Preface |
|
xiii | |
|
|
1 | (12) |
|
|
1 | (4) |
|
1.1.1 Atmosphere as Perturbing Environment |
|
|
1 | (3) |
|
1.1.2 Gravity as the Governing Force |
|
|
4 | (1) |
|
1.1.3 Topics in Space Dynamics |
|
|
5 | (1) |
|
1.2 Reference Frames and Time Scales |
|
|
5 | (5) |
|
|
5 | (3) |
|
|
8 | (1) |
|
|
8 | (1) |
|
|
8 | (2) |
|
1.3 Classification of Space Missions |
|
|
10 | (1) |
|
|
10 | (1) |
|
|
11 | (2) |
|
|
13 | (28) |
|
|
13 | (1) |
|
|
14 | (2) |
|
|
16 | (1) |
|
|
17 | (3) |
|
|
20 | (4) |
|
|
24 | (3) |
|
2.7 Gravity Field of a Body |
|
|
27 | (14) |
|
2.7.1 Legendre Polynomials |
|
|
29 | (2) |
|
2.7.2 Spherical Coordinates |
|
|
31 | (3) |
|
|
34 | (3) |
|
2.7.4 Spherical Body with Radially Symmetric Mass Distribution |
|
|
37 | (1) |
|
|
37 | (3) |
|
|
40 | (1) |
|
|
41 | (28) |
|
|
41 | (2) |
|
3.2 Orbital Angular Momentum |
|
|
43 | (2) |
|
3.3 Orbital Energy Integral |
|
|
45 | (1) |
|
|
46 | (3) |
|
|
49 | (11) |
|
|
53 | (3) |
|
|
56 | (1) |
|
|
56 | (2) |
|
|
58 | (2) |
|
3.6 Orbital Velocity and Flight Path Angle |
|
|
60 | (3) |
|
3.7 Perifocal Frame and Lagrange's Coefficients |
|
|
63 | (6) |
|
|
65 | (4) |
|
|
69 | (22) |
|
4.1 Position and Velocity in an Elliptic Orbit |
|
|
70 | (5) |
|
4.2 Solution to Kepler's Equation |
|
|
75 | (5) |
|
|
76 | (2) |
|
4.2.2 Solution by Bessel Functions |
|
|
78 | (2) |
|
4.3 Position and Velocity in a Hyperbolic Orbit |
|
|
80 | (4) |
|
4.4 Position and Velocity in a Parabolic Orbit |
|
|
84 | (2) |
|
4.5 Universal Variable for Keplerian Motion |
|
|
86 | (5) |
|
|
88 | (1) |
|
|
89 | (2) |
|
|
91 | (26) |
|
|
91 | (3) |
|
5.2 Euler Axis and Principal Angle |
|
|
94 | (3) |
|
5.3 Elementary Rotations and Euler Angles |
|
|
97 | (4) |
|
5.4 Euler-Angle Representation of the Orbital Plane |
|
|
101 | (10) |
|
5.4.1 Celestial Reference Frame |
|
|
103 | (1) |
|
5.4.2 Local-Horizon Frame |
|
|
104 | (2) |
|
5.4.3 Classical Euler Angles |
|
|
106 | (5) |
|
5.5 Planet-Fixed Coordinate System |
|
|
111 | (6) |
|
|
114 | (3) |
|
|
117 | (28) |
|
6.1 Single-Impulse Orbital Manoeuvres |
|
|
119 | (4) |
|
6.2 Multi-impulse Orbital Transfer |
|
|
123 | (10) |
|
|
124 | (3) |
|
6.2.2 Rendezvous in Circular Orbit |
|
|
127 | (3) |
|
6.2.3 Outer Bi-elliptic Transfer |
|
|
130 | (3) |
|
6.3 Continuous Thrust Manoeuvres |
|
|
133 | (12) |
|
|
134 | (1) |
|
6.3.2 Constant Radial Acceleration from Circular Orbit |
|
|
135 | (1) |
|
6.3.3 Constant Circumferential Acceleration from Circular Orbit |
|
|
136 | (3) |
|
6.3.4 Constant Tangential Acceleration from Circular Orbit |
|
|
139 | (2) |
|
|
141 | (2) |
|
|
143 | (2) |
|
7 Relative Motion In Orbit |
|
|
145 | (16) |
|
7.1 Hill-Clohessy-Wiltshire Equations |
|
|
148 | (3) |
|
7.2 Linear State-Space Model |
|
|
151 | (2) |
|
7.3 Impulsive Manoeuvres About a Circular Orbit |
|
|
153 | (2) |
|
|
153 | (2) |
|
7.4 Keplerian Relative Motion |
|
|
155 | (6) |
|
|
158 | (3) |
|
|
161 | (30) |
|
8.1 Two-Point Orbital Transfer |
|
|
161 | (3) |
|
8.1.1 Transfer Triangle and Terminal Velocity Vectors |
|
|
162 | (2) |
|
|
164 | (4) |
|
8.2.1 Locus of the Vacant Focii |
|
|
165 | (1) |
|
8.2.2 Minimum-Energy and Minimum-Eccentricity Transfers |
|
|
166 | (2) |
|
|
168 | (9) |
|
8.3.1 Time in Elliptic Transfer |
|
|
169 | (4) |
|
8.3.2 Time in Hyperbolic Transfer |
|
|
173 | (2) |
|
8.3.3 Time in Parabolic Transfer |
|
|
175 | (2) |
|
8.4 Solution to Lambert's Problem |
|
|
177 | (14) |
|
8.4.1 Parameter of Transfer Orbit |
|
|
178 | (1) |
|
8.4.2 Stumpff Function Method |
|
|
179 | (6) |
|
