Verfügbarkeit: Hamiltonian perturbation solutions for spacecraft orbit prediction

Hamiltonian perturbation solutions for spacecraft orbit prediction: the method of lie transforms

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Bibliographische Detailangaben
1. Verfasser:	Lara, Martín (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin ; Boston De Gruyter [2021]
Schriftenreihe:	De Gruyter studies in mathematical physics Volume 54
Schlagworte:	Hamilton-Jacobi-Differentialgleichung Störungstheorie Umlaufbahn
Online-Zugang:	https://www.degruyter.com/books/9783110667226 Inhaltsverzeichnis
Beschreibung:	XIV, 377 Seiten Illustrationen 24 cm x 17 cm
ISBN:	9783110667226 3110667223

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MARC


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245	1	0	\|a Hamiltonian perturbation solutions for spacecraft orbit prediction \|b the method of lie transforms \|c Martín Lara
264		1	\|a Berlin ; Boston \|b De Gruyter \|c [2021]
300			\|a XIV, 377 Seiten \|b Illustrationen \|c 24 cm x 17 cm
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337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
490	1		\|a De Gruyter studies in mathematical physics \|v Volume 54
653			\|a Hamilton-Jacobi-Differentialgleichung
653			\|a Störungstheorie
653			\|a Umlaufbahn
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Datensatz im Suchindex

_version_	1804182468245323776
adam_text	CONTENTS PREFACE - V 1 1.1 1.2 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6 1.3 1.3.1 1.3.2 1.3.3 1.3.4 1.3.5 INTRODUCTION - 1 PERTURBED INTEGRABLE PROBLEMS - 2 ARTIFICIAL SATELLITE THEORY - 5 SIGNIFICANCE OF LYAPUNOV INSTABILITY - 7 GEOPOTENTIAL LONG-PERIOD EFFECTS IN CLOSED FORM - 8 TESSERAL EFFECTS - 10 LUNISOLAR PERTURBATIONS - 12 NON-CONSERVATIVE PERTURBATIONS - 14 ACTION-ANGLE AND NON-SINGULAR VARIABLES - 16 NON-EARTH ORBITS AND PERTURBED NON-KEPLERIAN ORBITS - 18 THE RESTRICTED THREE-BODY PROBLEM - 18 HILL PROBLEM SIMPLIFICATIONS - 19 MOTION ABOUT PLANETARY SATELLITES - 21 LIBRATION POINTS ORBITS - 22 COORBITAL MOTION WITH LOW ECCENTRICITY - 24 PART 1: HAMILTONIAN PERTURBATIONS BY LIE TRANSFORMS 2 2.1 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5 2.2 2.2.1 2.2.2 2.2.3 THE METHOD OF LIE TRANSFORMS - 29 LIE TRANSFORMATION OF A FUNCTION - 29 THE FUNDAMENTAL RECURSION - 31 DEPRIT S TRIANGLE - 33 THE DIRECT TRANSFORMATION - 34 COMPOSITION OF LIE TRANSFORMATIONS ---- 35 THE INVERSE TRANSFORMATION - 36 DEPRIT S PERTURBATIONS APPROACH - 37 HAMILTONIAN SIMPLIFICATION BY LIE TRANSFORMS - 37 EXAMPLE: SMALL OSCILLATIONS OF THE SIMPLE PENDULUM - 39 THE HOMOLOGICAL EQUATION - 42 3 3.1 3.1.1 3.1.2 3.1.3 3.2 3.2.1 APPLICATION TO INTEGRABLE PROBLEMS - 45 THE SIMPLE