Index Page ckw02_c
A B C D E F G H I J K L M N O P Q R S T U V W X
Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries
#### Procedure
       void ckw02_c ( SpiceInt            handle,
                      SpiceDouble         begtim,
                      SpiceDouble         endtim,
                      SpiceInt            inst,
                      ConstSpiceChar    * ref,
                      ConstSpiceChar    * segid,
                      SpiceInt            nrec,
                      ConstSpiceDouble    start  [],
                      ConstSpiceDouble    stop   [],
                      ConstSpiceDouble    quats  [][4],
                      ConstSpiceDouble    avvs   [][3],
                      ConstSpiceDouble    rates  []    )
#### Abstract
       Write a type 2 segment to a C-kernel.
#### Required_Reading
       CK
       DAF
       SCLK
#### Keywords
       POINTING
       UTILITY
#### Brief_I/O
       Variable  I/O  Description
       --------  ---  --------------------------------------------------
       handle     I   Handle of an open CK file.
       begtim     I   The beginning encoded SCLK of the segment.
       endtim     I   The ending encoded SCLK of the segment.
       inst       I   The NAIF instrument ID code.
       ref        I   The reference frame of the segment.
       segid      I   Segment identifier.
       nrec       I   Number of pointing records.
       start      I   Encoded SCLK interval start times.
       stop       I   Encoded SCLK interval stop times.
       quats      I   Quaternions representing instrument pointing.
       avvs       I   Angular velocity vectors.
       rates      I   Number of seconds per tick for each interval.
#### Detailed_Input
       handle     is the handle of the CK file to which the segment will
                  be written. The file must have been opened with write
                  access.

       begtim     is the beginning encoded SCLK time of the segment. This
                  value should be less than or equal to the first START
                  time in the segment.

       endtim     is the encoded SCLK time at which the segment ends.
                  This value should be greater than or equal to the last
                  STOP time in the segment.

       inst       is the NAIF integer ID code for the instrument.

       ref        is a character string that specifies the
                  reference frame of the segment. This should be one of
                  the frames supported by the SPICELIB routine NAMFRM
                  which is an entry point of FRAMEX.

       segid      is the segment identifier.  A CK segment identifier may
                  contain up to 40 characters.

       nrec       is the number of pointing intervals that will be
                  written to the segment.

       start      are the start times of each interval in encoded
                  spacecraft clock. These times must be strictly
                  increasing.

       stop       are the stop times of each interval in encoded
                  spacecraft clock. These times must be greater than
                  the START times that they correspond to but less
                  than or equal to the START time of the next interval.

       quats      are the quaternions representing the C-matrices
                  associated with the start times of each interval. See the
                  discussion of "Quaternion Styles" in the Particulars
                  section below.

       AVVS       are the angular velocity vectors for each interval.

       RATES      are the number of seconds per encoded spacecraft clock
                  tick for each interval.

                  In most applications this value will be the same for
                  each interval within a segment.  For example, when
                  constructing a predict C-kernel for Mars Observer, the
                  rate would be 1/256 for each interval since this is
                  the smallest time unit expressible by the MO clock. The
                  nominal seconds per tick rates for Galileo and Voyager
                  are 1/120 and 0.06 respectively.
#### Detailed_Output
       None.  See Files section.
#### Parameters
       None.
#### Exceptions
       1)  If handle is not the handle of a C-kernel opened for writing
           the error will be diagnosed by routines called by this
           routine.

       2)  If segid is more than 40 characters long, the error
           SPICE(SEGIDTOOLONG) is signaled.

       3)  If segid contains any nonprintable characters, the error
           SPICE(NONPRINTABLECHARS) is signaled.

       4)  If the first START time is negative, the error
           SPICE(INVALIDSCLKTIME) is signaled. If any of the subsequent
           START times are negative the error SPICE(TIMESOUTOFORDER)
           will be signaled.

       5)  If any of the STOP times are negative, the error
           SPICE(DEGENERATEINTERVAL) is signaled.

       6)  If the STOP time of any of the intervals is less than or equal
           to the START time, the error SPICE(DEGENERATEINTERVAL) is
           signaled.

       7)  If the START times are not strictly increasing, the
           error SPICE(TIMESOUTOFORDER) is signaled.

       8)  If the STOP time of one interval is greater than the START
           time of the next interval, the error SPICE(BADSTOPTIME)
           is signaled.

