Spacecraft Attitude Dynamics

From its roots in classical mechanics and reliance on stability theory to the evolution of practical stabilization ideas, this volume offers comprehensive coverage of environmental torques encountered in space; energy dissipation and its effects on the attitude stability of spinning bodies; motion equations for four archetypical systems; orientation parameters; illustrations of key concepts with on-orbit flight data; and typical engineering hardware, with examples of the implementation of dynamic ideas. The sole prerequisites are a fundamental knowledge of vector dynamics and matrix algebra; suitable for use as a text for advanced undergraduates and graduate students, this unified treatment is also a valuable reference for professionals. 1986 ed.

CHAPTER 1 INTRODUCTION

1

(5)

CHAPTER 2 ROTATIONAL KINEMATICS

6

(33)

2.1 Reference Frames and Rotations

6

(9)

2.2 Angular Displacement Parameters

15

(7)

2.3 Angular Velocity

22

(7)

2.4 Comments on Parameter Alternatives

29

(2)

2.5 Problems

31

(8)

CHAPTER 3 ATTITUDE MOTION EQUATIONS

39

(54)

3.1 Motion Equations for a Point Mass, P

40

(2)

3.2 Motion Equations for a System of Point Masses, ΣPn

42

(13)

3.3 Motion Equations for a Rigid Body, R

55

(6)

3.4 A System with Damping, R+P

61

(4)

3.5 A Dual-Spin System, R+ W

65

(5)

3.6 A Simple Multi-Rigid-Body System, R1 + R2

70

(6)

3.7 Dynamics of a System of Rigid Bodies

76

(7)

3.8 Problems

83

(10)

CHAPTER 4 ATTITUDE DYNAMICS OF A RIGID BODY

93

(46)

4.1 Basic Motion Equations

93

(3)

4.2 Torque-Free Motion; R Inertially Axisymmetrical

96

(8)

4.3 Torque-Free Motion; R Tri-inertial

104

(10)

4.4 Stability of Motion for R

114

(10)

4.5 Motion of a Rigid Body Under Torque

124

(5)

4.6 Problems

129

(10)

CHAPTER 5 EFFECT OF INTERNAL ENERGY DISSIPATION ON THE DIRECTIONAL STABILITY OF SPINNING BODIES

139

(17)

5.1 Quasi-Rigid Body with an Energy Sink, 2

140

(6)

5.2 Rigid Body with a Point Mass Damper, R + P

146

(6)

5.3 Problems

152

(4)

CHAPTER 6 DIRECTIONAL STABILITY OF MULTISPIN VEHICLES

156

(36)

6.1 The R + W Gyrostat

156

(5)

6.2 Gyrostat with Nonspinning Carrier

161

(3)

6.3 The Zero Momentum Gyrostat

164

(1)

6.4 The General Case

165

(13)

6.5 System of Coaxial Wheels

178

(6)

6.6 Problems

184

(8)

CHAPTER 7 EFFECT OF INTERNAL ENERGY DISSIPATION ON THE DIRECTIONAL STABILITY OF GYROSTATS

192

(40)

7.1 Energy Sink Analyses

193

(24)

7.2 Gyrostats with Discrete Dampers

217

(8)

7.3 Problems

225

(7)

CHAPTER 8 SPACECRAFT TORQUES

232

(49)

8.1 Gravitational Torque

233

(15)

8.2 Aerodynamic Torque

248

(12)

8.3 Radiation Torques

260

(4)

8.4 Other Environmental Torques

264

(5)

8.5 Nonenvironmental Torques

269

(2)

8.6 Closing Remarks

271

(1)

8.7 Problems

272

(9)

CHAPTER 9 GRAVITATIONAL STABILIZATION

281

(73)

9.1 Context

282

(11)

9.2 Equilibria for a Rigid Body in a Circular Orbit

293

(20)

9.3 Design of Gravitationally Stabilized Satellites

313

(22)

9.4 Flight Experience

335

(11)

9.5 Problems

346

(8)

CHAPTER 10 SPIN STABILIZATION IN ORBIT

354

(69)

10.1 Spinning Rigid Body in Orbit

356

(25)

10.2 Design of Spin-Stabilized Satellites

381

(19)

10.3 Long-Term Effects of Environmental Torques, and Flight Data

400

(16)

10.4 Problems

416

(7)

CHAPTER 11 DUAL-STABILIZATION IN ORBIT: GYROSTATS AND BIAS MOMENTUM SATELLITES

423

(57)

11.1 The Gyrostat in Orbit

424

(20)

11.2 Gyrostats with External Rotors

444

(11)

11.3 Bias Momentum Satellites

455

(15)

11.4 Problems

470

(10)

APPENDIX A ELEMENTS OF STABILITY THEORY

480

(42)

A.1 Stability Definitions

481

(11)

A.2 Stability of the Origin

492

(1)

A.3 The Linear Approximation

493

(9)

A.4 Nonlinear Inferences from Infinitesimal Stability Properties

502

(2)

A.5 Liapunov's Method

504

(6)

A.6 Stability of Linear Stationary Mechanical Systems

510

(10)

A.7 Stability Ideas Specialized to Attitude Dynamics

520

(2)

APPENDIX B VECTRICES

522

(13)

B.1 Remarks on Terminology

523

(1)

B.2 Vectrices

523

(4)

B.3 Several Reference Frames

527

(3)

B.4 Kinematics of Vectrices

530

(2)

B.5 Derivative with Respect to a Vector

532

(3)

APPENDIX C LIST OF SYMBOLS

535

(6)

C.1 Lowercase Symbols

535

(1)

C.2 Uppercase Symbols

536

(2)

C.3 Lowercase Greek Symbols

538

(1)

C.4 Uppercase Greek Symbols

539

(1)

C.5 Other Notational Conventions

539

(2)

REFERENCES

541

(18)

ERRATA

559

(6)

INDEX

565

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Spacecraft Attitude Dynamics

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