**ACTION:**- Form a rotation matrix from the Euler angles - three
successive rotations about specified Cartesian axes
(double precision).
**CALL:**`CALL sla_DEULER (ORDER, PHI, THETA, PSI, RMAT)`

**GIVEN:**-

*ORDER***C**specifies about which axes the rotations occur *PHI***D**1st rotation (radians) *THETA***D**2nd rotation (radians) *PSI***D**3rd rotation (radians)

**RETURNED:**-

*RMAT***D(3,3)**rotation matrix

**NOTES:**- 1.
- A rotation is positive when the reference frame rotates anticlockwise as seen looking towards the origin from the positive region of the specified axis.
- 2.
- The characters of ORDER define which axes the three successive
rotations are about. A typical value is `ZXZ', indicating that
RMAT is to become the direction cosine matrix corresponding to
rotations of the reference frame through PHI radians about the
old
*z*-axis, followed by THETA radians about the resulting*x*-axis, then PSI radians about the resulting*z*-axis. - 3.
- The axis names can be any of the following, in any order or
combination: X, Y, Z, uppercase or lowercase, 1, 2, 3. Normal
axis labelling/numbering conventions apply; the
*xyz*() triad is right-handed. Thus, the `ZXZ' example given above could be written `zxz' or `313' (or even `ZxZ' or `3xZ'). ORDER is terminated by length or by the first unrecognized character. Fewer than three rotations are acceptable, in which case the later angle arguments are ignored. Zero rotations produces a unit RMAT.

Starlink User Note 67

P. T. Wallace

12 October 1999

E-mail:ptw@star.rl.ac.uk