE DERIVATIONS 88
6.3 SINGULARITY-FREE BASIC LAGRANGIAN EQUATIONS OF MOTION 93
6.4 SIMPLIFYING ALGORITHMS 94
6.5 SOLUTIONS OF GEOPOTENTIAL DISTURBANCE 97
6.5.1 SOLUTIONS OF D20 PERTURBATION 100
6.5.2 SOLUTIONS OF D
2
\ PERTURBATION 102
6.5.3 SOLUTIONS OF D
22
PERTURBATION 105
6.5.4 SOLUTIONS OF D30 PERTURBATION 109
6.5.5 SOLUTIONS OF D
3
I
PERTURBATION ILL
6.5.6 SOLUTIONS OF D32 PERTURBATION 116
6.5.7 SOLUTIONS OF 33
PERTURBATION 124
6.5.8 SOLUTIONS OF D
40
PERTURBATION 134
6.5.9 SOLUTIONS OF 4I PERTURBATION 137
6.5.10 SOLUTIONS OF D
42
PERTURBATION 145
6.5.11 SOLUTIONS OF
43
~ )
88
PERTURBATIONS 159
6.6 PROPERTIES OF THE SOLUTIONS OF GEOPOTENTIAL PERTURBATIONS 159
6.6.1 LONG TERM PERTURBATIONS 159
6.6.2 LONG AND SHORT PERIODIC PERTURBATIONS 159
7 SOLUTIONS OF EXTRATERRESTRIAL DISTURBANCES 161
7.1 ANALYTICAL SOLUTION OF SATELLITE ORBIT DISTURBED BY SOLAR RADIATION
PRESSURE 161
7.1.1 INTRODUCTION 161
7.1.2 DISTURBING FORCE OF SOLAR RADIATION PRESSURE 162
7.1.3 BASIC GAUSSIAN EQUATIONS OF MOTION 165
7.1.4 EXPANSIONS OF SOLAR RADIATION PRESSURE FORCE . .' 168
7.1.5 SOLUTIONS OF THE DISTURBED EQUATIONS 169
7.1.6 LONG PERIODIC AND SECULAR SOLUTIONS 171
7.1.7 MORE PRECISE SOLUTIONS 173
7.1.8 SUMMARY 183
7.2 DISCRETE SOLUTION OF SATELLITE ORBIT DISTURBED BY SOLAR RADIATION
PRESSURE 183
7.2.1 THREE APPROXIMATIONS 183
7.2.2 DISCRETIZATION AND SOLUTION 184
7.2.3 PROPERTIES OF THE SOLUTION 185
CONTENTS XIX
7.3 ANALYTICAL SOLUTION OF SATELLITE ORBIT DISTURBED BY
ATMOSPHERIC DRAG 186
7.3.1 INTRODUCTION 186
7.3.2 DISTURBING FORCE OF ATMOSPHERIC DRAG 187
7.3.3 BASIC GAUSSIAN EQUATIONS AND EXPANSIONS OF ATMOSPHERIC
DRAG FORCE 189
7.3.4 SHORT PERIODIC SOLUTIONS 192
7.3.5 LONG PERIODIC AND SECULAR SOLUTIONS 198
7.3.6 SUMMARY 199
7.4 DISCRETE SOLUTIONS OF DISTURBANCE OF ATMOSPHERIC DRAG 200
7.5 ANALYTICAL SOLUTIONS OF SATELLITE ORBIT DISTURBED BY LUNAR AND
SOLAR AS WELL AS PLANETARY GRAVITATIONS 201
7.5.1 INTRODUCTION 202
7.5.2 POTENTIAL FUNCTIONS OF THE LUNAR AND SOLAR GRAVITATIONAL
FORCES 202
7.5.3 DISTURBED EQUATIONS OF MOTION AND SOLUTIONS OF THE FIRST
TERM 205
7.5.4 SOLUTIONS OF THE SECOND TERM 209
7.5.5 SOLUTIONS OF THE THIRD TERM 215
7.5.6 SOLUTIONS OF THE FOURTH TERM 222
7.5.7 SUMMARY 224
7.6 EPHEMERIS OF THE MOON, THE SUN AND PLANETS 224
8 NUMERICAL ORBIT DETERMINATION 229
8.1 PRINCIPLE OF GPS PRECISE ORBIT DETERMINATION 229
8.1.1 ALGEBRAIC SOLUTION OF THE VARIATION EQUATION 231
8.2 NUMERICAL INTEGRATION AND INTERPOLATION ALGORITHMS 233
8.2.1 RUNGE-KUTTA ALGORITHMS 233
8.2.2 ADAMS ALGORITHMS 238
8.2.3 COWELL ALGORITHMS 241
8.2.4 MIXED ALGORITHMS AND DISCUSSIONS 243
8.2.5 INTERPOLATION ALGORITHMS 244
8.3 ORBIT-RELATED PARTIAL DERIVATIVES 246
8.3.1 GEOPOTENTIAL DISTURBING FORCE 247
8.3.2 PERTURBATION FORCES OF THE SUN AND THE MOON AS WELL AS
PLANETS 250
8.3.3 TIDAL DISTURBING FORCES 251
8.3.4 SOLAR RADIATION PRESSURE 254
8.3.5 ATMOSPHERIC DRAG 256
9 ANALYTICAL ORBIT DETERMINATION 259
9.1 PRINCIPLE OF ANALYTICAL ORBIT DETERMINATION 259
9.2 REAL TIME ABILITY OF ANALYTICAL ORBIT DETERMINATION 261
