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Index Page dvcrss_c

Table of contents

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

       dvcrss_c ( Derivative of Vector cross product )

       void dvcrss_c ( ConstSpiceDouble s1  [6],
                       ConstSpiceDouble s2  [6],
                       SpiceDouble      sout[6] )

#### Abstract

       Compute the cross product of two 3-dimensional vectors
       and the derivative of this cross product.

#### Required_Reading

       None.

#### Keywords

       DERIVATIVE
       VECTOR

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       s1         I   Left hand state for cross product and derivative.
       s2         I   Right hand state for cross product and derivative.
       sout       O   State associated with cross product of positions.

#### Detailed_Input

       s1          is any state vector. Typically, this might represent the
                   apparent state of a planet or the Sun, which defines the
                   orientation of axes of some coordinate system.

       s2          is any state vector.

#### Detailed_Output

       sout        is the state associated with the cross product of the
                   position components of `s1' and `s2'. In other words, if
                   `s1' = (p1,v1) and `s2' = (p2,v2) then `sout' is
                   ( p1xp2, d/dt( p1xp2 ) ).

#### Parameters

       None.

#### Exceptions

       Error free.

       1)  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.

           dvcrss_c does NOT check the magnitude of `s1' or `s2' to
           insure that overflow will not occur.

#### Files

       None.

#### Particulars

       dvcrss_c calculates the three-dimensional cross product of two
       vectors and the derivative of that cross product according to
       the definition. The components of this state are stored
       in a local buffer vector until the calculation is complete.
       Thus sout may overwrite 's1' or 's2'  without interfering with
       intermediate computations.

#### Examples

       The numerical results shown for these examples may differ across
       platforms. The results depend on the SPICE kernels used as
       input, the compiler and supporting libraries, and the machine
       specific arithmetic implementation.

       1) Compute the cross product of two 3-dimensional vectors
          and the derivative of this cross product.

          Example code begins here.

          /.
             Program dvcrss_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local variables
             ./
             SpiceDouble          sout   [6];

             SpiceInt             i;

             /.
             Set `s1' and `s2' vectors.
             ./
             SpiceDouble          s1     [2][6] = {
                                                {0.0, 1.0, 0.0, 1.0, 0.0, 0.0},
                                                {5.0, 5.0, 5.0, 1.0, 0.0, 0.0}  };
             SpiceDouble          s2     [2][6] = {
                                             { 1.0,  0.0,  0.0, 1.0, 0.0, 0.0},
                                             {-1.0, -1.0, -1.0, 2.0, 0.0, 0.0}  };

             /.
             For each vector `s1' and `s2', compute their cross product
             and its derivative.
             ./
             for ( i = 0; i < 2; i++ )
             {

                dvcrss_c ( s1[i], s2[i], sout );

                printf( "S1  : %6.1f %6.1f %6.1f %6.1f %6.1f %6.1f\n",
                                         s1[i][0], s1[i][1], s1[i][2],
                                         s1[i][3], s1[i][4], s1[i][5] );
                printf( "S2  : %6.1f %6.1f %6.1f %6.1f %6.1f %6.1f\n",
                                         s2[i][0], s2[i][1], s2[i][2],
                                         s2[i][3], s2[i][4], s2[i][5] );
                printf( "SOUT: %6.1f %6.1f %6.1f %6.1f %6.1f %6.1f\n",
                                            sout[0], sout[1], sout[2],
                                            sout[3], sout[4], sout[5] );
                printf( "\n" );

             }

             return ( 0 );
          }

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

          S1  :    0.0    1.0    0.0    1.0    0.0    0.0
          S2  :    1.0    0.0    0.0    1.0    0.0    0.0
          SOUT:    0.0    0.0   -1.0    0.0    0.0   -1.0

          S1  :    5.0    5.0    5.0    1.0    0.0    0.0
          S2  :   -1.0   -1.0   -1.0    2.0    0.0    0.0
          SOUT:    0.0    0.0    0.0    0.0   11.0  -11.0

       2) 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: dvcrss_ex2.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.

