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]