Quaternion Math and Relationships in Flight Simulation

Figure 1, at right, coupled with the equations shown following relate the various system conversions:

  1. Euler to Matrix
  2. Matrix to Euler
  3. Quaternion to Matrix
  4. Matrix to Quaternion
  5. Euler to Quaternion
  6. Quaternion to Euler

[The information presented here is derived from a diagram by P.M. O'Neill, September 1981, and from a NASA training manual on quaternions]