GRAVITY PENDULUM - 46 HAMILTONIAN REDUCTION - 46 ROTATION REGIME. SOLUTION IN ACTION-ANGLE VARIABLES - 48 EXPANDED SOLUTION BY LIE TRANSFORMS - 50 THE FREE RIGID BODY - 52 ROTATION IN THE BODY FRAME - 53 X CONTENTS 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 ATTITUDE IN THE SPACE FRAME - 55 THE INVARIABLE PLANE ---- 56 HAMILTONIAN FORMULATION - 58 CLOSED-FORM SOLUTION BY COMPLETE REDUCTION - 59 THE CASE OF LOW TRIAXIALITY - 65 SHORT-AXIS-MODE ROTATION ---- 67 PART II: PERTURBED ELLIPTIC MOTION: ARTIFICIAL SATELLITE THEORY 4 4.1 4.2 4.3 4.4 4.5 4.5.1 4.5.2 4.5.3 4.5.4 THE KEPLER PROBLEM - 77 THE ORBITAL FRAME - 77 KEPLER HAMILTONIAN - 78 HAMILTON-JACOBI REDUCTION - 80 SOLUTION IN DELAUNAY VARIABLES - 83 USEFUL RELATIONS FOR PERTURBED KEPLERIAN MOTION - 86 THE APSIDAL FRAME. FUNDAMENTAL VECTORS - 86 VARIATION EQUATIONS IN VECTORIAL ELEMENTS - 87 DIFFERENTIAL RELATIONS AND CLOSED-FORM INTEGRATION - 88 PRINCIPAL RELATIONS OF THE ELLIPSE - 90 5 5.1 5.2 5.3 5.3.1 5.3.2 5.4 5.4.1 5.4.2 5.4.3 5.5 5.6 5.6.1 5.6.2 5.6.3 5.6.4 5.7 5.7.1 5.7.2 THE MAIN PROBLEM OF THE ARTIFICIAL SATELLITE - 92 GEOPOTENTIAL HAMILTONIAN - 92 PARTICULAR SOLUTIONS - 94 SECULAR EFFECTS - 95 PICARD ITERATIONS - 97 INCLINATION RESONANCES - 99 INTERMEDIARIES - 100 COMMON INTERMEDIARIES - 101 NATURAL INTERMEDIARIES - 102 TORSIONS FOR QUASI-KEPLERIAN SYSTEMS - 105 DISCRETIZATION OF THE FLOW - 106 THE CRITICAL INCLINATION - 110 FIRST ORDER - 110 SECOND ORDER - 111 THE REDUCED PHASE SPACE. FROZEN ORBITS - 113 REDUCED DYNAMICS ON THE SPHERE - 116 SEMI-ANALYTICAL INTEGRATION - 119 SHORT-PERIOD CORRECTIONS IN DELAUNAY VARIABLES - 120 SHORT-PERIOD CORRECTIONS IN NON-SINGULAR VARIABLES - 121 6 ZONAL PERTURBATIONS - 124 CONTENTS - XI 6.1 ZONAL PROBLEM IN MEAN ELEMENTS - 124 6.1.1 AVERAGED FLOW ---- 127 6.1.2 INCLINATION-ECCENTRICITY DIAGRAMS OF FROZEN ORBITS - 129 6.1.3 LOCAL DYNAMICS: ECCENTRICITY-VECTOR DIAGRAMS - 131 6.2 HAMILTONIAN SIMPLIFICATION - 133 6.2.1 DEPRIT S ELIMINATION OF THE PARALLAX - 134 6.2.2 DELAUNAY NORMALIZATION - 137 6.2.3 SHORT-PERIOD CORRECTIONS - 139 6.3 BROUWER S SOLUTION BY COMPLETE REDUCTION - 141 6.3.1 SECULAR TERMS - 141 6.3.2 LONG-PERIOD CORRECTIONS ---- 143 6.4 REVERSE NORMALIZATION. LONG PERIODS REMOVED FIRST - 144 6.4.1 NORMALIZATION OF THE TOTAL ANGULAR MOMENTUM - 145 6.4.2 NORMALIZATION OF THE SEMIMAJOR AXIS - 149 6.4.3 ALFRIEND AND COFFEY S ELIMINATION OF THE PERIGEE - 151 6.5 HIGHER ORDERS OF THE PERTURBATION SOLUTION. A TEST CASE - 153 6.5.1 PRELIMINARY SIMPLIFICATION. ELIMINATION OF THE PARALLAX - 154 6.5.2 PARTIAL NORMALIZATION. LONG-PERIOD ELIMINATION - 156 6.5.3 COMPLETE HAMILTONIAN REDUCTION. SHORT-PERIOD ELIMINATION - 159 6.5.4 SECULAR FREQUENCIES - 162 6.5.5 SAMPLE APPLICATION. THE