Atmospheric And Space Flight Dynamics

by Tewari, Ashish

• ISBN13: 9780817644376
• ISBN10: 0817644377
• Format: Hardcover
• Copyright: 2006-11-30
• Publisher: Birkhauser

Summary

Modern aerospace vehicles, such as the space shuttle, other launch vehicles, and long-range ballistic missiles, do not discriminate between atmospheric and space flight. Most texts on flight dynamics, however, make this artificial distinction and therefore do not simultaneously cover aircraft and spacecraft. Bridging this gap in the literature, Atmospheric and Space Flight Dynamics is a unified presentation, demonstrating that the two disciplines have actually evolved from the same set of physical principles. Readers are introduced to a broad range of modern topics in an accessible, yet mathematically rigorous presentation, with many numerical examples and simulations utilizing MATLAB and Simulink fully integrated throughout the work. The simulations presented---usually not found in books on the same topic---are both realistic and instructive. From the examples, readers may easily build their own simulations for aircraft, missiles, launch vehicles, re-entry vehicles, and spacecraft. The author uses the software as an instructional, hands-on tool, moving away from the "cook book" approach found in other works. Replete with illustrations, end-of-chapter exercises, and selected solutions, the work is primarily useful as a textbook for advanced undergraduate and beginning graduate-level students. The book is also an excellent reference or self-study guide for researchers and practitioners in aerospace engineering, aviation, mechanical engineering, dynamics, astrodynamics, aeronautics, and astronautics. The MATLAB/Simulink codes used in this book may be downloaded from http://home.iitk.ac.in/~ashtew/page10.html .

