Weiland Computational Space Flight Mechanics

1. Auflage 2010
ISBN: 978-3-642-13583-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 300 Seiten

Themechanicsofspace?ightisan olddiscipline.Itstopicoriginallywasthemotion of planets, moons and other celestial bodies in gravitational ?elds. Kepler's (1571 - 1630) observations and measurements have led to probably the ?rst mathematical description of planet's motion. Newton (1642 - 1727) gave then, with the devel- ment of his principles of mechanics, the physical explanation of these motions. Since then man has started in the second half of the 20th centuryto capture ph- ically the Space in the sense that he did develop arti?cial celestial bodies, which he brought into Earth's orbits, like satellites or space stations, or which he did send to planets or moons of our planetary system, like probes, or by which p- ple were brought to the moon and back, like capsules. Further he developed an advanced space transportation system, the U.S. Space Shuttle Orbiter, which is the only winged space vehicle ever in operation. In the last two and a half decades there were several activities in the world in order to succeed the U.S. Orbiter, like the HERMES project in Europe, the HOPE project in Japan, the X-33, X-34 and X-37 studies and demonstrators in the United States and the joint U.S. - European project X-38. However, all these projects were cancelled. The motion of these vehicles can be described by Newton's equation of motion.

Autoren/Hrsg.

Weiland, Claus

Inhaltsverzeichnis

1;Title Page;1
2;Preface;4
3;Acknowledgements;6
4;Table of Contents;7
5;Introduction;12
5.1;References;15
6;Coordinate Transformations;17
6.1;Basic Rotational Transformations;18
6.2;Time Derivative of Vectors in Moving Frames;21
6.2.1;The Velocity Vector;21
6.2.2;The Acceleration Vector;24
6.3;The Angular Velocity in a Body Frame: Euler Angles;27
6.4;Problems;32
6.5;References;33
7;Transformations between Often Used Coordinate Systems;34
7.1;Transformation from Geodetic to Body Frame;34
7.2;Transformation from Air Path to Body Frame;35
7.3;Transformation from Geodetic to Flight Path Frame;36
7.4;Transformation from Planetocentric to Orbital Frame;37
7.5;Problems;39
7.6;References;40
8;Kepler’s Laws of Planetary Motion and Newton’s Celestial Mechanics;41
8.1;Kepler’s 1. Law;41
8.2;Kepler’s 2. Law;42
8.3;Kepler’s 3. Law;44
8.4;Newton’s Celestial Mechanics;45
8.5;Problems;50
8.6;References;51
9;The Two-Body Problem;52
9.1;The Equation of Motion;52
9.2;The Energy Conservation;54
9.3;The Angular Momentum Conservation;55
9.4;The Orbit Equation;56
9.5;The Various Orbits;58
9.5.1;The Eccentricity e < 1;58
9.5.2;The Eccentricity e = 1;60
9.6;Test Cases for the Three Classes of Orbits;61
9.7;Time Dependency of the Orbital Variables r and . and Kepler’s Equation;63
9.7.1;The Elliptical Orbit;66
9.7.2;Solutions of the Elliptical Test Case 1;69
9.7.3;The Hyperbolic Orbit;71
9.7.4;Solutions of the Hyperbolic Test Case 3;73
9.8;The Classical Orbital Elements;74
9.8.1;Derivation of Relations;74
9.8.2;Sample Calculations of Test Case 1 Using Orbital Elements;78
9.8.3;Sample Calculations of Test Case 1 Using the General Equations of Planetary Flight;80
9.9;Perturbations of Orbital Dynamics;82
9.9.1;Lagrange’s Planet Equations;83
9.9.2;Numerical Solutions of Lagrange’s Planet Equations;87
9.9.3;Numerical Solution of the General Equations of Planetary Flight for an Aspherical Earth;94
9.10;Problems;98
9.11;References;99
10;General Equations for Planetary Flight;100
10.1;Equations of Translational Motion;100
10.1.1;Flight without Bank Angle;100
