Orbital Mechanics: For Engineering Students (2005)(1st ed.)(en)(704s)

Howard Curtis0750661690, 9780750661690, 9780080470542

Orbital Mechanics for Engineering Students is a foundation text for this cornerstone aerospace subject. It offers a rigorous and contemporary introduction to the physical phenomena and analytical procedures required to understand and predict the behavior of orbiting spacecraft. Structured to cover the requirements of one and two semester courses in orbital mechanics, it is also a springboard to more advanced study.Written for undergraduate students of aerospace engineering, astronautical engineering, engineering mechanics and engineering physics who have completed first courses in physics, vector dynamics and mathematics (through to differential equations and linear algebra), it will also be appropriate for graduate students new to the subject. The book otherwise assumes no previous experience and is self-contained. All of the required basic dynamics principles are developed in detail so that neither student nor instructor will have to refer to other sources.

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Table of contents :
COVER……Page 1
ORBITAL MECHANICS FOR ENGINEERING STUDENTS……Page 4
CONTENTS……Page 6
PREFACE……Page 12
SUPPLEMENTS TO THE TEXT……Page 16
1.1 INTRODUCTION……Page 18
1.2 KINEMATICS……Page 19
1.3 MASS, FORCE AND NEWTON’S LAW OF GRAVITATION……Page 24
1.4 NEWTON’S LAW OF MOTION……Page 27
1.5 TIME DERIVATIVES OF MOVING VECTORS……Page 32
1.6 RELATIVE MOTION……Page 37
PROBLEMS……Page 46
2.1 INTRODUCTION……Page 50
2.2 EQUATIONS OF MOTION IN AN INERTIAL FRAME……Page 51
2.3 EQUATIONS OF RELATIVE MOTION……Page 54
2.4 ANGULAR MOMENTUM AND THE ORBIT FORMULAS……Page 59
2.5 THE ENERGY LAW……Page 67
2.6 CIRCULAR ORBITS (e = 0)……Page 68
2.7 ELLIPTICAL ORBITS (0 < e < 1)……Page 72
2.8 PARABOLIC TRAJECTORIES (e = 1)……Page 82
2.9 HYPERBOLIC TRAJECTORIES (e > 1)……Page 86
2.10 PERIFOCAL FRAME……Page 93
2.11 THE LAGRANGE COEFFICIENTS……Page 95
2.12 RESTRICTED THREE-BODY PROBLEM……Page 106
2.12.1 Lagrange points……Page 109
2.12.2 Jacobi constant……Page 113
PROBLEMS……Page 118
3.1 INTRODUCTION……Page 124
3.3 CIRCULAR ORBITS……Page 125
3.4 ELLIPTICAL ORBITS……Page 126
3.5 PARABOLIC TRAJECTORIES……Page 141
3.6 HYPERBOLIC TRAJECTORIES……Page 142
3.7 UNIVERSAL VARIABLES……Page 151
PROBLEMS……Page 162
4.1 INTRODUCTION……Page 166
4.2 GEOCENTRIC RIGHT ASCENSION–DECLINATION FRAME……Page 167
4.3 STATE VECTOR AND THE GEOCENTRIC EQUATORIAL FRAME……Page 171
4.4 ORBITAL ELEMENTS AND THE STATE VECTOR……Page 175
4.5 COORDINATE TRANSFORMATION……Page 181
4.6 TRANSFORMATION BETWEEN GEOCENTRIC EQUATORIAL AND PERIFOCAL FRAMES……Page 189
4.7 EFFECTS OF THE EARTH’S OBLATENESS……Page 194
PROBLEMS……Page 204
5.1 INTRODUCTION……Page 210
5.2 GIBBS’ METHOD OF ORBIT DETERMINATION FROM THREE POSITION VECTORS……Page 211
5.3 LAMBERT’S PROBLEM……Page 219
5.4 SIDEREAL TIME……Page 230
5.5 TOPOCENTRIC COORDINATE SYSTEM……Page 235
5.6 TOPOCENTRIC EQUATORIAL COORDINATE SYSTEM……Page 238
5.7 TOPOCENTRIC HORIZON COORDINATE SYSTEM……Page 240
5.8 ORBIT DETERMINATION FROM ANGLE AND RANGE MEASUREMENTS……Page 245
5.9 ANGLES-ONLY PRELIMINARY ORBIT DETERMINATION……Page 252
5.10 GAUSS’S METHOD OF PRELIMINARY ORBIT DETERMINATION……Page 253
PROBLEMS……Page 267
6.1 INTRODUCTION……Page 272
6.2 IMPULSIVE MANEUVERS……Page 273
6.3 HOHMANN TRANSFER……Page 274
6.4 BI-ELLIPTIC HOHMANN TRANSFER……Page 281
6.5 PHASING MANEUVERS……Page 285
6.6 NON-HOHMANN TRANSFERS WITH A COMMON APSE LINE……Page 290
6.7 APSE LINE ROTATION……Page 296
6.8 CHASE MANEUVERS……Page 302
6.9 PLANE CHANGE MANEUVERS……Page 307
PROBLEMS……Page 321
7.1 INTRODUCTION……Page 332
7.2 RELATIVE MOTION IN ORBIT……Page 333
7.3 LINEARIZATION OF THE EQUATIONS OF RELATIVE MOTION IN ORBIT……Page 339
