Procedure

     PCKE20 ( PCK, evaluate record, type 20 )

     SUBROUTINE PCKE20 ( ET, RECORD, EULANG )

Abstract

     Evaluate a single PCK data record from a segment of type 20
     (Chebyshev Polynomials, rotation derivative only).

Required_Reading

     PCK

Keywords

     ORIENTATION
     ROTATION
     TRANSFORMATION

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION      ET
     DOUBLE PRECISION      RECORD   ( * )
     DOUBLE PRECISION      EULANG   ( 6 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     ET         I   Evaluation epoch.
     RECORD     I   Data record.
     EULANG     O   Euler angles and their derivatives.

Detailed_Input

     ET       is an epoch at which the Euler angles state is to be
              computed. The epoch is represented as seconds past
              J2000 TDB.


     RECORD   is a data record which, when evaluated at epoch ET,
              will yield Euler angles and Euler angle rates
              representing the orientation and angular velocity,
              with respect to its base frame, of the reference
              frame associated with the input record.

              The structure of the record is as follows:

                 +--------------------------------------+
                 | record size (excluding this element) |
                 +--------------------------------------+
                 | Coverage interval midpoint           |
                 +--------------------------------------+
                 | Coverage interval radius             |
                 +--------------------------------------+
                 | Coeffs for ANGLE_1 rate              |
                 +--------------------------------------+
                 | Coeffs for ANGLE_2 rate              |
                 +--------------------------------------+
                 | Coeffs for ANGLE_3 rate              |
                 +--------------------------------------+
                 | ANGLE_1 at interval midpoint         |
                 +--------------------------------------+
                 | ANGLE_2 at interval midpoint         |
                 +--------------------------------------+
                 | ANGLE_3 at interval midpoint         |
                 +--------------------------------------+

              In the above record

                 - Times are expressed as seconds past J2000 TDB.
                 - Angular components have units of radians.
                 - Rate coefficients have units of radians/s.

              RECORD must be declared by the caller with size large
              enough to accommodate the largest record that can be
              returned by PCKR20.

Detailed_Output

     EULANG   is a 6-vector containing Euler angles and their
              derivatives at time ET. The angles occupy the first
              three elements of EULANG; the rates follow. The order
              of the components is

                 ( ANGLE_1, ANGLE_2, ANGLE_3,
                   rate_1,  rate_2,  rate_3  )

              The angular units are radians; the rate units are
              radians/second.

              The Euler angles represent the orientation, relative
              to its base frame, of the PCK frame associated with
              the input record. The angles, which are numbered
              according to their ordinal position in the logical
              records, define a transformation matrix R as follows:

                 R = [ ANGLE_3 ]  [ ANGLE_2 ]  [ ANGLE_1 ]
                                3            1            3

              Here the notation

                 [ THETA ]
                          i

              denotes a reference frame rotation of THETA radians
              in the right-hand sense about the ith coordinate
              axis. See the Rotation Required Reading for further
              discussion of this notation.

              The matrix R transforms vectors expressed in the base
              frame to vectors expressed in the PCK frame associated
              with RECORD by left multiplication:

                 V    = R * V
                  PCK        FRAME

              In cases where the PCK frame is a body-fixed,
              right-handed frame with its +Z axis aligned with a
              body's north pole, the orientation angles are related
              to right ascension (RA) and declination (DEC) of the
              PCK frame's north pole, and prime meridian
              orientation (W), by the equations

                 ANGLE_1 = RA   + pi/2 radians
                 ANGLE_2 = pi/2 - DEC  radians
                 ANGLE_3 = W           radians

Parameters

     None.

Exceptions

     1)  If the input record contains an invalid coefficient count, an
         error is signaled by a routine in the call tree of this
         routine.

     2)  If the input record contains invalid domain transformation
         parameters, an error is signaled by a routine in the
         call tree of this routine.

Files

     None.

Particulars

     The exact format and structure of type 20 (Chebyshev polynomials,
     position only) segments are described in the PCK Required Reading
     file.

     A type 20 segment contains three sets of Chebyshev coefficients,
     one set each for the derivatives with respect to time of the
     Euler angles phi, delta and psi. PCKE20 calls the routine SPKE20
     for each set to evaluate the polynomial and its first derivative.

Examples

     The PCKEnn routines are almost always used in conjunction with
        the corresponding PCKRnn routines, which read the records from
        binary PCK files.

        The data returned by the PCKRnn routine are in their rawest
        form, taken directly from the segment. As such, they will be
        meaningless to a user unless he/she understands the structure
        of the data type completely. Given that understanding, however,
        the PCKRnn routines might be used to examine raw segment data
        before evaluating it with the PCKEnn routines.


        Here we load a binary PCK files and use PCKE20 to get the
        Euler angles.

     C
     C     Load binary PCK file.
     C
           CALL PCKLOF ('example.pck', HANDLE)

     C
     C     Get a segment applicable to a specified body and epoch.
     C
           CALL PCKSFS ( BODY, ET, HANDLE, DESCR, IDENT, FOUND )

           IF ( FOUND ) THEN
     C
     C        Look at parts of the descriptor.
     C
              CALL DAFUS ( DESCR, ND, NI, DCD, ICD )
              TYPE   = ICD( NT )
              REF    = ICD( NR )

              IF ( TYPE .EQ. 20 ) THEN
     C
     C           Read in Chebyshev coefficients from segment.
     C
                 CALL PCKR20 ( HANDLE, DESCR, ET, RECORD )
     C
     C           Call evaluation routine to get Euler angles
     C           phi, delta, w.
     C
                 CALL PCKE20 ( ET, RECORD, EULANG )


        The Euler angles and their derivatives are returned
        in EULANG.

Restrictions

     None.

Literature_References

     None.

Author_and_Institution

     N.J. Bachman       (JPL)
     J. Diaz del Rio    (ODC Space)
     K.S. Zukor         (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 1.0.0, 17-JAN-2014 (NJB) (KSZ)