TABLE OF CONTENTS Early in the aerospace program, especially as computer system resources became available to the aerospace engineer, Kimball73 realized the importance of the 12 Euler rotation transformation matrices, which have now become an integral part of the analysis of the dynamics of flight vehicles. Today, the Euler transformation matrices remain an essential part of these analyses and are required in many aerospace applications. The 12 Euler transformation matrices, as described in Sec. 1.3.3, are presented here for each rotation sequence based on the single-axis rotation Eqs. (1.81), (1.82), and (1.83). The Euler matrices, as presented in this appendix, transform vectors from the system that has been rotated into vectors in the system considered to be stationary. Also presented are the equations for the quaternion as a function of the Euler angles and the Euler angles as a function of the matrix elements for each rotation sequence.74
NOTE: This Euler sequence of rotations is used in GNC software for transformations and representations for the attitude-direction indicators. It is also used in the analysis of aeronautical problems and is referred to as the standard roll-pitch-yaw sequence.
