
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 zaxis, followed by THETA radians about the resulting xaxis, then PSI
radians about the resulting zaxis.

(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 ($\equiv 123$)
triad is righthanded. 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 the identity RMAT.