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ANALYTICAL MECHANICS of AEROSPACE SYSTEMS ebook 电子书代购

ANALYTICAL MECHANICS of AEROSPACE SYSTEMS ebook 电子书代购

Contents
Preface ix
I BASIC MECHANICS 1
1 Particle Kinematics 3
1.1 Particle Position Description 3
1.1.1 Basic Geometry 3
1.1.2 Cylindrical and Spherical Coordinate Systems 6
1.2 Vector Di erentiation 8
1.2.1 Angular Velocity Vector 8
1.2.2 Rotation about a Fixed Axis 10
1.2.3 Transport Theorem 11
1.2.4 Particle Kinematics with Moving Frames 15
2 Newtonian Mechanics 25
2.1 Newton's Laws 25
2.2 Single Particle Dynamics 29
2.2.1 Constant Force 29
2.2.2 Time-Varying Force 32
2.2.3 Kinetic Energy 34
2.2.4 Linear Momentum 35
2.2.5 Angular Momentum 35
2.3 Dynamics of a System of Particles 38
2.3.1 Equations of Motion 38
2.3.2 Kinetic Energy 41
2.3.3 Linear Momentum 43
2.3.4 Angular Momentum 45
2.4 Dynamics of a Continuous System 47
2.4.1 Equations of Motion 47
2.4.2 Kinetic Energy 49
2.4.3 Linear Momentum 50
2.4.4 Angular Momentum 51
2.5 The Rocket Problem 52
iii
iv CONTENTS
3 Rigid Body Kinematics 63
3.1 Direction Cosine Matrix 64
3.2 Euler Angles 70
3.3 Principal Rotation Vector 78
3.4 Euler Parameters 85
3.5 Classical Rodrigues Parameters 91
3.6 Modi ed Rodrigues Parameters 96
3.7 Other Attitude Parameters 103
3.7.1 Stereographic Orientation Parameters 103
3.7.2 Higher Order Rodrigues Parameters 105
3.7.3 The (w,z) Coordinates 106
3.7.4 Cayley-Klein Parameters 107
3.8 Homogeneous Transformations 107
4 Eulerian Mechanics 115
4.1 Rigid Body Dynamics 115
4.1.1 Angular Momentum 115
4.1.2 Inertia Matrix Properties 118
4.1.3 Euler's Rotational Equations of Motion 123
4.1.4 Kinetic Energy 124
4.2 Torque-Free Rigid Body Rotation 128
4.2.1 Energy and Momentum Integrals 128
4.2.2 General Free Rigid Body Motion 133
4.2.3 Axisymmetric Rigid Body Motion 135
4.3 Momentum Exchange Devices 137
4.3.1 Spacecraft with Single VSCMG 138
4.3.2 Spacecraft with Multiple VSCMGs 143
4.4 Gravity Gradient Satellite 145
4.4.1 Gravity Gradient Torque 145
4.4.2 Rotational - Translational Motion Coupling 148
4.4.3 Small Departure Motion about Equilibrium Attitudes 149
5 Generalized Methods of Analytical Dynamics 159
5.1 Generalized Coordinates 159
5.2 D'Alembert's Principle 162
5.2.1 Virtual Displacements and Virtual Work 163
5.2.2 Classical Developments of D'Alembert's Principle 164
5.2.3 Holonomic Constraints 170
5.2.4 Newtonian Constrained Dynamics of N Particles 177
5.2.5 Lagrange Multiplier Rule for Constrained Optimization 178
5.3 Lagrangian Dynamics 182
5.3.1 Minimal Coordinate Systems and Unconstrained Motion 183
5.3.2 Lagrange's Equations for Conservative Forces 187
5.3.3 Redundant Coordinate Systems and Constrained Motion 190
5.3.4 Vector-Matrix Form of the Lagrangian Equations of Motion195
CONTENTS v
6 Advanced Methods of Analytical Dynamics 203
6.1 The Hamiltonian Function 203
6.1.1 Some Special Properties of The Hamiltonian 203
6.1.2 Relationship of the Hamiltonian to Total Energy andWork
Energy 203
6.1.3 Hamilton's Canonical Equations 203
6.1.4 Hamilton's Principal Function and the Hamilton-Jacobi
Equation 203
6.2 Hamilton's Principles 203
6.2.1 Variational Calculus Fundamentals 204
6.2.2 Path Variations versus Virtual Displacements 204
6.2.3 Hamilton's Principles from D'Alembert's Principle 204
6.3 Dynamics of Distributed Parameter Systems 204
6.3.1 Elementary DPS: Newton-Euler Methods 204
6.3.2 Energy Functions for Elastic Rods and Beams 204
6.3.3 Hamilton's Principle Applied for DPS 204
6.3.4 Generalized Lagrange's Equations for Multi-Body DPS 204
7 Nonlinear Spacecraft Stability and Control 205
7.1 Nonlinear Stability Analysis 206
7.1.1 Stability De nitions 206
7.1.2 Linearization of Dynamical Systems 210
7.1.3 Lyapunov's Direct Method 212
7.2 Generating Lyapunov Functions 219
7.2.1 Elemental Velocity-Based Lyapunov Functions 221
