AE345CourseNotesMarch92008 - AIRCRAFT FLIGHT DYNAMICS AND...

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AIRCRAFT FLIGHT DYNAMICS AND CONTROL March 9, 2008 Dennis S. Bernstein Department of Aerospace Engineering The University of Michigan Ann Arbor, MI 48109-2140 [email protected] C o p y r i g h t 2 0 0 8
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Contents Chapter 1. Review of Kinematics 3 1.1 Points, Particles, and Bodies 3 1.2 Physical and Mathematical Vectors 3 1.3 Dot Product 5 1.4 Angle Vector and Cross Product 6 1.5 Frames 8 1.6 Signed Angles 11 1.7 Particle-Fixed Frames 11 1.8 Physical Matrices 12 1.9 Physical Cross Product 15 1.10 Orientation Matrices 19 1.11 Euler Angles 24 1.12 Frame Derivatives 28 1.13 Momentum 29 1.14 Angular Momentum 30 1.15 Angular Velocity Vector 30 1.16 Euler Angle Derivatives 35 1.17 Transport Theorem 36 1.18 Double Transport Theorem 37 1.19 Solid and Open Frame Dots 38 1.20 Problems 38 Chapter 2. Aircraft Kinematics 41 2.1 Frames Used in Aircraft Dynamics 41 2.2 Velocity Vector 44 2.3 Rotational Kinematics 49 2.4 Vector Derivatives in Rotating Frames 51 2.5 Cross Product 52 2.6 Problems 53 Chapter 3. Review of Dynamics 57 3.1 Newton’s First Law for Particles 57 3.2 Newton’s Second Law for Particles 58 3.3 Forces and Moments 58
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iv CONTENTS 3.4 Change in Angular Momentum 60 3.5 Continuum Bodies 65 3.6 Momentum and Angular Momentum Relative to Center of Mass 66 3.7 The Inertia Matrix 70 3.8 Problems 71 Chapter 4. Aircraft Dynamics 73 4.1 Flight Dynamics and Control 73 4.2 History of Aircraft Stability and Control 73 4.3 Aerodynamic Forces 73 4.4 Translational Momentum Equations 75 4.5 Rotational Momentum Equations 79 4.6 Aircraft Equations of Motion Resolved in F AC 81 4.7 Problems 82 Chapter 5. Linearization 85 5.1 Taylor series 85 5.2 Alternative Linearization Procedure 86 5.3 Trigonometric Functions 87 5.4 Steady Flight 87 5.5 Linearization in F AC 88 5.6 Linearization in F S f 90 5.7 Problems 92 Chapter 6. Static Stability and Stability Derivatives 95 6.1 Control Surface Deflections 95 6.2 Aerodynamic Force Coefficients 95 6.3 Linearization of Forces in F S f 98 6.4 Aerodynamic Moment Coefficients 104 6.5 Linearization of Moments in F S f 114 6.6 Effect of Adverse Control Derivatives 115 6.7 Problems 117 Chapter 7. Linearized Equations of Motion 119 7.1 Longitudinal Equations of Motion 119 7.2 Lateral Equations of Motion 120 7.3 Linearized Longitudinal Equations and Transfer Functions 122 7.4 Linearized Lateral Equations and Transfer Functions 124 7.5 Problems 126 Chapter 8. Analysis of Flight Modes 127 8.1 Eigenflight 127 8.2 Phugoid Mode 128 8.3 Short Period Mode 131
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CONTENTS v 8.4 Phugoid Approximation 132 8.5 Short Period Approximation 133 8.6 Problems 134 Chapter 9. Control Concepts 137 9.1 Problems 137 Chapter 10. Control of Aircraft 141 10.1 Problems 141 Appendix A. Mathematical Background 143 A.1 Vectors and Matrices 143 A.2 Complex Numbers, Vectors and Matrices 145 A.3 Eigenvalues and Eigenvectors 148 A.4 Single-Degree-of-Freedom Systems 151 A.5 Matrix Differential Equations 153 A.6 Eigensolutions 155 A.7 State Space Form 156 A.8 Linear Systems with Forcing 157 A.9 Standard Input Signals 157 A.10 Laplace Transforms 160 A.11 Solution of ODE’s 162 A.12 Initial Value and Slope Theorems 164 A.13 Final Value Theorem 164 A.14 Laplace Transforms of State Space Models 165 A.15 Pole Locations and Response 167 A.16 Stability 170 A.17
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