Atmospheric Re-Entry Vehicle Mechanics

Contents......Page 6
1.1.1 Fundamental Principles......Page 20
1.1.2 Noninertial Frames......Page 21
1.1.3 Linear and Angular Momentum......Page 22
1.1.5 Conservation of Energy......Page 23
1.1.6 Isolated System......Page 25
1.2.1 Linear Momentum and Angular Momentum......Page 26
1.2.2 Center of Mass and Equations of Movement......Page 27
1.2.3 Eulerian Frames......Page 28
2.1 The Geodetic Frame of Reference......Page 33
2.1.1 Coordinates of a Point Relating to the Earth......Page 34
2.1.2 The Geodetic Systems......Page 35
2.1.3 Calculation of the Geographical Latitude and Height......Page 36
2.2 The Terrestrial Field of Gravitation......Page 37
3.1 Main Parameters and Hypotheses......Page 39
3.2 The Isothermal Exponential Model......Page 40
3.3 Standard Models of Earth's Atmosphere......Page 41
3.4 Martian Models......Page 44
4. Aerodynamics......Page 48
4.1 Aerodynamic Coefficients......Page 50
4.1.1 Static Coefficients......Page 51
4.1.2 Dynamic Derivatives......Page 53
4.1.3 Axisymmetric Vehicles......Page 54
4.2.1 Parameters of Similarity......Page 55
4.2.2 Characteristics of the Main Flow Modes......Page 56
4.3.2 Numerical [sup([AND])]......Page 57
4.3.3 Approximate Analytical Method [sup([TRU])]......Page 58
4.3.4 Continuous Coefficients by Newton's Method......Page 60
4.4.1 Free Molecular Flow......Page 69
4.4.2 Intermediate Flow......Page 73
4.5 Qualities of Flight......Page 75
4.5.1 Static Stability......Page 76
4.5.2 Gyroscopic Stability......Page 81
4.6 Characteristics of a Family of Sphere Cones......Page 82
4.6.1 Mach Number Influence......Page 83
4.6.2 Influence of Angle of Attack......Page 87
4.6.3 Aerodynamic Modeling for Trajectory Codes......Page 91
4.7 Planetary Entry Capsule......Page 93
5.1 Moments of Inertia......Page 101
5.2 CG Offset and Principal Axis Misalignment......Page 102
6.1 Direction Cosine Matrices......Page 105
6.1.1 Angular Velocity......Page 107
6.1.2 Composition of Angular Velocities......Page 110
6.1.3 Evolution of the Direction Cosine Matrices......Page 111
6.2.1 Euler Rotation Matrix......Page 112
6.2.2 Evolution of Euler Angles......Page 115
6.3.1 Vectorial Representation......Page 119
6.3.2 Quaternion......Page 120
7.1.1 Keplerian Trajectories......Page 125
7.1.2 Ballistic Trajectories......Page 134
7.1.3 Influence of Earth Rotation......Page 144
7.2.1 Rotation Around a Principal Axis......Page 152
7.2.2 Coning Motion......Page 154
8.1 General Equations of Motion......Page 158
8.2 Solutions of General Equations......Page 161
9.1 Allen's Reentry Results......Page 163
9.1.2 Heat Flux......Page 165
9.1.3 Thermal Energy at Stagnation Point......Page 166
9.1.4 Duration of Reentry......Page 168
9.2 Influence of Ballistic Coefficient and Flight Path Angle......Page 170
9.3 Influence of Range......Page 171
10. Decay of Initial Incidence......Page 176
10.1 Zero Spin Rate......Page 178
10.1.1 First Approximate Solution......Page 179
10.1.2 Second Approximate Solution......Page 181
10.2 Nonzero Spin......Page 185
11. End of the Convergence of the Incidence......Page 192
11.1 Linear Equations......Page 193
11.2 Instantaneous Angular Movement......Page 198
11.2.1 Epicyclic Movement......Page 199
11.2.2 Tricyclic Movement......Page 203
11.3 Real Angular Motion......Page 211
12. Roll-lock-in Phenomenon......Page 214
12.1 Association of Aerodynamic Asymmetry and CG Offset......Page 215
12.1.1 Equilibrium on Critical Frequency......Page 217
12.1.2 Lock-in Near Resonance......Page 219
12.1.4 Criterion for Out-of-plane Asymmetries......Page 222
12.2 Isolated Center of Gravity Offset......Page 229
12.3 Isolated Principal Axis Misalignment......Page 230
12.4 Combined CG Offset and Principal Axis Misalignment......Page 233
12.4.1 Out-of-plane Misalignment......Page 234
12.4.2 In-plane Misalignment......Page 239
13.1 Static Instabilities......Page 244
13.2.1 Approximate Study at Low Angle of Attack......Page 251
13.2.2 Examples of Unstable Dynamic Behaviors......Page 254
14.1.1 Initial Conditions......Page 258
14.1.2 Consequences of Drag Dispersions......Page 259
14.1.3 Sensitivity to Initial Conditions......Page 263
14.2.1 Effects of Incidence on Aerodynamic Loads......Page 264
14.2.2 Effects of Initial Angle-of-attack......Page 266
Epilog......Page 294
Exercises......Page 298
1. Equations of Motion Relating to a Reference Frame in Rotation......Page 309
2. Accelerometer Measurements......Page 311
3. Vertical and Apparent Gravity......Page 312
4. Coriolis Force......Page 313
5. Quaternions......Page 314
6. Quaternions and Euler Angles......Page 315
7. Equivalence of Changing Frame and Rotation Quaternion Operators for Euler Angle Sequence......Page 316
8. Pendulum of Foucault......Page 317
11. Energy of a Solid in Free Rotation......Page 323
12. Total Angular Momentum of a Deformable System in Gravitation......Page 324
14. Angular Stabilization with Inertia Wheels......Page 327
15. Balancing Machines......Page 328
16. Aerodynamics of Apollo Reentry Capsule in Continuous Flow......Page 330
17. Aerodynamics of Apollo Reentry Capsule in Free Molecular Flow......Page 332
18. Aerodynamics of Viking Reentry Capsule in Continuous Flow......Page 333
19. Aerodynamics of Viking Reentry Capsule in Free Molecular Flow......Page 336
20. Aerodynamics of Pathfinder Entry Capsule in Intermediate Flow......Page 337
21. Aerodynamics of a Biconic Reentry Vehicle in Continuous Mode......Page 339
22. Targeting Errors of Ballistic Trajectories......Page 342
23. Stability of Free Rotational Motion of a Satellite with Spin......Page 344
24. Allen and Eggers Reentry......Page 345
25. Mars Atmosphere Measurement......Page 346
26. Entry of Meteorites......Page 348
27. Normal Load Factor Related to Incidence......Page 350
28. Artefact in Computer Codes......Page 351
29. Gyroscopic Stabilization of an Entry Capsule......Page 352
30. Effect of Equilibrium Lift on CG Motion......Page 353
31. Effects of Drag Dispersions......Page 356
32. Wind Effects......Page 357
33. Effect of a Sharp Stability Variation, Case of a Plane Oscillation......Page 360
34. Mars Skip Out Trajectories......Page 361