Table of Contents

Preface	v
1 Introduction	1
1.1 Aims and Objectives	1
1.2 Atmospheric and Space Flight	1
1.3 Modeling and Simulation	3
1.4 Summary	7
2 Attitude and Kinematics of Coordinate Frames	9
2.1 Aims and Objectives	9
2.2 Basic Definitions and Vector Operations	9
2.3 Coordinate Systems and Rotation Matrix	13
2.4 Euler Axis and Principal Angle	16
2.5 Euler Angles	19
2.6 Euler Symmetric Parameters (Quaternion)	23
2.7 Rodrigues Parameters (Gibbs Vector)	27
2.8 Modified Rodrigues Parameters	28
2.9 Attitude Kinematics	30
2.10 Summary	42
Exercises	42
3 Planetary Form and Gravity	45
3.1 Aims and Objectives	45
3.2 Newton's Law of Gravitation	45
3.3 Gravity of an Axisymmetric Planet	46
3.4 Radius of a Nonspherical Planet	54
3.5 Gravitational Anomalies	56
3.6 Summary	57
Exercises	58
4 Translational Motion of Aerospace Vehicles	59
4.1 Aims and Objectives	59
4.2 Particle and Body	59
4.2.1 Particle Kinematics in a Moving Frame	61
4.3 Newton's Laws of Motion	70
4.3.1 Variable Mass Bodies	74
4.3.2 Rotation and Translation of a Body	76
4.4 Energy and Angular Momentum	81
4.4.1 The N-Body Problem	87
4.5 The Two-Body Problem	89
4.5.1 Geometry of Two-Body Trajectories	94
4.5.2 Lagrange's Coefficients	98
4.5.3 Kepler's Equation for Elliptical Orbit	101
4.5.4 Position and Velocity in a Hyperbolic Trajectory	108
4.5.5 Parabolic Escape Trajectory	111
4.6 Summary	112
Exercises	113
5 Orbital Mechanics	117
5.1 Aims and Objectives	117
5.2 Celestial Frame and Orbital Elements	117
5.2.1 Orbit Determination	120
5.3 Spherical Celestial Coordinates and Local Horizon	123
5.4 Planet Fixed Frame	126
5.5 Single Impulse Orbital Maneuvers	129
5.6 Multi-Impulse Orbital Transfer	135
5.7 Relative Motion in Orbit	138
5.8 Lambert's Problem	140
5.9 Summary	149
Exercises	149
6 Perturbed Orbits	153
6.1 Aims and Objectives	153
6.2 Perturbing Acceleration	153
6.3 Effects of Planetary Oblateness	154
6.3.1 Sun Synchronous Orbits	156
6.3.2 Molniya Orbits	157
6.4 Effects of Atmospheric Drag	157
6.5 Third-Body Perturbation and Interplanetary Flight	159
6.5.1 Sphere of Influence and Patched Conics	161
6.6 Numerical Solution to the Perturbed Problem	164
6.7 Summary	170
Exercises	170
7 The Three-Body Problem	173
7.1 Aims and Objectives	173
7.2 Equations of Motion	173
7.3 Lagrange's Solution	175
7.4 Restricted Three-Body Problem	178
7.4.1 Lagrangian Points and Their Stability	180
7.4.2 Jacobi's Integral	183
7.4.3 Numerical Solution of the Restricted Problem	185
7.5 Summary	191
Exercises	191
8 Rocket Propulsion	193
8.1 Aims and Objectives	193
8.2 The Rocket Engine	193
8.3 The Rocket Equation and Staging	197
8.3.1 The Single-Stage Rocket	199
8.3.2 The Multi-Stage Rocket	201
8.3.3 Parallel Staging	205
8.3.4 Mission Trade-Off	208
8.4 Optimal Rockets	210
8.4.1 Optimal Two-Stage Rocket	211
8.4.2 Optimal Three-Stage Rocket	213
8.5 Summary	216
Exercises	216
9 Planetary Atmosphere	219
9.1 Aims and Objectives	219
9.2 Introduction	219
9.3 Hydrostatic Equilibrium	221
9.4 Standard Atmosphere	223
9.5 Exponential Model for Planetary Atmospheres	230
9.6 Summary	231
Exercises	231
10 Elements of Aerodynamics	233
10.1 Aims and Objectives	233
10.2 Basic Concepts	233
10.2.1 Aerodynamic Force and Moment	233
10.3 Fluid Dynamics	238
10.3.1 Flow Regimes	238
10.3.2 Continuum Flow	239
10.3.3 Continuum Viscous Flow and the Boundary Layer	242
10.3.4 Continuum Compressible Flow	247
10.3.5 Rarefied Flow	253
10.4 Force and Moment Coefficients	255
10.5 Summary	261
Exercises	262
11 Airbreathing Propulsion	265
11.1 Aims and Objectives	265
11.2 Ideal Momentum Theory	265
11.3 Propeller Engines	268
11.4 Jet Engines	273
11.4.1 Ramjet Engines	273
11.4.2 Turbojet and Turbofan Engines	275
11.5 Summary	279
Exercises	280
12 Atmospheric and Transatmospheric Trajectories	283
12.1 Aims and Objectives	283
12.2 Equations of Motion	283
12.3 Airplane Flight Paths	290
12.3.1 Long-Range Cruising Flight	297
12.3.2 Effect of a Steady Wind on an Airplane Flight	304
12.3.3 Take-Off Maneuver	308
12.3.4 Accelerated Climb	316
12.3.5 Maneuvers and Supermaneuvers	325
12.4 Entry Trajectories	334
12.4.1 Ballistic Entry	338
12.4.2 Maneuvering Entry	349
12.5 Rocket Ascent Trajectories	353
12.6 Summary	363
Exercises	364
13 Attitude Dynamics	369
13.1 Aims and Objectives	369
13.2 Euler Equations of Rotational Motion	369
13.3 Rotational Kinetic Energy	373
13.4 Principal Body Frame	374
13.5 Torque-Free Rotation of Spacecraft	376
13.5.1 Axisymmetric Spacecraft	377
13.5.2 Asymmetric Spacecraft	381
13.6 Spacecraft with Attitude Thrusters	384
13.6.1 Single-Axis Impulsive Rotation	386
13.6.2 Attitude Maneuvers of Spin-Stabilized Spacecraft	387
13.6.3 Asymmetric Spacecraft Maneuvers by Attitude Thrusters	394
13.7 Spacecraft with Rotors	397
13.7.1 Variable-Speed Control Moment Gyroscope	400
13.7.2 Dual-Spin Spacecraft	404
13.7.3 Gravity Gradient Spacecraft	409
13.8 Attitude Motion in Atmospheric Flight	414
13.8.1 Equations of Motion with Small Disturbance	416
13.8.2 Stability Derivatives and De-coupled Dynamics	425
13.8.3 Longitudinal Dynamics	427
13.8.4 Airplane Longitudinal Modes	431
13.8.5 Lateral Dynamics	436
13.8.6 Airplane Lateral Modes	439
13.8.7 Rotational Motion of a Launch Vehicle	442
13.8.8 Inertia Coupled Dynamics	446
13.9 Summary	450
Exercises	452
14 Attitude Control Systems	457
14.1 Aims and Objectives	457
14.2 Introduction	457
14.3 Linear Systems	461
14.3.1 Time-invariant, Linear Systems	462
14.3.2 Linear Stability Criteria	463
14.3.3 Transfer Matrix and Second-Order Systems	465
14.4 Basic Closed-Loop Systems	468
14.5 Implementation of Control System Elements	472
14.5.1 Gyroscopic Sensors	474
14.6 Single-Axis, Closed-Loop Attitude Control	479
14.6.1 Control of Single-Axis Spacecraft Maneuvers	479
14.6.2 Roll Control of Aircraft and Missiles	484
14.7 Multi-Axis Closed-Loop Attitude Control	486
14.7.1 Attitude Stabilization of a Launch Vehicle	486
14.7.2 Reaction Wheel and Magnetic Denutation of Gravity Gradient Spacecraft	491
14.7.3 Control of Aircraft and Missiles with Inertia Coupling	499
14.8 Summary	501
Exercises	504
15 Advanced Modeling and Simulation Concepts	507
15.1 Aims and Objectives	507
15.2 Six-Degree-of-Freedom Simulation	507
15.2.1 Wing-Rock Motion of a Fighter Airplane	510
15.2.2 Trajectory and Attitude of a Ballistic Entry Vehicle	512
15.3 Structural Dynamics	518
15.4 Unsteady Aerodynamics and Aeroelasticity	521
15.5 Propellant Slosh Dynamics	527
15.6 Summary	528
Exercises	529
A Numerical Integration of Ordinary Differential Equations	531
A.1 Fixed-Step Runge—Kutta Algorithms	531
A.2 Variable-Step Runge—Kutta Algorithms	532
A.3 Runge—Kutta—Nystrom Algorithms	534
Answers to Selected Exercises	537
References	543
Index	547