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cspice_ckw02

Table of contents
Abstract
I/O
Parameters
Examples
Particulars
Exceptions
Files
Restrictions
Required_Reading
Literature_References
Author_and_Institution
Version
Index_Entries

Abstract


   CSPICE_CKW02 adds a type 2 segment to a C-kernel.

I/O


   Given:

      handle   file handle for an open CK file, returned from cspice_ckopn.

               [1,1] = size(handle); int32 = class(handle)

      begtim   encoded SCLK segment begin time.

               [1,1] = size(begtim); double = class(begtim)

      endtim   encoded SCLK segment end time.

               [1,1] = size(endtim); double = class(endtim)

      inst     NAIF instrument ID code.

               [1,1] = size(inst); int32 = class(inst)

      ref      name of the reference frame for the segment.

               [1,c1] = size(ref); char = class(ref)

                  or

               [1,1] = size(ref); cell = class(ref)

      segid    name to identify the segment.

               [1,c2] = size(segid); char = class(segid)

                  or

               [1,1] = size(segid); cell = class(segid)

      start    an array containing encoded SCLK interval start times.

               [n,1] = size(start); double = class(start)

      stop     an array containing the encoded SCLK interval stop times.

               [n,1] = size(stop); double = class(stop)

      quats    array of SPICE style quaternions representing instrument
               pointing.

               [4,n] = size(quats); double = class(quats)

      avvs     array of angular velocity vectors in units of radians per
               second.

               [3,n] = size(avvs); double = class(avvs)

      rates    the number of seconds per tick for each interval.

               [n,1] = size(rates); double = class(rates)

   the call:

      cspice_ckw02( handle, ...
                    begtim, ...
                    endtim, ...
                    inst,   ...
                    ref,    ...
                    segid,  ...
                    start,  ...
                    stop,   ...
                    quats,  ...
                    avvs,   ...
                    rates )

   returns:

      None.

Parameters


   None.

Examples


   Any numerical results shown for this example may differ between
   platforms as the results depend on the SPICE kernels used as input
   and the machine specific arithmetic implementation.

   1) The following example creates a CK file with a type-2 segment,
      with data for a simple time dependent rotation and angular
      velocity.

      Example code begins here.


      function ckw02_ex1()

         %
         % Define needed parameters
         %
         CK2        = 'ckw02_ex1.bc';
         INST       = -77702;
         MAXREC     = 21;
         SECPERTICK = 0.001;
         IFNAME     = 'Test CK type 2 segment created by cspice_ckw02';
         SEGID      = 'Test type 2 CK segment';

         %
         % NCOMCH is the number of characters to reserve for the kernel's
         % comment area. This example doesn't write comments, so set to
         % zero.
         %
         NCOMCH = 0;

         %
         % The base reference from for the rotation data.
         %
         REF = 'J2000';

         %
         % Time spacing in encoded ticks.
         %
         SPACING_TICKS = 10.;

         %
         % Time spacing in seconds
         %
         SPACING_SECS = SPACING_TICKS * SECPERTICK;

         %
         % Declare an angular rate in radians per sec.
         %
         RATE = 1.e-2;

         %
         % Create a 4xMAXREC matrix for quaternions, and a
         % 3xMAXREC for expavs.
         %
         quats = zeros( [4, MAXREC] );
         av    = zeros( [3, MAXREC] );

         %
         % Create a 3x3 double precision identity matrix.
         %
         work_mat = eye( 3 );

         %
         % Convert the `work_mat' to quaternion.
         %
         work_quat = cspice_m2q( work_mat);

         %
         % Copy the work quaternion to the first row of
         % `quats'.
         %
         quats(:,1) = work_quat;

         %
         % Create an angular velocity vector. Copy to the third (Z) row
         % of `av'. This vector is in the `REF' reference frame and
         % indicates a constant rotation about the Z axis.
         %
         av(3,:) = RATE;

         %
         % Create arrays of interval start and stop times.  The interval
         % associated with each quaternion will start at the epoch of
         % the quaternion and will extend 0.8 * SPACING_TICKS forward in
         % time, leaving small gaps between the intervals.
         %
         % Fill in the clock rates array with a constant `SECPERTICK' for
         % all values.
         %
         rates  = zeros( [MAXREC,1] ) + SECPERTICK;

         %
         % Create an array of encoded tick values in increments of
         % `SPACING_TICKS' with an initial value of 1000 ticks.
         %
         sclkdp = [0:MAXREC-1]' * SPACING_TICKS + 1000;

         starts = sclkdp;
         stops  = sclkdp + ( 0.8 * SPACING_TICKS );

         %
         % Fill the rest of the `av' and `quats' matrices
         % with simple data.
         %
         for i = 2:MAXREC

            %
            % Create the transformation matrix for a rotation of `theta'
            % about the Z axis. Calculate `theta' from the constant
            % angular rate RATE at increments of SPACING_SECS.
            %
            theta    = (i-1) * RATE * SPACING_SECS;
            work_mat = cspice_rotmat( work_mat, theta, 3 );

            %
            % Convert the `work_mat' matrix to SPICE type quaternion.
            %
            work_quat = cspice_m2q( work_mat );

            %
            % Store the quaternion in the `quats' matrix.
            %
            quats(:,i) = work_quat;

         end

         %
         % Set the segment boundaries equal to the first and last
         % time in the segment.
         %
         begtim = starts(1);
         endtim = stops(MAXREC);