       9)  If begtim is greater than START[0] or endtim is less than
           STOP[NREC-1], the error SPICE(INVALIDDESCRTIME) is
           signaled.

      10)  If the name of the reference frame is not one of those
           supported by the routine NAMFRM, the error
           SPICE(INVALIDREFFRAME) is signaled.

      11)  If nrec, the number of pointing records, is less than or
           equal to 0, the error SPICE(INVALIDNUMRECS) is signaled.

      12)  If any quaternion has magnitude zero, the error
           SPICE(ZEROQUATERNION) is signaled.
#### Files
       This routine adds a type 2 segment to a C-kernel.  The C-kernel
       may be either a new one or an existing one opened for writing.
#### Particulars
       For a detailed description of a type 2 CK segment please see the
       CK Required Reading.

       This routine relieves the user from performing the repetitive
       calls to the DAF routines necessary to construct a CK segment.

       Quaternion Styles
       -----------------

       There are different "styles" of quaternions used in
       science and engineering applications. Quaternion styles
       are characterized by

          - The order of quaternion elements

          - The quaternion multiplication formula

          - The convention for associating quaternions
            with rotation matrices

       Two of the commonly used styles are

          - "SPICE"

             > Invented by Sir William Rowan Hamilton
             > Frequently used in mathematics and physics textbooks

          - "Engineering"

             > Widely used in aerospace engineering applications

       CSPICE function interfaces ALWAYS use SPICE quaternions.
       Quaternions of any other style must be converted to SPICE
       quaternions before they are passed to CSPICE functions.

       Relationship between SPICE and Engineering Quaternions
       ------------------------------------------------------

       Let M be a rotation matrix such that for any vector V,

          M*V

       is the result of rotating V by theta radians in the
       counterclockwise direction about unit rotation axis vector A.
       Then the SPICE quaternions representing M are

          (+/-) (  cos(theta/2),
                   sin(theta/2) A(1),
                   sin(theta/2) A(2),
                   sin(theta/2) A(3)  )

       while the engineering quaternions representing M are

          (+/-) ( -sin(theta/2) A(1),
                  -sin(theta/2) A(2),
                  -sin(theta/2) A(3),
                   cos(theta/2)       )

       For both styles of quaternions, if a quaternion q represents
       a rotation matrix M, then -q represents M as well.

       Given an engineering quaternion

          QENG   = ( q0,  q1,  q2,  q3 )

       the equivalent SPICE quaternion is

          QSPICE = ( q3, -q0, -q1, -q2 )

       Associating SPICE Quaternions with Rotation Matrices
       ----------------------------------------------------

       Let FROM and TO be two right-handed reference frames, for
       example, an inertial frame and a spacecraft-fixed frame. Let the
       symbols

          V    ,   V
           FROM     TO

       denote, respectively, an arbitrary vector expressed relative to
       the FROM and TO frames. Let M denote the transformation matrix
       that transforms vectors from frame FROM to frame TO; then

          V   =  M * V
           TO         FROM

       where the expression on the right hand side represents left
       multiplication of the vector by the matrix.

       Then if the unit-length SPICE quaternion q represents M, where

          q = (q0, q1, q2, q3)

       the elements of M are derived from the elements of q as follows:

            +-                                                         -+
            |           2    2                                          |
            | 1 - 2*( q2 + q3 )   2*(q1*q2 - q0*q3)   2*(q1*q3 + q0*q2) |
            |                                                           |
            |                                                           |
            |                               2    2                      |
        M = | 2*(q1*q2 + q0*q3)   1 - 2*( q1 + q3 )   2*(q2*q3 - q0*q1) |
            |                                                           |
            |                                                           |
            |                                                   2    2  |
            | 2*(q1*q3 - q0*q2)   2*(q2*q3 + q0*q1)   1 - 2*( q1 + q2 ) |
            |                                                           |
            +-                                                         -+

       Note that substituting the elements of -q for those of q in the
       right hand side leaves each element of M unchanged; this shows
       that if a quaternion q represents a matrix M, then so does the
       quaternion -q.

