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Abstract
I/O
Examples
Particulars
Required Reading
Version
Index_Entries

Abstract


   CSPICE_DUCRSS calculates the unit vector parallel to the cross product
   of the position components of two state vectors and the time derivative
   of this unit vector.

I/O


   Given:

      s1   a SPICE state(s);

              s1 = (r1, dr1 ).
                         --
                         dt

           [6,n] = size(s1); double = class(s1)

      s2   a second SPICE state(s);

              s2 = (r2, dr2 ).
                        --
                        dt

           [6,n] = size(s2); double = class(s2)

      An implicit assumption exists that 's1' and 's2' are specified
      in the same reference frame. If this is not the case, the numerical
      result has no meaning.

   the call:

      ducrss = cspice_ducrss ( s1, s2 )

   returns:

      ducrss   the unit vector(s) parallel to the cross product(s) of the
               position components of 's1' and 's2' and the derivative
               of the unit vector(s).

               If the cross product of the position components is the zero
               vector, then the position component of the output will be the
               zero vector. The velocity component of the output will simply
               be the derivative of the cross product of the position
               components of 's1' and 's2'.

               'ducrss' returns with the same vectorization measure (N)
               as 's1' and 's2'

               Programmatically:

                  crss   = cspice_dvcrss( s1, s2 )
                  ducrss = cspice_dvhat( crss )

               [6,n] = size(ducrss); double = class(ducrss)

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.

      One can construct non-inertial coordinate frames from apparent
      positions of objects or defined directions.  However, if one wants
      to convert states in this non-inertial frame to states in an inertial
      reference frame, the derivatives of the axes of the non-inertial
      frame are required.

      Define a reference frame with the apparent direction of the sun
      as seen from earth as the primary axis (x). Use the earth pole vector
      to define with the primary axis a primary plane of the frame.


      %
      % Load SPK, PCK, and LSK kernels, use a meta kernel for convenience.
      %
      cspice_furnsh( 'standard.tm' )

      %
      % Define the earth body-fixed pole vector (z). The pole
      % has no velocity in the earth fixed frame "IAU_EARTH."
      %
      z_earth = [ 0, 0, 1, 0, 0, 0 ]';

      %
      % Calculate the state transformation between IAU_EARTH and J2000
      % at an arbitrary epoch.
      %
      utc     = 'Jan 1, 2009';
      et      = cspice_str2et( utc );
      trans   = cspice_sxform( 'IAU_EARTH', 'J2000', et );

      %
      % Transform the earth pole vector from the IAU_EARTH frame to J2000.
      %
      z_j2000 = trans * z_earth;

      %
      % Calculate the apparent state of the sun from earth at the epoch
      % 'et' in the J2000 frame.
      %
      target   = 'Sun';
      observer = 'Earth';

      [state, ltime] = cspice_spkezr( target, et, 'J2000', 'LT+S', observer);

      %
      % Define the z axis of the new frame as the cross product between
      % the apparent direction of the sun and the earth pole. 'z_new' cross
      % 'x_new' defines the y axis of the derived frame.
      %
      x_new = cspice_dvhat( state )
      z_new = cspice_ducrss( state, z_j2000 )
      y_new = cspice_ducrss( z_new, state   )

      %
      % It's always good form to unload kernels after use,
      % particularly in Matlab due to data persistence.
      %
      cspice_kclear

   MATLAB outputs:

      x_new =

           1.834466375917397e-01
          -9.019196633169827e-01
          -3.910092736476536e-01
           2.024497675152527e-07
           3.466010606102513e-08
           1.503314202237741e-08


      y_new =

           7.884654015638601e-02
          -3.829780802895584e-01
           9.203863390571874e-01
           8.238367850215384e-08
           3.230941292533659e-08
           6.386588623423665e-09


      z_new =

          -9.798625180410016e-01
          -1.996715075815909e-01
           8.572038510978363e-04
           4.453114222022677e-08
          -2.185310696303958e-07
          -3.614002123088436e-11

      These vectors define the transformation between the new frame and J2000.

              -            -
             |       :      |
             |   R   :  0   |
         M = | ......:......|
             |       :      |
             | dRdt  :  R   |
             |       :      |
              -            -

      with

         R    = [ x_new(1:3): y_new(1:3); z_new(1:3) ]

         dRdt = [ x_new(4:6): y_new(4:6); z_new(4:6) ]

Particulars


   The frame transformation described in the Example may also be implemented
   using a dynamic frames kernel.

Required Reading


   For important details concerning this module's function, please refer to
   the CSPICE routine ducrss_c.

   FRAMES.REQ
   MICE.REQ

Version


   -Mice Version 1.0.0, 09-NOV-2012, EDW (JPL)

Index_Entries


   compute a unit cross product and its derivative


Wed Apr  5 18:00:31 2017