BRA LEC NOTES ,FLIGHT MECH

BRA LEC NOTES ,FLIGHT MECH - 1 AAE 421 Notes Martin Corless...

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Unformatted text preview: 1 AAE 421 Notes Martin Corless January 13, 2010 2 Contents 1 Introduction 9 1.1 Ingredients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Some general concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.1 Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.2 Systems and control . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 State space representation of dynamical systems 11 2.1 Linear examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.1 A rst example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.2 The unattached mass . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.3 Spring-mass-damper . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.4 A simple structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Nonlinear examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.1 Planar solid pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.2 Body in central force motion . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.3 The Lunicycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 General representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3.1 Higher order ODE descriptions . . . . . . . . . . . . . . . . . . . . . 18 2.4 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.5 Vector representation of dynamical systems . . . . . . . . . . . . . . . . . . . 26 2.6 Solutions and equilibrium states . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.6.1 Controlled equilibrium states and trim conditions . . . . . . . . . . . 31 2.7 Numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.7.1 MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.7.2 SIMULINK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3 Equations of motion 35 3.1 Aerodynamic forces and trim . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.1.1 Uniform translation of a rigid body in air . . . . . . . . . . . . . . . . 37 3.1.2 Some trim conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2 Bodies in drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.2.1 Simple oscillator in drag . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2.2 The cannonball: ballistics in drag . . . . . . . . . . . . . . . . . . . . 42 3 4 CONTENTS 3.2.3 A simple weathercock . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.3 Lift, drag and pitching moment . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.4 Trim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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This note was uploaded on 02/22/2011 for the course AAE 421 taught by Professor Prof.carollivermore during the Spring '11 term at MIT.

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BRA LEC NOTES ,FLIGHT MECH - 1 AAE 421 Notes Martin Corless...

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