PRISMA ORBIT ---- 165 6.6 INITIALIZATION ISSUES. BREAKWELL AND VAGNERS APPROACH - 173 6.7 CENTERED ELEMENTS - 174 7 TESSERAL PERTURBATIONS - 176 7.1 TESSERAL POTENTIAL IN ORBITAL ELEMENTS - 176 7.2 LOW-EARTH ORBITS. GARFINKEL S PERTURBATION APPROACH - 177 7.2.1 ELIMINATION OF THE PARALLAX OF TESSERAL TERMS - 178 7.2.2 DELAUNAY NORMALIZATION, M-DAILY TERMS - 180 7.2.3 ELIMINATION OF THE NODE. LONG-TERM HAMILTONIAN - 182 7.3 EXACT INTEGRATION TO THE SECOND ORDER OF/ 2 ---- 183 7.4 RELEGATION OF TESSERAL EFFECTS - 186 7.4.1 BASIC ALGORITHM ---- 186 7.4.2 TESSERAL RELEGATION WITH LOW ECCENTRICITY - 187 7.4.3 SAMPLE APPLICATIONS - 189 7.5 TESSERAL RESONANCES - 193 7.5.1 RESONANT TERMS OF THE GEOPOTENTIAL - 194 7.5.2 SHORT-PERIOD ELIMINATION ----- 196 7.5.3 THE 2:1 RESONANCE. GPS ORBITS ---- 199 7.5.4 THE 5:3 RESONANCE. GALILEO DISPOSAL ORBITS ---- 201 8 LUNISOLAR PERTURBATIONS - 203 XII - CONTENTS 8.1 8.1.1 8.1.2 8.2 8.2.1 8.2.2 8.2.3 8.3 8.3.1 8.3.2 8.4 8.4.1 8.4.2 8.4.3 8.4.4 8.5 8.5.1 8.5.2 8.5.3 THE THIRD-BODY POTENTIAL - 203 EXPANSION OF THE POTENTIAL FOR A CLOSE-EARTH SATELLITE - 204 THE DISTURBING POTENTIAL IN THE APSIDAL FRAME - 205 LONG-TERM MOTION. THE EXTENDED PHASE SPACE - 206 SHORT-PERIOD ELIMINATION BY LIE TRANSFORMS - 207 AVERAGED FLOW IN VECTORIAL ELEMENTS - 208 SAMPLE APPLICATION. THE CASE OF HIGH EARTH ORBITS - 211 THIRD-BODY S MEAN ANOMALY AVERAGING - 213 MOON AND SUN DISTURBING EFFECTS - 214 ADDITIONAL SIMPLIFICATIONS. LONG-TERM HAMILTONIAN - 217 PERTURBATIONS IN THE ECLIPTIC FRAME - 219 THE DISTURBING POTENTIAL - 220 REMOVING SHORT-PERIOD EFFECTS - 221 REMOVING MONTHLY AND ANNUAL EFFECTS - 224 ELIMINATION OF THE MOON S LONGITUDE OF THE NODE - 226 KUDIELKA S BALANCED ORBITS - 227 THE MANIFOLD OF CIRCULAR ORBITS - 229 THE MANIFOLD OF POLAR ORBITS ORTHOGONAL TO THE EQUINOX - 232 OTHER EQUILIBRIA - 234 9 9.1 9.1.1 9.1.2 9.1.3 9.1.4 9.1.5 9.1.6 9.2 9.2.1 9.2.2 9.2.3 9.2.4 NON-CONSERVATIVE EFFECTS - 235 SOLAR-RADIATION PRESSURE - 235 THE DISTURBING SRP POTENTIAL - 236 HAMILTONIAN SHORT-PERIOD REDUCTION IN THE SYNODIC FRAME - 236 PARTICULAR SOLUTIONS - 238 GENERAL SOLUTION IN VECTORIAL ELEMENTS - 239 COMPLETE HAMILTONIAN REDUCTION IN ACTION-ANGLE VARIABLES - 241 SHORT-PERIOD REDUCTION IN THE EQUATORIAL FRAME - 242 ATMOSPHERIC DRAG - 243 ATMOSPHERIC DENSITY - 243 ROTATING ATMOSPHERE - 244 GAUSS EQUATIONS OF VARIATION - 245 PERTURBATION EQUATIONS - 247 PART III: RELATIVE MOTION AND PERTURBED NON-KEPLERIAN MOTION 10 10.1 10.1.1 10.1.2 10.1.3 THE HILL PROBLEM ---- 253 THE CIRCULAR RESTRICTED THREE-BODY PROBLEM ---- 253 SYNODIC FRAME. THE JACOBI INTEGRAL ---- 254 HAMILTONIAN FORMULATION ---- 255 SURFACES AND CURVES OF ZERO VELOCITY - 256 CONTENTS - XIII 10.2 HILL S SIMPLIFYING