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   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  []    )


   Write a type 2 segment to a C-kernel. 






   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. 


   handle     is the handle of the CK file to which the segment will 
              be written. The file must have been opened with write 
   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 
   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. 


   None.  See Files section. 




   1)  If handle is not the handle of a C-kernel opened for writing 
       the error will be diagnosed by routines called by this 
   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 
   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 
  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.


   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. 


   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,


   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

      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:

      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.


      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


   represents the matrix product



   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  ); 






   N.J. Bachman    (JPL)
   K.R. Gehringer  (JPL) 
   J.M. Lynch      (JPL) 


   -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)


   write ck type_2 pointing data segment 
Wed Apr  5 17:54:30 2017