Computational Space Flight Mechanics (eBook)

Title Page 1
Preface 4
Acknowledgements 6
Table of Contents 7
Introduction 12
References 15
Coordinate Transformations 17
Basic Rotational Transformations 18
Time Derivative of Vectors in Moving Frames 21
The Velocity Vector 21
The Acceleration Vector 24
The Angular Velocity in a Body Frame: Euler Angles 27
Problems 32
References 33
Transformations between Often Used Coordinate Systems 34
Transformation from Geodetic to Body Frame 34
Transformation from Air Path to Body Frame 35
Transformation from Geodetic to Flight Path Frame 36
Transformation from Planetocentric to Orbital Frame 37
Problems 39
References 40
Kepler’s Laws of Planetary Motion and Newton’s Celestial Mechanics 41
Kepler’s 1. Law 41
Kepler’s 2. Law 42
Kepler’s 3. Law 44
Newton’s Celestial Mechanics 45
Problems 50
References 51
The Two-Body Problem 52
The Equation of Motion 52
The Energy Conservation 54
The Angular Momentum Conservation 55
The Orbit Equation 56
The Various Orbits 58
The Eccentricity e < 1
The Eccentricity e = 1 60
Test Cases for the Three Classes of Orbits 61
Time Dependency of the Orbital Variables r and . and Kepler’s Equation 63
The Elliptical Orbit 66
Solutions of the Elliptical Test Case 1 69
The Hyperbolic Orbit 71
Solutions of the Hyperbolic Test Case 3 73
The Classical Orbital Elements 74
Derivation of Relations 74
Sample Calculations of Test Case 1 Using Orbital Elements 78
Sample Calculations of Test Case 1 Using the General Equations of Planetary Flight 80
Perturbations of Orbital Dynamics 82
Lagrange’s Planet Equations 83
Numerical Solutions of Lagrange’s Planet Equations 87
Numerical Solution of the General Equations of Planetary Flight for an Aspherical Earth 94
Problems 98
References 99
General Equations for Planetary Flight 100
Equations of Translational Motion 100
Flight without Bank Angle 100
Flight with Bank Angle 108
Equations Including Side Forces 110
Flight with Propulsion Force 112
Orbital Flight Around an Aspherical Earth 113
Equations of Rotational Motion 116
Set of Equations for Six Degree of Freedom Simulations 121
Problems 125
References 126
A Resum/'{e} of the Aerothermodynamics of Space Flight Vehicles 128
Conventions for Aerothermodynamic Data 128
Flow Regimes and Physical Phenomena 130
Aerothermodynamic Data of the X-38 Vehicle 133
Data of Longitudinal Motion 135
Data of Lateral Motion 139
Problems 142
References 142
Three and Six Degree of Freedom Trajectory Simulations 144
Three Degree of Freedom Simulation for a Winged Space Vehicle 144
Three Degree of Freedom Simulation for a Non-Winged Space Vehicle 148
Six Degree of Freedom Simulations for a Winged Space Vehicle 152
Flight with Statically Stable Longitudinal Motion 152
Flight with Statically Stable Longitudinal and Yaw Motion 157
Problems 159
References 159
Numerical Applications of the General Equations for Planetary Flight 160
Flight in Geostationary Orbit 161
Flight in Low Earth Orbit 163
Circular Equatorial Orbit (Inclination Angle f = 0) 163
Circular Orbit with Inclination Angle f = 0 165
Elliptical Orbits 167
Elliptical Orbit without Aerodynamic Forces 169
Elliptical Orbit with Aerodynamic Forces 174
Elliptical Orbits with Flight in Other Directions Than West-East 179
Re-entry Flight 181
Deceleration of Space Vehicles and g-Loads 187
Planetary Flight and Aerocapturing Mission 193
Artillery Ballistics 200
Projectile’s Flight without Aerodynamic Drag 200
Projectile’s Flight with Aerodynamic Drag 202
The Principle Equation of Ballistics 206
Approximate Solutions of the Principle Equation of Ballistics 210
Shots of Shells towards the Four Cardinal Points 213
Another Illustrating Case 215
Conclusion 219
Problems 220
References 221
The Earth Atmosphere 222
References 228
Solution of Problems 229
Problems of Chapter 2 229
Problems of Chapter 3 230
Problems of Chapter 4 231
Problems of Chapter 5 234
Problems of Chapter 6 235
Problems of Chapter 7 237
Problems of Chapter 8 238
Problems of Chapter 9 238
Reference 239
Appendix A 240
Our Planetary System 240
The First Four Planets in the Solar System 240
The First Six Planets in the Solar System 241
The Entire Solar System 242
References 243
Appendix B 244
FORTRAN Codes 244
General Equations for Planetary Flight – Three Degree of Freedom Simulation 244
Orbit Determination with Orbital Elements 250
Lagrange’s Planet Equations 255
References 264
Appendix C 265
MATLAB Codes 265
Kepler’s Equation for Elliptical Orbits 265
Area Approach for Elliptical Orbits 267
Area Approach for Hyperbolic Orbits 270
Six Degree of Freedom Simulation 272
References 286
Appendix D 287
Constants, Relations, Units and Conversions 287
Constants and Relations 287
Units and Conversions 288
References 290
Appendix E 291
Symbols 291
Latin Letters 291
Greek Letters 294
Indices 295
Upper Indices 295
Lower Indices 295
Other Symbols 296
Appendix F 297
Glossary, Abbreviations, Acronyms 297
Glossary 297
Abbreviations, Acronyms 298
Name Index 299
Subject Index 301