ASSUMPTIONS - 257 10.2.1 EQUILIBRIA. HILL S SPHERE - 260 10.2.2 MOTION NEAR THE EQUILIBRIUM POINTS - 262 10.2.3 BASIC FAMILIES OF PERIODIC ORBITS - 263 11 MOTION INSIDE HILL S SPHERE - 265 11.1 PERTURBED KEPLERIAN MOTION - 265 11.1.1 SHORT-PERIOD ELIMINATION - 266 11.1.2 ELIMINATION OF THE NODE IN THE ROTATING FRAME - 267 11.1.3 THIRD-BODY CRITICAL INCLINATION. THE LIDOV-KOZAI RESONANCE - 268 11.2 HIGHER-ORDER DYNAMICS - 271 11.2.1 DEGENERACY AT THE THIRD ORDER - 271 11.2.2 FOURTH-ORDER CORRECTIONS - 274 11.2.3 HIGHER-ORDER REFINEMENTS - 276 11.3 THE CASE OF PLANETARY SATELLITES - 278 11.3.1 ELIMINATION OF THE MEAN ANOMALY - 280 11.3.2 ELIMINATION OF THE LONGITUDE OF THE NODE - 281 11.3.3 REDUCED PHASE SPACE IN THE PARAMETERS PLANE - 282 11.3.4 THIRD-ORDER EFFECTS. THE SPACE OF PARAMETERS - 287 11.4 APPLICATION. COMPUTATION OF THE SCIENCE ORBIT - 288 11.4.1 MEAN TO OSCULATING TRANSFORMATION - 291 11.4.2 MAPPING ORBITS ---- 293 12 MOTION ABOUT THE LIBRATION POINTS - 295 12.1 PERTURBATION SOLUTION - 295 12.1.1 THE CENTER MANIFOLD - 296 12.1.2 HOMOLOGICAL EQUATION IN COMPLEX VARIABLES - 298 12.1.3 DETUNING. THE PERTURBED ELLIPTIC OSCILLATOR - 299 12.1.4 HAMILTONIAN NORMALIZATION - 302 12.2 REDUCED DYNAMICS IN THE CENTER MANIFOLD - 303 12.2.1 VISUALIZATION OF THE REDUCED FLOW - 304 12.2.2 EQUILIBRIA AND BIFURCATIONS. ANALYTICAL COMPUTATION - 304 12.2.3 PARTNER ORBITS OF THE EQUILIBRIA IN THE CENTER MANIFOLD - 306 12.3 HIGHER ORDERS ---- 308 12.3.1 LYAPUNOV ORBITS - 310 12.3.2 RESONANT ORBITS - 310 13 QUASI-SATELLITE ORBITS - 313 13.1 PLANAR CASE. EPICYCLIC COORDINATES - 313 13.2 ELIMINATION OF SHORT-PERIOD EFFECTS - 316 13.2.1 LOWER ORDERS - 317 13.2.2 HIGHER ORDERS ---- 318 XIV CONTENTS 13.2.3 ADDITIONAL HAMILTONIAN TERMS - 321 13.2.4 LONG-PERIOD HAMILTONIAN - 322 13.3 THE NATURE OF THE LONG-TERM SOLUTION - 322 13.4 COMPLETE HAMILTONIAN REDUCTION - 324 13.4.1 EXTENDED HARMONIC TRANSFORMATION - 324 13.4.2 SECULAR HAMILTONIAN - 325 13.4.3 LONG-PERIOD CORRECTIONS - 327 13.4.4 ORBIT DESIGN PARAMETERS - 329 13.4.5 PERIODIC ORBITS - 329 13.5 EXAMPLES - 331 13.5.1 LARGE AMPLITUDE LIBRATION - 331 13.5.2 1:1 RESONANCE - 334 BIBLIOGRAPHY - 337 INDEX - 371
adam_txt	CONTENTS PREFACE - V 1 1.1 1.2 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6 1.3 1.3.1 1.3.2 1.3.3 1.3.4 1.3.5 INTRODUCTION - 1 PERTURBED INTEGRABLE PROBLEMS - 2 ARTIFICIAL SATELLITE THEORY - 5 SIGNIFICANCE OF LYAPUNOV INSTABILITY - 7 GEOPOTENTIAL LONG-PERIOD EFFECTS IN CLOSED FORM - 8 TESSERAL EFFECTS - 10 LUNISOLAR PERTURBATIONS - 12 NON-CONSERVATIVE PERTURBATIONS - 14 ACTION-ANGLE AND NON-SINGULAR VARIABLES - 16 NON-EARTH ORBITS AND PERTURBED NON-KEPLERIAN ORBITS - 18 THE RESTRICTED THREE-BODY PROBLEM - 18 HILL PROBLEM