       To map the rotation matrix M to a unit quaternion, we start by
       decomposing the rotation matrix as a sum of symmetric
       and skew-symmetric parts:

                                          2
          M = [ I  +  (1-cos(theta)) OMEGA  ] + [ sin(theta) OMEGA ]

                       symmetric                   skew-symmetric

       OMEGA is a skew-symmetric matrix of the form

                     +-             -+
                     |  0   -n3   n2 |
                     |               |
           OMEGA  =  |  n3   0   -n1 |
                     |               |
                     | -n2   n1   0  |
                     +-             -+

       The vector N of matrix entries (n1, n2, n3) is the rotation axis
       of M and theta is M's rotation angle.  Note that N and theta
       are not unique.

       Let

          C = cos(theta/2)
          S = sin(theta/2)

       Then the unit quaternions Q corresponding to M are

          Q = +/- ( C, S*n1, S*n2, S*n3 )

       The mappings between quaternions and the corresponding rotations
       are carried out by the CSPICE routines

          q2m_c {quaternion to matrix}
          m2q_c {matrix to quaternion}

       m2q_c always returns a quaternion with scalar part greater than
       or equal to zero.

       SPICE Quaternion Multiplication Formula
       ---------------------------------------

       Given a SPICE quaternion

          Q = ( q0, q1, q2, q3 )

       corresponding to rotation axis A and angle theta as above, we can
       represent Q using "scalar + vector" notation as follows:

          s =   q0           = cos(theta/2)

          v = ( q1, q2, q3 ) = sin(theta/2) * A

          Q = s + v

       Let Q1 and Q2 be SPICE quaternions with respective scalar
       and vector parts s1, s2 and v1, v2:

          Q1 = s1 + v1
          Q2 = s2 + v2

       We represent the dot product of v1 and v2 by

          <v1, v2>

       and the cross product of v1 and v2 by

          v1 x v2

       Then the SPICE quaternion product is

          Q1*Q2 = s1*s2 - <v1,v2>  + s1*v2 + s2*v1 + (v1 x v2)

       If Q1 and Q2 represent the rotation matrices M1 and M2
       respectively, then the quaternion product

          Q1*Q2

       represents the matrix product

          M1*M2
#### Examples
       This example writes a predict type 2 C-kernel segment for
       the Mars Observer spacecraft bus to a previously opened CK file
       attached to handle.

          /.
          Assume arrays of quaternions, angular velocities, and interval
          start and stop times are produced elsewhere.
          ./

          .
          .
          .

          /.
          The nominal number of seconds in a tick for MO is 1/256.
          ./
          sectik = 1. / 256.;

          for ( i = 0; i < nrec;  i++ )
          {
             rate[i] = sectik;
          }

          /.
          The subroutine ckw02_c needs the following components of the
          segment descriptor:

             1) SCLK limits of the segment.
             2) Instrument code.
             3) Reference frame.
          ./
          begtim  =  start [    0 ];
          endtim  =  stop  [nrec-1];

          inst    =  -94000;
          ref     =  "j2000";

          segid = "mo predict seg type 2";

          /.
          Write the segment.
          ./
          ckw02_c ( handle, begtim, endtim, inst, ref, segid,
                    nrec,   start,  stop,   quat, avv, rates  );
#### Restrictions
       None.
#### Literature_References
       None.
#### Author_and_Institution
       N.J. Bachman    (JPL)
       K.R. Gehringer  (JPL)
       J.M. Lynch      (JPL)
#### Version
       -CSPICE Version 2.0.0, 01-JUN-2010 (NJB)

          The check for non-unit quaternions has been replaced
          with a check for zero-length quaternions. (The
          implementation of the check is located in ckw02_.)

       -CSPICE Version 1.2.1, 27-FEB-2008 (NJB)

          Updated header; added information about SPICE
          quaternion conventions.

       -CSPICE Version 1.2.0, 28-AUG-2001 (NJB)

           Changed prototype:  inputs start, stop, sclkdp, quats,
           and avvs are now const-qualified.  Implemented interface
           macros for casting these inputs to const.

       -CSPICE Version 1.1.0, 08-FEB-1998 (NJB)

           References to C2F_CreateStr_Sig were removed; code was
           cleaned up accordingly.  String checks are now done using
           the macro CHKFSTR.

       -CSPICE Version 1.0.0, 25-OCT-1997 (NJB)

          Based on SPICELIB Version 2.0.0, 28-DEC-1993 (WLT)
#### Index_Entries
       write ck type_2 pointing data segment
#### Link to routine ckw02_c source file ckw02_c.c

    Wed Jun  9 13:05:19 2010