Recursive relationships for body axis rotation rates using quaternions

The advantages of using quaternions in attitude computations, strapdown navigation, and a four axis gimbal Space Shuttle inertial management unit, are related to the possibility to define the rotational relationship between two coordinate frames using only four numbers as opposed to nine elements of the direction cosine matrix. Henderson (1983) has developed the recursive relationships for body rotation rates using the direction cosine matrix. The present paper has the objective to develop recursive relationships for body axis rotation rates using quaternions. The number of arithmetic operations needed for the determination of body axis rotation rates by means of the new procedure using quaternions is less than the number of operations required when the direction cosine matrix approach is employed. Storage requirements are also reduced.