8.4.3 Hypergeometric Function Method |
|
|
185 | (3) |
|
|
188 | (2) |
|
|
190 | (1) |
|
|
191 | (64) |
|
9.1 Perturbing Acceleration |
|
|
191 | (1) |
|
|
192 | (2) |
|
9.3 Variation of Parameters |
|
|
194 | (5) |
|
|
197 | (2) |
|
9.4 Lagrange Planetary Equations |
|
|
199 | (10) |
|
9.5 Gauss Variational Model |
|
|
209 | (5) |
|
|
214 | (5) |
|
9.7 Mean Orbital Perturbation |
|
|
219 | (1) |
|
9.8 Orbital Perturbation Due to Oblateness |
|
|
220 | (7) |
|
9.8.1 Sun-Synchronous Orbits |
|
|
225 | (1) |
|
|
226 | (1) |
|
9.9 Effects of Atmospheric Drag |
|
|
227 | (8) |
|
9.9.1 Life of a Satellite in a Low Circular Orbit |
|
|
228 | (1) |
|
9.9.2 Effect on Orbital Angular Momentum |
|
|
229 | (2) |
|
9.9.3 Effect on Orbital Eccentricity and Periapsis |
|
|
231 | (4) |
|
9.10 Third-Body Perturbation |
|
|
235 | (11) |
|
9.10.1 Lunar and Solar Perturbations on an Earth Satellite |
|
|
238 | (5) |
|
9.10.2 Sphere of Influence and Conic Patching |
|
|
243 | (3) |
|
9.11 Numerical Methods for Perturbed Keplerian Motion |
|
|
246 | (9) |
|
|
246 | (1) |
|
|
246 | (4) |
|
|
250 | (4) |
|
|
254 | (1) |
|
|
255 | (30) |
|
|
256 | (1) |
|
10.2 Particular Solutions by Lagrange |
|
|
257 | (4) |
|
Equilibrium Solutions in a Rotating Frame |
|
|
257 | (2) |
|
|
259 | (2) |
|
10.3 Circular Restricted Three-Body Problem |
|
|
261 | (2) |
|
10.3.1 Equations of Motion in the Inertial Frame |
|
|
261 | (2) |
|
10.4 Non-dimensional Equations in the Synodic Frame |
|
|
263 | (4) |
|
10.5 Lagrangian Points and Stability |
|
|
267 | (3) |
|
10.5.1 Stability Analysis |
|
|
268 | (2) |
|
10.6 Orbital Energy and Jacobi's Integral |
|
|
270 | (6) |
|
10.6.1 Zero-Relative-Speed Contours |
|
|
272 | (3) |
|
10.6.2 Tisserand's Criterion |
|
|
275 | (1) |
|
10.7 Canonical Formulation |
|
|
276 | (2) |
|
10.8 Special Three-Body Trajectories |
|
|
278 | (7) |
|
10.8.1 Perturbed Orbits About a Primary |
|
|
279 | (1) |
|
10.8.2 Free-Return Trajectories |
|
|
279 | (3) |
|
|
282 | (1) |
|
|
283 | (2) |
|
|
285 | (38) |
|
11.1 Euler's Equations of Attitude Kinetics |
|
|
286 | (2) |
|
|
288 | (2) |
|
11.3 Rotational Kinetic Energy |
|
|
290 | (2) |
|
|
292 | (2) |
|
11.5 Torque-Free Rotation of Spacecraft |
|
|
294 | (4) |
|
11.5.7 Stability of Rotational States |
|
|
295 | (3) |
|
11.6 Precession and Nutation |
|
|
298 | (1) |
|
11.7 Semi-Rigid Spacecraft |
|
|
299 | (4) |
|
11.7.1 Dual-Spin Stability |
|
|
301 | (2) |
|
11.8 Solution to Torque-Free Euler's Equations |
|
|
303 | (9) |
|
11.8.1 Axisymmetric Spacecraft |
|
|
304 | (3) |
|
11.8.2 Jacobian Elliptic Functions |
|
|
307 | (1) |
|
11.5.3 Runge-Kutta Solution |
|
|
308 | (4) |
|
11.9 Gravity-Gradient Stabilization |
|
|
312 | (11) |
|
|
321 | (2) |
|
|
323 | (16) |
|
12.1 Impulsive Manoeuvres with Attitude Thrusters |
|
|
323 | (7) |
|
12.1.1 Single-Axis Rotation |
|
|
324 | (2) |
|
12.1.2 Rigid Axisymmetric Spin-Stabilized Spacecraft |
|
|
326 | (4) |
|
12.1.3 Spin-Stabilized Asymmetric Spacecraft |
|
|
330 | (1) |
|
12.2 Attitude Manoeuvres with Rotors |
|
|
330 | (9) |
|
|
332 | (1) |
|
12.2.2 Control-Moment Gyro |
|
|
333 | (1) |
|
12.2.3 Variable-Speed Control-Moment Gyro |
|
|
334 | (1) |
|
|
335 | (2) |
|
|
337 | (2) |
|
A Numerical Solution of Ordinary Differential Equations |
|
|
339 | (6) |
|
A.1 Fixed-Step Runge-Kutta Algorithms |
|
|
339 | (1) |
|
A.2 Variable-Step Runge-Kutta Algorithms |
|
|
340 | (2) |
|
A.3 Runge-Kutta-Nystrom Algorithms |
|
|
342 | (3) |
|
|
343 | (2) |
|
B Jacobian Elliptic Functions |
|
|
345 | (2) |
|
|
346 | (1) |
Index |
|
347 | |