10.1.2;Flight with Bank Angle;108
10.1.3;Equations Including Side Forces;110
10.1.4;Flight with Propulsion Force;112
10.1.5;Orbital Flight Around an Aspherical Earth;113
10.2;Equations of Rotational Motion;116
10.3;Set of Equations for Six Degree of Freedom Simulations;121
10.4;Problems;125
10.5;References;126
11;A Resum\'{e} of the Aerothermodynamics of Space Flight Vehicles;128
11.1;Conventions for Aerothermodynamic Data;128
11.2;Flow Regimes and Physical Phenomena;130
11.3;Aerothermodynamic Data of the X-38 Vehicle;133
11.3.1;Data of Longitudinal Motion;135
11.3.2;Data of Lateral Motion;139
11.4;Problems;142
11.5;References;142
12;Three and Six Degree of Freedom Trajectory Simulations;144
12.1;Three Degree of Freedom Simulation for a Winged Space Vehicle;144
12.2;Three Degree of Freedom Simulation for a Non-Winged Space Vehicle;148
12.3;Six Degree of Freedom Simulations for a Winged Space Vehicle;152
12.3.1;Flight with Statically Stable Longitudinal Motion;152
12.3.2;Flight with Statically Stable Longitudinal and Yaw Motion;157
12.4;Problems;159
12.5;References;159
13;Numerical Applications of the General Equations for Planetary Flight;160
13.1;Flight in Geostationary Orbit;161
13.2;Flight in Low Earth Orbit;163
13.2.1;Circular Equatorial Orbit (Inclination Angle f = 0);163
13.2.2;Circular Orbit with Inclination Angle f = 0;165
13.3;Elliptical Orbits;167
13.3.1;Elliptical Orbit without Aerodynamic Forces;169
13.3.2;Elliptical Orbit with Aerodynamic Forces;174
13.3.3;Elliptical Orbits with Flight in Other Directions Than West-East;179
13.4;Re-entry Flight;181
13.4.1;Deceleration of Space Vehicles and g-Loads;187
13.5;Planetary Flight and Aerocapturing Mission;193
13.6;Artillery Ballistics;200
13.6.1;Projectile’s Flight without Aerodynamic Drag;200
13.6.2;Projectile’s Flight with Aerodynamic Drag;202
13.6.3;The Principle Equation of Ballistics;206
13.6.4;Approximate Solutions of the Principle Equation of Ballistics;210
13.6.5;Shots of Shells towards the Four Cardinal Points;213
13.7;Another Illustrating Case;215
13.8;Conclusion;219
13.9;Problems;220
13.10;References;221
14;The Earth Atmosphere;222
14.1;References;228
15;Solution of Problems;229
15.1;Problems of Chapter 2;229
15.2;Problems of Chapter 3;230
15.3;Problems of Chapter 4;231
15.4;Problems of Chapter 5;234
15.5;Problems of Chapter 6;235
15.6;Problems of Chapter 7;237
15.7;Problems of Chapter 8;238
15.8;Problems of Chapter 9;238
15.9;Reference;239
16;Appendix A;240
16.1;Our Planetary System;240
16.2;The First Four Planets in the Solar System;240
16.3;The First Six Planets in the Solar System;241
16.4;The Entire Solar System;242
16.5;References;243
17;Appendix B;244
17.1;FORTRAN Codes;244
17.2;General Equations for Planetary Flight – Three Degree of Freedom Simulation;244
17.3;Orbit Determination with Orbital Elements;250
17.4;Lagrange’s Planet Equations;255
17.5;References;264
18;Appendix C;265
18.1;MATLAB Codes;265
18.2;Kepler’s Equation for Elliptical Orbits;265
18.3;Area Approach for Elliptical Orbits;267
18.4;Area Approach for Hyperbolic Orbits;270
18.5;Six Degree of Freedom Simulation;272
18.6;References;286
19;Appendix D;287
19.1;Constants, Relations, Units and Conversions;287
19.2;Constants and Relations;287
19.3;Units and Conversions;288
19.4;References;290
20;Appendix E;291
20.1;Symbols;291
20.2;Latin Letters;291
20.3;Greek Letters;294
20.4;Indices;295
20.4.1;Upper Indices;295
20.4.2;Lower Indices;295
20.4.3;Other Symbols;296
21;Appendix F;297
21.1;Glossary, Abbreviations, Acronyms;297
21.2;Glossary;297
21.3;Abbreviations, Acronyms;298
22;Name Index;299
23;Subject Index;301