Attitude Coordinate Transformations

25 August 2003

We use four ways of expressing an attitude:

We have routines that let you flow freely between these different represenations. The basic routines do actual math, others just call the basic routines in a certain order. Here is a table that shows how we do the transformations.

Attitude Matrix Quaternion Euler Axis Euler Angles
Attitude Matrix
-
A -> E axis
12-11
12-9
12-10
E-14
Quaternion 12-13b
-
Q -> A
A -> E axis
Q -> A
A -> E angles
Euler Axis 12-7b 12-11
(E-7a)
-
E axis -> A
A -> E angles
Euler Angles 12-20 E-10 E angles -> A
A -> E axis
-

How to use this table: the row indicates where you are, the columns where you want to be.

For example, the routine that converts quaternions into Euler angles (row 2 column 4) first converts the quaternion into an attitude matrix, and that into Euler angles. That particular routine does no math.

When converting an attitude matrix into an Euler axis representation, the table (row 1 column 3) shows that Wertz Equations 12-9 and 12-10 are evaluated (i.e. the math is done here, no other routines called).