SIMPLIFICATIONS - 19 MOTION ABOUT PLANETARY SATELLITES - 21 LIBRATION POINTS ORBITS - 22 COORBITAL MOTION WITH LOW ECCENTRICITY - 24 PART 1: HAMILTONIAN PERTURBATIONS BY LIE TRANSFORMS 2 2.1 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5 2.2 2.2.1 2.2.2 2.2.3 THE METHOD OF LIE TRANSFORMS - 29 LIE TRANSFORMATION OF A FUNCTION - 29 THE FUNDAMENTAL RECURSION - 31 DEPRIT ' S TRIANGLE - 33 THE DIRECT TRANSFORMATION - 34 COMPOSITION OF LIE TRANSFORMATIONS ---- 35 THE INVERSE TRANSFORMATION - 36 DEPRIT ' S PERTURBATIONS APPROACH - 37 HAMILTONIAN SIMPLIFICATION BY LIE TRANSFORMS - 37 EXAMPLE: SMALL OSCILLATIONS OF THE SIMPLE PENDULUM - 39 THE HOMOLOGICAL EQUATION - 42 3 3.1 3.1.1 3.1.2 3.1.3 3.2 3.2.1 APPLICATION TO INTEGRABLE PROBLEMS - 45 THE SIMPLE GRAVITY PENDULUM - 46 HAMILTONIAN REDUCTION - 46 ROTATION REGIME. SOLUTION IN ACTION-ANGLE VARIABLES - 48 EXPANDED SOLUTION BY LIE TRANSFORMS - 50 THE FREE RIGID BODY - 52 ROTATION IN THE BODY FRAME - 53 X CONTENTS 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 ATTITUDE IN THE SPACE FRAME - 55 THE INVARIABLE PLANE ---- 56 HAMILTONIAN FORMULATION - 58 CLOSED-FORM SOLUTION BY COMPLETE REDUCTION - 59 THE CASE OF LOW TRIAXIALITY - 65 SHORT-AXIS-MODE ROTATION ---- 67 PART II: PERTURBED ELLIPTIC MOTION: ARTIFICIAL SATELLITE THEORY 4 4.1 4.2 4.3 4.4 4.5 4.5.1 4.5.2 4.5.3 4.5.4 THE KEPLER PROBLEM - 77 THE ORBITAL FRAME - 77 KEPLER HAMILTONIAN - 78 HAMILTON-JACOBI REDUCTION - 80 SOLUTION IN DELAUNAY VARIABLES - 83 USEFUL RELATIONS FOR PERTURBED KEPLERIAN MOTION - 86 THE APSIDAL FRAME. FUNDAMENTAL VECTORS - 86 VARIATION EQUATIONS IN VECTORIAL ELEMENTS - 87 DIFFERENTIAL RELATIONS AND CLOSED-FORM INTEGRATION - 88 PRINCIPAL RELATIONS OF THE ELLIPSE - 90 5 5.1 5.2 5.3 5.3.1 5.3.2 5.4 5.4.1 5.4.2 5.4.3 5.5 5.6 5.6.1 5.6.2 5.6.3 5.6.4 5.7 5.7.1 5.7.2 THE MAIN PROBLEM OF THE ARTIFICIAL SATELLITE - 92 GEOPOTENTIAL HAMILTONIAN - 92 PARTICULAR SOLUTIONS - 94 SECULAR EFFECTS - 95 PICARD ITERATIONS - 97 INCLINATION RESONANCES - 99 INTERMEDIARIES - 100 COMMON INTERMEDIARIES - 101 NATURAL INTERMEDIARIES - 102 TORSIONS FOR QUASI-KEPLERIAN SYSTEMS - 105 DISCRETIZATION OF THE FLOW - 106 THE CRITICAL INCLINATION - 110 FIRST ORDER - 110 SECOND ORDER - 111 THE REDUCED PHASE SPACE. FROZEN ORBITS - 113 REDUCED DYNAMICS ON THE SPHERE - 116 SEMI-ANALYTICAL INTEGRATION - 119 SHORT-PERIOD CORRECTIONS IN DELAUNAY VARIABLES - 120 SHORT-PERIOD CORRECTIONS IN NON-SINGULAR VARIABLES - 121 6 ZONAL PERTURBATIONS - 124 CONTENTS - XI 6.1 ZONAL PROBLEM IN MEAN ELEMENTS - 124 6.1.1 AVERAGED FLOW ---- 127 6.1.2 INCLINATION-ECCENTRICITY DIAGRAMS OF FROZEN ORBITS - 129 6.1.3 LOCAL DYNAMICS: ECCENTRICITY-VECTOR DIAGRAMS - 131 6.2 HAMILTONIAN SIMPLIFICATION - 133 6.2.1 DEPRIT ' S