7.4 CLOHESSY–WILTSHIRE EQUATIONS……Page 341
7.5 TWO-IMPULSE RENDEZVOUS MANEUVERS……Page 347
7.6 RELATIVE MOTION IN CLOSE-PROXIMITY CIRCULAR ORBITS……Page 355
PROBLEMS……Page 357
8.1 INTRODUCTION……Page 364
8.2 INTERPLANETARY HOHMANN TRANSFERS……Page 365
8.3 RENDEZVOUS OPPORTUNITIES……Page 366
8.4 SPHERE OF INFLUENCE……Page 371
8.5 METHOD OF PATCHED CONICS……Page 376
8.6 PLANETARY DEPARTURE……Page 377
8.7 SENSITIVITY ANALYSIS……Page 383
8.8 PLANETARY RENDEZVOUS……Page 385
8.9 PLANETARY FLYBY……Page 392
8.10 PLANETARY EPHEMERIS……Page 404
8.11 NON-HOHMANN INTERPLANETARY TRAJECTORIES……Page 408
PROBLEMS……Page 415
9.1 INTRODUCTION……Page 416
9.2 KINEMATICS……Page 417
9.3 EQUATIONS OF TRANSLATIONAL MOTION……Page 425
9.4 EQUATIONS OF ROTATIONAL MOTION……Page 427
9.5 MOMENTS OF INERTIA……Page 431
9.5.1 Parallel axis theorem……Page 445
9.6 EULER’S EQUATIONS……Page 452
9.7 KINETIC ENERGY……Page 458
9.8 THE SPINNING TOP……Page 460
9.9 EULER ANGLES……Page 465
9.10 YAW, PITCH AND ROLL ANGLES……Page 476
PROBLEMS……Page 480
10.1 INTRODUCTION……Page 492
10.2 TORQUE-FREE MOTION……Page 493
10.3 STABILITY OF TORQUE-FREE MOTION……Page 503
10.4 DUAL-SPIN SPACECRAFT……Page 508
10.5 NUTATION DAMPER……Page 512
10.6 CONING MANEUVER……Page 520
10.7 ATTITUDE CONTROL THRUSTERS……Page 523
10.8 YO-YO DESPIN MECHANISM……Page 526
10.9 GYROSCOPIC ATTITUDE CONTROL……Page 533
10.10 GRAVITY-GRADIENT STABILIZATION……Page 547
PROBLEMS……Page 560
11.1 INTRODUCTION……Page 568
11.2 EQUATIONS OF MOTION……Page 569
11.3 THE THRUST EQUATION……Page 572
11.4 ROCKET PERFORMANCE……Page 574
11.5 RESTRICTED STAGING IN FIELD-FREE SPACE……Page 577
11.6.1 Lagrange multiplier……Page 587
PROBLEMS……Page 595
REFERENCES AND FURTHER READING……Page 598
APPENDIX A PHYSICAL DATA……Page 600
APPENDIX B A ROAD MAP……Page 602
APPENDIX C NUMERICAL INTEGRATION OF THE n-BODY EQUATIONS OF MOTION……Page 604
C.1 FUNCTION FILE accel_3body.m……Page 607
C.2 SCRIPT FILE threebody.m……Page 609
APPENDIX D MATLAB ALGORITHMS……Page 612
D.2 ALGORITHM 3.1: SOLUTION OF KEPLER’S EQUATION BY NEWTON’S METHOD……Page 613
D.3 ALGORITHM 3.2: SOLUTION OF KEPLER’S EQUATION FOR THE HYPERBOLA USING NEWTON’S METHOD……Page 615
D.4 CALCULATION OF THE STUMPFF FUNCTIONS S(z) AND C(z)……Page 617
D.5 ALGORITHM 3.3: SOLUTION OF THE UNIVERSAL KEPLER’S EQUATION USING NEWTON’S METHOD……Page 618
D.6 CALCULATION OF THE LAGRANGE COEFFICIENTS f AND g AND THEIR TIME DERIVATIVES……Page 620
D.7 ALGORITHM 3.4: CALCULATION OF THE STATE VECTOR (r, v) GIVEN THE INITIAL STATE VECTOR (r[sub(0)], v[sub(0)]) AND THE TIME LAPSE Δt……Page 621
D.8 ALGORITHM 4.1: CALCULATION OF THE ORBITAL ELEMENTS FROM THE STATE VECTOR……Page 623
D.9 ALGORITHM 4.2: CALCULATION OF THE STATE VECTOR FROM THE ORBITAL ELEMENTS……Page 627
D.10 ALGORITHM 5.1: GIBBS’ METHOD OF PRELIMINARY ORBIT DETERMINATION……Page 630
D.11 ALGORITHM 5.2: SOLUTION OF LAMBERT’S PROBLEM……Page 633
D.12 CALCULATION OF JULIAN DAY NUMBER AT 0 HR UT……Page 638
D.13 ALGORITHM 5.3: CALCULATION OF LOCAL SIDEREAL TIME……Page 640
D.14 ALGORITHM 5.4: CALCULATION OF THE STATE VECTOR FROM MEASUREMENTS OF RANGE, ANGULAR POSITION AND THEIR RATES……Page 643
D.15 ALGORITHMS 5.5 AND 5.6: GAUSS’S METHOD OF PRELIMINARY ORBIT DETERMINATION WITH ITERATIVE IMPROVEMENT……Page 648
D.16 CONVERTING THE NUMERICAL DESIGNATION OF A MONTH OR A PLANET INTO ITS NAME……Page 657
D.17 ALGORITHM 8.1: CALCULATION OF THE STATE VECTOR OF A PLANET AT A GIVEN EPOCH……Page 658
D.18 ALGORITHM 8.2: CALCULATION OF THE SPACECRAFT TRAJECTORY FROM PLANET 1 TO PLANET 2……Page 665
APPENDIX E GRAVITATIONAL POTENTIAL ENERGY OF A SPHERE……Page 674
A……Page 678
C……Page 679
E……Page 680
G……Page 681
I……Page 682
M……Page 683
O……Page 684
P……Page 685
R……Page 686
S……Page 687
T……Page 688
U……Page 689
Z……Page 690