7.2.2 Elemental Position-Based Lyapunov Functions 227
7.3 Nonlinear Feedback Control Laws 233
7.3.1 Unconstrained Control Law 233
7.3.2 Asymptotic Stability Analysis 236
7.3.3 Feedback Gain Selection 242
7.4 Lyapunov Optimal Control Laws 247
7.5 Linear Closed-Loop Dynamics 253
7.6 Reaction Wheel Control Devices 258
7.7 Variable Speed Control Moment Gyroscopes 260
7.7.1 Control Law 261
7.7.2 Velocity Based Steering Law 264
7.7.3 VSCMG Null Motion 269
II CELESTIAL MECHANICS 283
8 Classical Two-Body Problem 285
8.1 Geometry of Conic Sections 286
8.2 Relative Two-Body Equations of Motion 294
8.3 Fundamental Integrals 296
8.3.1 Conservation of Angular Momentum 296
vi CONTENTS
8.3.2 The Eccentricity Vector Integral 297
8.3.3 Conservation of Energy 300
8.4 Classical Solutions 306
8.4.1 Kepler's Equation 307
8.4.2 Orbit Elements 310
8.4.3 Lagrange/Gibbs F and G Solution 316
9 Restricted Three-Body Problem 325
9.1 Lagrange's Three-Body Solution 326
9.1.1 General Conic Solutions 326
9.1.2 Circular Orbits 335
9.2 Circular Restricted Three-Body Problem 339
9.2.1 Jacobi Integral 341
9.2.2 Zero Relative Velocity Surfaces 346
9.2.3 Lagrange Libration Point Stability 353
9.3 Periodic Stationary Orbits 357
9.4 The Disturbing Function 358
10 Gravitational Potential Field Models 365
10.1 Gravitational Potential of Finite Bodies 366
10.2 MacCullagh's Approximation 369
10.3 Spherical Harmonic Gravity Potential 372
10.4 Multi-Body Gravitational Acceleration 381
10.5 Spheres of Gravitational In
uence 383
11 Perturbation Methods 389
11.1 Encke's Method 390
11.2 Variation of Parameters 392
11.2.1 General Methodology 393
11.2.2 Lagrangian Brackets 395
11.2.3 Lagrange's Planetary Equations 401
11.2.4 Poisson Brackets 408
11.2.5 Gauss' Variational Equations 415
11.3 State Transition and Sensitivity Matrix 417
11.3.1 Linear Dynamic Systems 418
11.3.2 Nonlinear Dynamic Systems 422
11.3.3 Symplectic State Transition Matrix 425
11.3.4 State Transition Matrix of Keplerian Motion 427
12 Transfer Orbits 433
12.1 Minimum Energy Orbit 434
12.2 The Hohmann Transfer Orbit 437
12.3 Lambert's Problem 442
12.3.1 General Problem Solution 443
12.3.2 Elegant Velocity Properties 447
12.4 Rotating the Orbit Plane 450
CONTENTS vii
12.5 Patched-Conic Orbit Solution 455
12.5.1 Establishing the Heliocentric Departure Velocity 457
12.5.2 Escaping the Departure Planet's Sphere of In
uence 461
12.5.3 Enter the Target Planet's Sphere of In
uence 467
12.5.4 Planetary Fly-By's 472
13 Spacecraft Formation Flying 477
13.1 General Relative Orbit Description 479
13.2 Cartesian Coordinate Description 480
13.2.1 Clohessy-Wiltshire Equations 481
13.2.2 Closed Relative Orbits in the Hill Reference Frame 484
13.3 Orbit Element Di erence Description 487
13.3.1 Linear Mapping Between Hill Frame Coordinates and Orbit
Element Di erences 489
13.3.2 Bounded Relative Motion Constraint 495
13.4 Relative Motion State Transition Matrix 497
13.5 Linearized Relative Orbit Motion 502
13.5.1 General Elliptic Orbits 502
13.5.2 Chief Orbits with Small Eccentricity 506
13.5.3 Near-Circular Chief Orbit 508
13.6 J2-Invariant Relative Orbits 511
13.6.1 Ideal Constraints 512
13.6.2 Energy Levels between J2-Invariant Relative Orbits 519
13.6.3 Constraint Relaxation Near Polar Orbits 520
13.6.4 Near-Circular Chief Orbit 524
13.6.5 Relative Argument of Perigee and Mean Anomaly Drift 526
13.6.6 Fuel Consumption Prediction 528
13.7 Relative Orbit Control Methods 531
13.7.1 Mean Orbit Element Continuous Feedback Control Laws 532
13.7.2 Cartesian Coordinate Continuous Feedback Control Law 539
13.7.3 Impulsive Feedback Control Law 542
13.7.4 Hybrid Feedback Control Law 546
APPENDIX A 553
APPENDIX B 557
APPENDIX C 559
APPENDIX D 563
APPENDIX E 565
APPENDIX F 569
APPENDIX G 573
viii CONTENTS
Preface

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