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cspice_ducrss

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

               Typically, this might represent the apparent state of a
               planet or the Sun, which defines the orientation of axes of
               some coordinate system.

      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:

      [sout] = cspice_ducrss( s1, s2 )

   returns:

      sout     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).

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

               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'.

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

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) 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 the XY plane of
      the frame, with the primary axis Y pointing in the direction
      of the pole.

      Use the meta-kernel shown below to load the required SPICE
      kernels.


         KPL/MK

         File name: ducrss_ex1.tm

         This meta-kernel is intended to support operation of SPICE
         example programs. The kernels shown here should not be
         assumed to contain adequate or correct versions of data
         required by SPICE-based user applications.

         In order for an application to use this meta-kernel, the
         kernels referenced here must be present in the user's
         current working directory.

         The names and contents of the kernels referenced
         by this meta-kernel are as follows:

            File name                     Contents
            ---------                     --------
            de421.bsp                     Planetary ephemeris
            pck00008.tpc                  Planet orientation and
                                          radii
            naif0009.tls                  Leapseconds


         \begindata

            KERNELS_TO_LOAD = ( 'de421.bsp',
                                'pck00008.tpc',
                                'naif0009.tls'  )

         \begintext

         End of meta-kernel


      Example code begins here.


      function ducrss_ex1()

         %
         % Load SPK, PCK, and LSK kernels, use a meta kernel for
         % convenience.
         %
         cspice_furnsh( 'ducrss_ex1.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, lt] = 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   );

         fprintf('New X-axis:\n' );
         fprintf('   position: %15.12f %15.12f %15.12f\n',   x_new(1:3) );
         fprintf('   velocity: %15.12f %15.12f %15.12f\n\n', x_new(4:6) );
         fprintf('New Y-axis:\n' );
         fprintf('   position: %15.12f %15.12f %15.12f\n',   y_new(1:3) );
         fprintf('   velocity: %15.12f %15.12f %15.12f\n\n', y_new(4:6) );
         fprintf('New Z-axis:\n' );
         fprintf('   position: %15.12f %15.12f %15.12f\n',   z_new(1:3) );
         fprintf('   velocity: %15.12f %15.12f %15.12f\n\n', z_new(4:6) );

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


      When this program was executed on a Mac/Intel/Octave5.x/64-bit
      platform, the output was:


      New X-axis:
         position:  0.183446637633 -0.901919663328 -0.391009273602
         velocity:  0.000000202450  0.000000034660  0.000000015033

      New Y-axis:
         position:  0.078846540163 -0.382978080242  0.920386339077
         velocity:  0.000000082384  0.000000032309  0.000000006387

      New Z-axis:
         position: -0.979862518033 -0.199671507623  0.000857203851
         velocity:  0.000000044531 -0.000000218531 -0.000000000036


      Note that these vectors define the transformation between the
      new frame and J2000 at the given `et':

              -            -
             |       :      |
             |   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


   cspice_ducrss calculates the unit vector parallel to the cross product
   of two vectors and the derivative of that unit vector.

Exceptions


   1)  If the position components of `s1' and `s2' cross together to
       give a zero vector, 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 vectors.

   2)  If `s1' and `s2' are large in magnitude (taken together,
       their magnitude surpasses the limit allowed by the
       computer) then it may be possible to generate a
       floating point overflow from an intermediate
       computation even though the actual cross product and
       derivative may be well within the range of double
       precision numbers.

   3)  If any of the input arguments, `s1' or `s2', is undefined, an
       error is signaled by the Matlab error handling system.

   4)  If any of the input arguments, `s1' or `s2', is not of the
       expected type, or it does not have the expected dimensions and
       size, an error is signaled by the Mice interface.

   5)  If the input vectorizable arguments `s1' and `s2' do not have
       the same measure of vectorization (N), an error is signaled by
       the Mice interface.

Files


   None.

Restrictions


   1)  No checking of `s1' or `s2' is done to prevent floating point
       overflow. The user is required to determine that the magnitude
       of each component of the states is within an appropriate range
       so as not to cause floating point overflow. In almost every
       case there will be no problem and no checking actually needs
       to be done.

Required_Reading


   MICE.REQ

Literature_References


   None.

Author_and_Institution


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

Version


   -Mice Version 1.1.0, 07-AUG-2020 (EDW) (JDR)

       Changed output argument name "ducrss" to "sout".

       Edited the header to comply with NAIF standard. Added example's
       problem statement and reference to required meta-kernel.
       Reformatted example's output.

       Added -Parameters, -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 1.0.0, 09-NOV-2012 (EDW)

Index_Entries


   Compute a unit cross product and its derivative


Fri Dec 31 18:44:24 2021