ELIMINATION OF THE PARALLAX - 134 6.2.2 DELAUNAY NORMALIZATION - 137 6.2.3 SHORT-PERIOD CORRECTIONS - 139 6.3 BROUWER ' S SOLUTION BY COMPLETE REDUCTION - 141 6.3.1 SECULAR TERMS - 141 6.3.2 LONG-PERIOD CORRECTIONS ---- 143 6.4 REVERSE NORMALIZATION. LONG PERIODS REMOVED FIRST - 144 6.4.1 NORMALIZATION OF THE TOTAL ANGULAR MOMENTUM - 145 6.4.2 NORMALIZATION OF THE SEMIMAJOR AXIS - 149 6.4.3 ALFRIEND AND COFFEY ' S ELIMINATION OF THE PERIGEE - 151 6.5 HIGHER ORDERS OF THE PERTURBATION SOLUTION. A TEST CASE - 153 6.5.1 PRELIMINARY SIMPLIFICATION. ELIMINATION OF THE PARALLAX - 154 6.5.2 PARTIAL NORMALIZATION. LONG-PERIOD ELIMINATION - 156 6.5.3 COMPLETE HAMILTONIAN REDUCTION. SHORT-PERIOD ELIMINATION - 159 6.5.4 SECULAR FREQUENCIES - 162 6.5.5 SAMPLE APPLICATION. THE PRISMA ORBIT ---- 165 6.6 INITIALIZATION ISSUES. BREAKWELL AND VAGNERS ' APPROACH - 173 6.7 CENTERED ELEMENTS - 174 7 TESSERAL PERTURBATIONS - 176 7.1 TESSERAL POTENTIAL IN ORBITAL ELEMENTS - 176 7.2 LOW-EARTH ORBITS. GARFINKEL ' S PERTURBATION APPROACH - 177 7.2.1 ELIMINATION OF THE PARALLAX OF TESSERAL TERMS - 178 7.2.2 DELAUNAY NORMALIZATION, M-DAILY TERMS - 180 7.2.3 ELIMINATION OF THE NODE. LONG-TERM HAMILTONIAN - 182 7.3 EXACT INTEGRATION TO THE SECOND ORDER OF/ 2 ---- 183 7.4 RELEGATION OF TESSERAL EFFECTS - 186 7.4.1 BASIC ALGORITHM ---- 186 7.4.2 TESSERAL RELEGATION WITH LOW ECCENTRICITY - 187 7.4.3 SAMPLE APPLICATIONS - 189 7.5 TESSERAL RESONANCES - 193 7.5.1 RESONANT TERMS OF THE GEOPOTENTIAL - 194 7.5.2 SHORT-PERIOD ELIMINATION ----- 196 7.5.3 THE 2:1 RESONANCE. GPS ORBITS ---- 199 7.5.4 THE 5:3 RESONANCE. GALILEO DISPOSAL ORBITS ---- 201 8 LUNISOLAR PERTURBATIONS - 203 XII - CONTENTS 8.1 8.1.1 8.1.2 8.2 8.2.1 8.2.2 8.2.3 8.3 8.3.1 8.3.2 8.4 8.4.1 8.4.2 8.4.3 8.4.4 8.5 8.5.1 8.5.2 8.5.3 THE THIRD-BODY POTENTIAL - 203 EXPANSION OF THE POTENTIAL FOR A CLOSE-EARTH SATELLITE - 204 THE DISTURBING POTENTIAL IN THE APSIDAL FRAME - 205 LONG-TERM MOTION. THE EXTENDED PHASE SPACE - 206 SHORT-PERIOD ELIMINATION BY LIE TRANSFORMS - 207 AVERAGED FLOW IN VECTORIAL ELEMENTS - 208 SAMPLE APPLICATION. THE CASE OF HIGH EARTH ORBITS - 211 THIRD-BODY ' S MEAN ANOMALY AVERAGING - 213 MOON AND SUN DISTURBING EFFECTS - 214 ADDITIONAL SIMPLIFICATIONS. LONG-TERM HAMILTONIAN - 217 PERTURBATIONS IN THE ECLIPTIC FRAME - 219 THE DISTURBING POTENTIAL - 220 REMOVING SHORT-PERIOD EFFECTS - 221 REMOVING MONTHLY AND ANNUAL EFFECTS - 224 ELIMINATION OF THE MOON ' S LONGITUDE OF THE NODE - 226 KUDIELKA ' S BALANCED ORBITS - 227 THE MANIFOLD OF CIRCULAR ORBITS - 229 THE MANIFOLD OF POLAR ORBITS ORTHOGONAL TO THE EQUINOX - 232 OTHER EQUILIBRIA - 234 9 9.1 9.1.1 9.1.2 9.1.3 9.1.4 9.1.5 9.1.6 9.2 9.2.1 9.2.2 9.2.3 9.2.4 NON-CONSERVATIVE EFFECTS - 235 