          /.
             Program dvcrss_ex2
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local variables
             ./
             SpiceDouble          et;
             SpiceDouble          lt;
             SpiceDouble          state  [6];
             SpiceDouble          tmpsta [6];
             SpiceDouble          trans  [6][6];
             SpiceDouble          x_new  [6];
             SpiceDouble          y_new  [6];
             SpiceDouble          z_new  [6];
             SpiceDouble          zinert [6];

             /.
             Define the earth body-fixed pole vector (z). The pole
             has no velocity in the Earth fixed frame IAU_EARTH.
             ./
             SpiceDouble          z      [6] = { 0.0, 0.0, 1.0, 0.0, 0.0, 0.0 };

             /.
             Load SPK, PCK, and LSK kernels, use a meta kernel for
             convenience.
             ./
             furnsh_c ( "dvcrss_ex2.tm" );

             /.
             Calculate the state transformation between IAU_EARTH and
             J2000 at an arbitrary epoch.
             ./
             str2et_c ( "Jan 1, 2009", &et );
             sxform_c ( "IAU_EARTH", "J2000", et, trans );

             /.
             Transform the earth pole vector from the IAU_EARTH frame
             to J2000.
             ./
             mxvg_c ( trans, z, 6, 6, zinert );

             /.
             Calculate the apparent state of the Sun from Earth at
             the epoch `et' in the J2000 frame.
             ./
             spkezr_c ( "Sun", et, "J2000", "lt+s", "Earth", state, &lt );

             /.
             Define the X axis of the new frame to aligned with
             the computed state. Calculate the state's unit vector
             and its derivative to get the X axis and its
             derivative.
             ./
             dvhat_c ( state, x_new );

             /.
             Define the Z axis of the new frame as the cross product
             between the computed state and the Earth pole.
             Calculate the Z direction in the new reference frame,
             then calculate the this direction's unit vector and its
             derivative to get the Z axis and its derivative.
             ./
             dvcrss_c ( state, zinert, tmpsta );
             dvhat_c ( tmpsta, z_new );

             /.
             As for `z_new', calculate the Y direction in the new
             reference frame, then calculate this direction's unit
             vector and its derivative to get the Y axis and its
             derivative.
             ./
             ducrss_c ( z_new, state, tmpsta );
             dvhat_c ( tmpsta, y_new );

             /.
             Display the results.
             ./
             printf( "New X-axis:\n" );
             printf( "   position: %15.12f %15.12f %15.12f\n",
                                  x_new[0], x_new[1], x_new[2] );
             printf( "   velocity: %15.12f %15.12f %15.12f\n",
                                  x_new[3], x_new[4], x_new[5] );
             printf( "New Y-axis:\n" );
             printf( "   position: %15.12f %15.12f %15.12f\n",
                                  y_new[0], y_new[1], y_new[2] );
             printf( "   velocity: %15.12f %15.12f %15.12f\n",
                                  y_new[3], y_new[4], y_new[5] );
             printf( "New Z-axis:\n" );
             printf( "   position: %15.12f %15.12f %15.12f\n",
                                  z_new[0], z_new[1], z_new[2] );
             printf( "   velocity: %15.12f %15.12f %15.12f\n",
                                  z_new[3], z_new[4], z_new[5] );

             return ( 0 );
          }

          When this program was executed on a Mac/Intel/cc/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[0], y_new[0], z_new[0]},
                      {x_new[1], y_new[1], z_new[1]},
                      {x_new[2], y_new[2], z_new[2]} }

             dRdt = { {x_new[3], y_new[3], z_new[3]},
                      {x_new[4], y_new[4], z_new[4]},
                      {x_new[5], y_new[5], z_new[5]} }

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

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

#### Version

       -CSPICE Version 1.0.1, 06-JUL-2021 (JDR)

           Edited the header to comply with NAIF standard. Added complete
           code examples.

       -CSPICE Version 1.0.0, 23-NOV-2009 (EDW)

#### Index_Entries

       Compute the derivative of a cross product

#### Link to routine dvcrss_c source file dvcrss_c.c

    Fri Dec 31 18:41:05 2021