9.2.1 LIMITATIONS OF THE NUMERICAL ORBIT DETERMINATION 261
9.2.2 REAL TIME ABILITY OF ANALYTICAL ORBIT DETERMINATION . 262
XX
CONTENTS
9.3 ALGORITHMS OF ANALYTICAL ORBIT DETERMINATION 262
9.3.1 INITIAL TIME SELECTION 262
9.3.2 SINES AND COSINES CURVE TABLES 262
9.3.3 INITIAL TIME DEALING 262
9.3.4 SUMMATION OF THE GEOPOTENTIAL DISTURBANCES 263
9.3.5 SUMMATION OF THE MULTI-BODY DISTURBANCES 263
9.3.6 SOLAR RADIATION DISTURBANCES 264
9.3.7 ATMOSPHERIC DRAG DISTURBANCES 264
10 SINGULARITY-FREE THEORY AND DISCUSSIONS 265
10.1 SINGULARITY-FREE ORBIT THEORY OF XU 2008/2010 265
10.1.1 PROBLEM OF SINGULARITY OF THE SOLUTIONS 265
10.1.2 DISTURBED EQUATIONS IN THE CASE OF CIRCULAR ORBIT. . . . 266
10.1.3 DISTURBED EQUATIONS IN THE CASE OF EQUATORIAL ORBIT. . . 267
10.1.4 DISTURBED EQUATIONS IN THE CASE OF CIRCULAR AND
EQUATORIAL ORBIT 267
10.1.5 SINGULARITY-FREE LAGRANGIAN EQUATIONS OF MOTION . . . . 268
10.1.6 SIMPLIFIED SINGULARITY-FREE LAGRANGIAN EQUATIONS . . . . 269
10.1.7 SINGULARITY-FREE GAUSSIAN EQUATIONS OF MOTION 269
10.2 ON THE SINGULARITY PROBLEM IN ORBITAL MECHANICS 270
10.2.1 INTRODUCTION 270
10.2.2 BASIC LAGRANGIAN AND GAUSSIAN EQUATIONS OF MOTION . 271
10.2.3 ALGORITHM FOR SOLVING SINGULARITY PROBLEM 275
10.2.4 APPLICATION 1: SOLUTIONS OF THE SOLAR OBLATENESS
DISTURBANCE 282
10.2.5 APPLICATION 2: SOLUTIONS OF THE SOLAR RADIATION PRESSURE
DISTURBANCE 285
10.2.6 PROBLEMS OF THE CRITICAL INCLINATION 287
10.2.7 PROBLEMS OF TRADITIONAL SINGULARITY-FREE VARIABLES . . . 287
10.2.8 SUMMARY 288
10.3 SUMMARY OF SINGULARITY-FREE THEORY 288
10.3.1 LAGRANGE-XU EQUATIONS OF SATELLITE MOTION 288
10.3.2 GAUSS-XU EQUATIONS OF SATELLITE MOTION 293
10.3.3 SINGULARITY-FREE SOLUTIONS OF ALL DISTURBANCES OF THE 2ND
ORDER 296
10.4 EQUATIONS OF MOTION IN NON-LNERTIAL FRAME 297
10.5 DISCUSSIONS 298
10.5.1 CONFUSION OF NON CONSERVATIVE FORCE WITH CONSERVATIVE
EFFECT 298
10.5.2 LONG TERM EFFECTS IN EXTRATERRESTRIAL DISTURBANCES . . . 298
10.5.3 FURTHER STUDIES 298
11 ORBIT IN SOLAR GRAVITY FIELD 299
11.1 SOLAR OBLATENESS AND MERCURY'S PERIHELION PRECESSION 299
11.1.1 INTRODUCTION 300
11.1.2 DISTURBING FUNCTION OF SOLAR OBLATENESS AND DISTURBED
EQUATIONS OF MOTION 300
CONTENTS XXI
11.1.3 SOLUTIONS FOR OBLATENESS DISTURBANCE 303
11.1.4 SUMMARY 312
11.2 ON ORBITAL DISTURBING EFFECTS OF THE SOLAR RADIATION 312
11.2.1 INTRODUCTION 313
11.2.2 DISTURBING FORCE OF SOLAR RADIATION PRESSURE 313
11.2.3 GAUSSIAN EQUATIONS OF PLANET MOTION 314
11.2.4 SOLUTIONS OF THE DISTURBED EQUATIONS 315
11.2.5 A MODIFICATION OF THE KEPLERIAN THIRD LAW 317
11.2.6 COMPARISON WITH THE RESULT OF TRADITIONAL MASS
CORRECTION 318
11.2.7 THE FOCI OF THE ORBITAL ELLIPSE 318
11.2.8 THE GEOMETRIC RELATIONSHIP BETWEEN THE TWO FOCI. 319
11.2.9 CONCLUSIONS OF ABOVE DISCUSSION AND DERIVATION . . . 321
11.2.10 A CLASS OF NON-KEPLERIAN ORBITS 322
11.2.11 SUMMARY 322
APPENDIX
1:
IAU
1980
THEORY OF NUTATION 325
APPENDIX 2: SOLUTIONS OF GEOPOTENTIAL
D
43
~
Z)
88
PERTURBATIONS 329
REFERENCES 409
INDEX 423 |
| any_adam_object | 1 |
| author | Xu, Guochang Xu, Jia |
| author_GND | (DE-588)14217162X |