SOLAR-RADIATION PRESSURE - 235 THE DISTURBING SRP " POTENTIAL " - 236 HAMILTONIAN SHORT-PERIOD REDUCTION IN THE SYNODIC FRAME - 236 PARTICULAR SOLUTIONS - 238 GENERAL SOLUTION IN VECTORIAL ELEMENTS - 239 COMPLETE HAMILTONIAN REDUCTION IN ACTION-ANGLE VARIABLES - 241 SHORT-PERIOD REDUCTION IN THE EQUATORIAL FRAME - 242 ATMOSPHERIC DRAG - 243 ATMOSPHERIC DENSITY - 243 ROTATING ATMOSPHERE - 244 GAUSS EQUATIONS OF VARIATION - 245 PERTURBATION EQUATIONS - 247 PART III: RELATIVE MOTION AND PERTURBED NON-KEPLERIAN MOTION 10 10.1 10.1.1 10.1.2 10.1.3 THE HILL PROBLEM ---- 253 THE CIRCULAR RESTRICTED THREE-BODY PROBLEM ---- 253 SYNODIC FRAME. THE JACOBI INTEGRAL ---- 254 HAMILTONIAN FORMULATION ---- 255 SURFACES AND CURVES OF ZERO VELOCITY - 256 CONTENTS - XIII 10.2 HILL ' S SIMPLIFYING ASSUMPTIONS - 257 10.2.1 EQUILIBRIA. HILL ' S SPHERE - 260 10.2.2 MOTION NEAR THE EQUILIBRIUM POINTS - 262 10.2.3 BASIC FAMILIES OF PERIODIC ORBITS - 263 11 MOTION INSIDE HILL ' S SPHERE - 265 11.1 PERTURBED KEPLERIAN MOTION - 265 11.1.1 SHORT-PERIOD ELIMINATION - 266 11.1.2 ELIMINATION OF THE NODE IN THE ROTATING FRAME - 267 11.1.3 THIRD-BODY CRITICAL INCLINATION. THE LIDOV-KOZAI RESONANCE - 268 11.2 HIGHER-ORDER DYNAMICS - 271 11.2.1 DEGENERACY AT THE THIRD ORDER - 271 11.2.2 FOURTH-ORDER CORRECTIONS - 274 11.2.3 HIGHER-ORDER REFINEMENTS - 276 11.3 THE CASE OF PLANETARY SATELLITES - 278 11.3.1 ELIMINATION OF THE MEAN ANOMALY - 280 11.3.2 ELIMINATION OF THE LONGITUDE OF THE NODE - 281 11.3.3 REDUCED PHASE SPACE IN THE PARAMETERS PLANE - 282 11.3.4 THIRD-ORDER EFFECTS. THE SPACE OF PARAMETERS - 287 11.4 APPLICATION. COMPUTATION OF THE SCIENCE ORBIT - 288 11.4.1 MEAN TO OSCULATING TRANSFORMATION - 291 11.4.2 MAPPING ORBITS ---- 293 12 MOTION ABOUT THE LIBRATION POINTS - 295 12.1 PERTURBATION SOLUTION - 295 12.1.1 THE CENTER MANIFOLD - 296 12.1.2 HOMOLOGICAL EQUATION IN COMPLEX VARIABLES - 298 12.1.3 DETUNING. THE PERTURBED ELLIPTIC OSCILLATOR - 299 12.1.4 HAMILTONIAN NORMALIZATION - 302 12.2 REDUCED DYNAMICS IN THE CENTER MANIFOLD - 303 12.2.1 VISUALIZATION OF THE REDUCED FLOW - 304 12.2.2 EQUILIBRIA AND BIFURCATIONS. ANALYTICAL COMPUTATION - 304 12.2.3 PARTNER ORBITS OF THE EQUILIBRIA IN THE CENTER MANIFOLD - 306 12.3 HIGHER ORDERS ---- 308 12.3.1 LYAPUNOV ORBITS - 310 12.3.2 RESONANT ORBITS - 310 13 QUASI-SATELLITE ORBITS - 313 13.1 PLANAR CASE. EPICYCLIC COORDINATES - 313 13.2 ELIMINATION OF SHORT-PERIOD EFFECTS - 316 13.2.1 LOWER ORDERS - 317 13.2.2 HIGHER ORDERS ---- 318 XIV CONTENTS 13.2.3 ADDITIONAL HAMILTONIAN TERMS - 321 13.2.4 LONG-PERIOD HAMILTONIAN - 322 13.3 THE NATURE OF THE LONG-TERM SOLUTION - 322 13.4 COMPLETE HAMILTONIAN REDUCTION - 324 13.4.1 EXTENDED HARMONIC TRANSFORMATION - 324 13.4.2 SECULAR HAMILTONIAN - 325 13.4.3 LONG-PERIOD CORRECTIONS - 327 13.4.4 ORBIT DESIGN PARAMETERS - 329 13.4.5 PERIODIC ORBITS - 329 13.5 EXAMPLES - 331 13.5.1 LARGE AMPLITUDE LIBRATION - 331 13.5.2 1:1 RESONANCE - 334 BIBLIOGRAPHY - 337 INDEX - 371
