SLA_EULER

Rotation Matrix from Euler Angles

ACTION:

Form a rotation matrix from the Euler angles – three successive rotations about specified Cartesian axes (single precision).

CALL:

CALL sla_EULER (ORDER, PHI, THETA, PSI, RMAT)

GIVEN:

RETURNED:

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. In detail:

• 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 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.

(3)

Zero rotations produces the identity RMAT.