| author_facet | Xu, Guochang Xu, Jia |
| author_role | aut aut |
| author_sort | Xu, Guochang |
| author_variant | g x gx j x jx |
| building | Verbundindex |
| bvnumber | BV041185574 |
| classification_rvk | US 1250 ZI 9120 |
| ctrlnum | (OCoLC)861220072 (DE-599)DNB1024510069 |
| dewey-full | 629.4113 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 629 - Other branches of engineering |
| dewey-raw | 629.4113 |
| dewey-search | 629.4113 |
| dewey-sort | 3629.4113 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik Geologie / Paläontologie Bauingenieurwesen Verkehr / Transport |
| edition | 2.ed. |
| format | Book |
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| id | DE-604.BV041185574 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T00:49:33Z |
| institution | BVB |
| isbn | 3642327923 9783642327926 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026160760 |
| oclc_num | 861220072 |
| open_access_boolean | |
| owner | DE-11 DE-83 |
| owner_facet | DE-11 DE-83 |
| physical | XXIII, 426 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| spelling | Xu, Guochang Verfasser aut Orbits 2nd order singularity-free solutions Guochang Xu ; Jia Xu 2.ed. Berlin [u.a.] Springer 2013 XXIII, 426 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Umlaufbahn (DE-588)4238276-2 gnd rswk-swf Satellit (DE-588)4136498-3 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Satellit (DE-588)4136498-3 s Umlaufbahn (DE-588)4238276-2 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Xu, Jia Verfasser (DE-588)14217162X aut Erscheint auch als Online-Ausgabe 978-3-642-32793-3 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4091101&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026160760&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Xu, Guochang Xu, Jia Orbits 2nd order singularity-free solutions Umlaufbahn (DE-588)4238276-2 gnd Satellit (DE-588)4136498-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4238276-2 (DE-588)4136498-3 (DE-588)4114528-8 |
| title | Orbits 2nd order singularity-free solutions |
| title_auth | Orbits 2nd order singularity-free solutions |
| title_exact_search | Orbits 2nd order singularity-free solutions |
| title_full | Orbits 2nd order singularity-free solutions Guochang Xu ; Jia Xu |
| title_fullStr | Orbits 2nd order singularity-free solutions Guochang Xu ; Jia Xu |
| title_full_unstemmed | Orbits 2nd order singularity-free solutions Guochang Xu ; Jia Xu |
| title_short | Orbits |
| title_sort | orbits 2nd order singularity free solutions |
| title_sub | 2nd order singularity-free solutions |
| topic | Umlaufbahn (DE-588)4238276-2 gnd Satellit (DE-588)4136498-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Umlaufbahn Satellit Mathematisches Modell |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4091101&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026160760&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT xuguochang orbits2ndordersingularityfreesolutions AT xujia orbits2ndordersingularityfreesolutions |