Procedure

     ROTATE ( Generate a rotation matrix )

     SUBROUTINE ROTATE ( ANGLE, IAXIS, MOUT )

Abstract

     Calculate the 3x3 rotation matrix generated by a rotation
     of a specified angle about a specified axis. This rotation
     is thought of as rotating the coordinate system.

Required_Reading

     None.

Keywords

     MATRIX
     ROTATION

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION   ANGLE
     INTEGER            IAXIS
     DOUBLE PRECISION   MOUT  ( 3,3 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     ANGLE      I   Angle of rotation (radians).
     IAXIS      I   Axis of rotation (X=1, Y=2, Z=3).
     MOUT       O   Resulting rotation matrix [ANGLE]
                                                    IAXIS

Detailed_Input

     ANGLE    is the angle, given in radians, through which the
              rotation is performed.

     IAXIS    is the index of the axis of rotation. The X, Y, and Z
              axes have indices 1, 2 and 3 respectively.

Detailed_Output

     MOUT     is the rotation matrix which describes the rotation of
              a reference frame through ANGLE radians about the axis
              whose index is IAXIS.

Parameters

     None.

Exceptions

     Error free.

     1)  If the axis index is not in the range 1 to 3, it will be
         treated the same as that integer 1, 2, or 3 that is congruent
         to it mod 3.

Files

     None.

Particulars

     A rotation about the first, i.e. x-axis, is described by

        .-                            -.
        |  1        0           0      |
        |  0   cos(theta)  sin(theta)  |
        |  0  -sin(theta)  cos(theta)  |
        `-                            -'

     A rotation about the second, i.e. y-axis, is described by

        .-                            -.
        |  cos(theta)  0  -sin(theta)  |
        |      0       1        0      |
        |  sin(theta)  0   cos(theta)  |
        `-                            -'

     A rotation about the third, i.e. z-axis, is described by

        .-                            -.
        |  cos(theta)  sin(theta)  0   |
        | -sin(theta)  cos(theta)  0   |
        |       0          0       1   |
        `-                            -'

     ROTATE decides which form is appropriate according to the value
     of IAXIS.

Examples

     If ROTATE is called from a FORTRAN program as follows:

           CALL ROTATE (PI/4, 3, MOUT)

     then MOUT will be given by

                  | SQRT(2)/2   SQRT(2)/2   0  |
           MOUT = |-SQRT(2)/2   SQRT(2)/2   0  |
                  |     0           0       1  |

Restrictions

     None.

Literature_References

     None.

Author_and_Institution

     J. Diaz del Rio    (ODC Space)
     W.M. Owen          (JPL)
     W.L. Taber         (JPL)

Version

    SPICELIB Version 1.1.0, 25-MAY-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard.

    SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)

        Comment section for permuted index source lines was added
        following the header.

    SPICELIB Version 1.0.0, 31-JAN-1990 (WMO) (WLT)