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spelling	Lara, Martín Verfasser aut Hamiltonian perturbation solutions for spacecraft orbit prediction the method of lie transforms Martín Lara Berlin ; Boston De Gruyter [2021] XIV, 377 Seiten Illustrationen 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematical physics Volume 54 Hamilton-Jacobi-Differentialgleichung Störungstheorie Umlaufbahn Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-066851-3 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-066732-5 De Gruyter studies in mathematical physics Volume 54 (DE-604)BV040141722 54 X:MVB https://www.degruyter.com/books/9783110667226 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032696750&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p npi 20210421 DE-101 https://d-nb.info/provenance/plan#npi
spellingShingle	Lara, Martín Hamiltonian perturbation solutions for spacecraft orbit prediction the method of lie transforms De Gruyter studies in mathematical physics
title	Hamiltonian perturbation solutions for spacecraft orbit prediction the method of lie transforms
title_auth	Hamiltonian perturbation solutions for spacecraft orbit prediction the method of lie transforms
title_exact_search	Hamiltonian perturbation solutions for spacecraft orbit prediction the method of lie transforms
title_exact_search_txtP	Hamiltonian perturbation solutions for spacecraft orbit prediction the method of lie transforms
title_full	Hamiltonian perturbation solutions for spacecraft orbit prediction the method of lie transforms Martín Lara
title_fullStr	Hamiltonian perturbation solutions for spacecraft orbit prediction the method of lie transforms Martín Lara
title_full_unstemmed	Hamiltonian perturbation solutions for spacecraft orbit prediction the method of lie transforms Martín Lara
title_short	Hamiltonian perturbation solutions for spacecraft orbit prediction
title_sort	hamiltonian perturbation solutions for spacecraft orbit prediction the method of lie transforms
title_sub	the method of lie transforms
url	https://www.degruyter.com/books/9783110667226 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032696750&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV040141722
work_keys_str_mv	AT laramartin hamiltonianperturbationsolutionsforspacecraftorbitpredictionthemethodoflietransforms AT walterdegruytergmbhcokg hamiltonianperturbationsolutionsforspacecraftorbitpredictionthemethodoflietransforms

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