Mathematics and Physics from the Ground Up
PLEN

Flight dynamics

Attitude and the rigid body in 3D, aircraft stability and modes, dampers and the autopilot, a full six-degree-of-freedom simulation and, at the end, rockets: thrust vectoring and guidance. Running example: a light aircraft at 55 m/s (data: Tewari, example 3.3). Builds on physics (chapter 10) and control engineering (parts I–IV).

I Attitude and the rigid body in 3D

  1. 1Attitude in 3D: rotation matrices, Euler angles, axis–angle and quaternions draft requires: Mathematics 2.2, Mathematics 2.3, Physics 4
  2. 2The rigid body in 3D: the inertia tensor, Euler's equations and the intermediate axis draft requires: Mathematics 4.6, 1
  3. 3Sensor fusion in 3D: attitude estimation with quaternions draft requires: Control engineering 4.5, 1

II The aircraft

  1. 4Static stability and trim: why an aircraft has a tail draft requires: Physics 4, Physics 10
  2. 5Flight in the plane of symmetry: the longitudinal model and stability derivatives draft requires: Mathematics 4.5, Mathematics 4.6, Mathematics 6.2, 4
  3. 6Longitudinal modes: the phugoid and the short period draft requires: Physics 2, 5
  4. 7Lateral motion: roll, spiral and Dutch roll draft requires: 2, 6
  5. 8Stability augmentation: yaw and pitch dampers draft requires: Control engineering 2.2, Control engineering 3.3, 7
  6. 9The autopilot: inner and outer loops draft requires: Control engineering 3.2, Control engineering 3.3, 6, 8
  7. 10Six-degree-of-freedom simulation: putting the aircraft together draft requires: Mathematics 6.2, 1, 2, 9

III The rocket

  1. 11The rocket: attitude and thrust vectoring draft requires: Control engineering 3.3, 2, Astronautics 4
  2. 12Guidance: the nominal trajectory and tracking deviations draft requires: Control engineering 4.3, Control engineering 5.1, 11, Astronautics 4