         %
         % All information ready to write. Write to a CK type 2 segment
         % to the file indicated by `handle'.
         %
         try
            handle = cspice_ckopn( CK2, IFNAME, NCOMCH );
            cspice_ckw02(  handle, ...
                           begtim, ...
                           endtim, ...
                           INST,   ...
                           REF,    ...
                           SEGID,  ...
                           starts, ...
                           stops,  ...
                           quats,  ...
                           av,     ...
                           rates )
         catch
            error( [ 'Failure: ' lasterr] )
         end

         %
         % SAFELY close the file.
         %
         cspice_ckcls( handle )


      When this program is executed, no output is presented on
      screen. After run completion, a new CK file exists in the
      output directory.

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


   Mice routine interfaces ALWAYS use SPICE quaternions.
   Quaternions of any other style must be converted to SPICE
   quaternions before they are passed to Mice routines.


   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 Mice routines

      cspice_q2m {quaternion to matrix}
      cspice_m2q {matrix to quaternion}

   cspice_m2q 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

Exceptions


   1)  If `handle' is not the handle of a C-kernel opened for writing,
       an error is signaled by a routine in the call tree of this
       routine.

   2)  If `segid' is more than 40 characters long, the error
       SPICE(SEGIDTOOLONG) is signaled by a routine in the call tree
       of this routine.

   3)  If `segid' contains any nonprintable characters, the error
       SPICE(NONPRINTABLECHARS) is signaled by a routine in the call
       tree of this routine.

   4)  If the first `start' time is negative, the error
       SPICE(INVALIDSCLKTIME) is signaled by a routine in the call
       tree of this routine.

   5)  If the second or any subsequent `start' times are negative, the
       error SPICE(TIMESOUTOFORDER) is signaled by a routine in the
       call tree of this routine.

   6)  If any of the `stop' times are negative, the error
       SPICE(DEGENERATEINTERVAL) is signaled by a routine in the call
       tree of this routine.

   7)  If the `stop' time of any of the intervals is less than or equal
       to the `start' time, the error SPICE(DEGENERATEINTERVAL) is
       signaled by a routine in the call tree of this routine.

   8)  If the `start' times are not strictly increasing, the error
       SPICE(TIMESOUTOFORDER) is signaled by a routine in the call
       tree of this routine.

   9)  If the `stop' time of one interval is greater than the `start'
       time of the next interval, the error SPICE(BADSTOPTIME)
       is signaled by a routine in the call tree of this routine.

   10) If `begtim' is greater than start(1) or `endtim' is less than
       stop(nrec), where `nrec' is the number of pointing records,
       the error SPICE(INVALIDDESCRTIME) is signaled by a routine in
       the call tree of this routine.

   11) If the name of the reference frame is not one of those
       supported by the routine cspice_namfrm, the error
       SPICE(INVALIDREFFRAME) is signaled by a routine in the call
       tree of this routine.

   12) If `nrec', the number of pointing records, is less than or
       equal to 0, the error SPICE(INVALIDNUMRECS) is signaled by a
       routine in the call tree of this routine.

   13) If any quaternion has magnitude zero, the error
       SPICE(ZEROQUATERNION) is signaled by a routine in the call
       tree of this routine.

   14) If any of the input arguments, `handle', `begtim', `endtim',
       `inst', `ref', `segid', `start', `stop', `quats', `avvs' or
       `rates', is undefined, an error is signaled by the Matlab
       error handling system.

   15) If any of the input arguments, `handle', `begtim', `endtim',
       `inst', `ref', `segid', `start', `stop', `quats', `avvs' or
       `rates', is not of the expected type, or it does not have the
       expected dimensions and size, an error is signaled by the Mice
       interface.

   16) If the input vector arguments `start', `stop', `quats', `avvs'
       and `rates' do not have the same dimension (N), an error is
       signaled by the Mice interface.

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.

Restrictions


   None.

Required_Reading


   MICE.REQ
   CK.REQ
   DAF.REQ
   SCLK.REQ

Literature_References


   None.

Author_and_Institution


   J. Diaz del Rio     (ODC Space)
   E.D. Wright         (JPL)

Version


   -Mice Version 1.1.0, 25-AUG-2021 (EDW) (JDR)

       Changed input argument names "begtime" and "endtime" to "begtim"
       and "endtim".

       Edited the header to comply with NAIF standard. Added example's
       problem statement.

       Added -Parameters, -Particulars, -Exceptions, -Files, -Restrictions,
       -Literature_References and -Author_and_Institution sections.

       Eliminated use of "lasterror" in rethrow.

       Removed reference to the function's corresponding CSPICE header from
       -Required_Reading section.

   -Mice Version 1.0.3, 29-OCT-2014 (EDW)

       Edited -I/O section to conform to NAIF standard for Mice
       documentation.

   -Mice Version 1.0.2, 11-JUN-2013 (EDW)

       -I/O descriptions edits to conform to Mice documentation format.

   -Mice Version 1.0.1, 30-DEC-2008 (EDW)

       Corrected misspellings.

   -Mice Version 1.0.0, 04-JAN-2008 (EDW)

Index_Entries


   write CK type_2 pointing data segment


Fri Dec 31 18:44:23 2021