Procedure

     DROTAT ( Derivative of a rotation matrix )

     SUBROUTINE DROTAT ( ANGLE, IAXIS, DMOUT )

Abstract

     Calculate the derivative with respect to the angle of rotation
     of a 3x3 coordinate system rotation matrix generated by a
     rotation of a specified angle about a specified axis.

Required_Reading

     ROTATION

Keywords

     DERIVATIVE
     MATRIX
     ROTATION

Declarations

     IMPLICIT NONE

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

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     ANGLE      I   Angle of rotation (radians).
     IAXIS      I   Coordinate axis number (X=1, Y=2, Z=3).
     DMOUT      O   Derivative of rotation matrix [ANGLE] w.r.t. angle
                                                         IAXIS

Detailed_Input

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

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

              Together ANGLE and IAXIS define the coordinate system
              rotation [ANGLE]     .
                              IAXIS

Detailed_Output

     DMOUT    is the derivative of the rotation matrix with respect to
              the angle of rotation. That is, DMOUT is the derivative
              with respect to ANGLE of the matrix [ANGLE]     .
                                                         IAXIS

              (The rotation matrix being differentiated describes
              the rotation of the COORDINATE system through ANGLE
              radians about the axis whose index is IAXIS.)

Parameters

     None.

Exceptions

     1)  If the axis index is not in the range 1 to 3, the error
         SPICE(BADAXIS) is signaled.

Files

     None.

Particulars

     A coordinate system rotation by ANGLE radians rotation about
     the first, i.e. x-axis, [ANGLE]  is described by
                                    1

           |  1        0          0      |
           |  0   cos(ANGLE) sin(ANGLE)  |
           |  0  -sin(ANGLE) cos(ANGLE)  |

     A coordinate system rotation by ANGLE radians rotation about the
     second, i.e. y-axis, [ANGLE]  is described by
                                 2

           |  cos(ANGLE)  0  -sin(ANGLE)  |
           |      0       1        0      |
           |  sin(ANGLE)  0   cos(ANGLE)  |

     A coordinate system rotation by ANGLE radians rotation about
     the third, i.e. z-axis, [ANGLE]  is described by
                         3

           |  cos(ANGLE) sin(ANGLE)   0   |
           | -sin(ANGLE) cos(ANGLE)   0   |
           |       0          0       1   |

     The derivatives of these matrices are:

     about the x-axis

           |  0        0           0      |
           |  0  -sin(ANGLE)  cos(ANGLE)  |
           |  0  -cos(ANGLE) -sin(ANGLE)  |

     about the y-axis

           | -sin(ANGLE)  0  -cos(ANGLE)  |
           |      0       0        0      |
           |  cos(ANGLE)  0  -sin(ANGLE)  |

     about the z-axis

           | -sin(ANGLE)  cos(ANGLE)   0   |
           | -cos(ANGLE) -sin(ANGLE)   0   |
           |       0           0       0   |

Examples

     If ROTATE is called from a FORTRAN program as follows:

           CALL DROTAT (PI()/4, 3, DMOUT)

     then DMOUT will be

           |-SQRT(2)/2   SQRT(2)/2   0  |
           |-SQRT(2)/2  -SQRT(2)/2   0  |
           |     0           0       0  |

Restrictions

     None.

Literature_References

     None.

Author_and_Institution

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

Version

    SPICELIB Version 1.1.0, 12-AUG-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, 05-NOV-1990 (WLT)