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Index Page ducrss_c

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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

       ducrss_c ( Unit Normalized Cross Product and Derivative )

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

#### Abstract

       Compute the unit vector parallel to the cross product of
       two 3-dimensional vectors and the derivative of this unit vector.

#### 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   Unit vector and derivative of the cross product.

#### 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 unit vector parallel to the cross product of the
                   position components of `s1' and `s2' and the derivative of
                   the unit vector.

                   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'.

#### Parameters

       None.

#### Exceptions

       Error free.

       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.

#### Files

       None.

#### Particulars

       ducrss_c calculates the unit vector parallel to the cross product
       of two vectors and the derivative of that unit vector.
       The results of the computation may overwrite either of the
       input vectors.

#### Examples

       The numerical results shown for this example 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) 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.

          /.
             Program ducrss_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local variables
             ./
             SpiceDouble          et;
             SpiceDouble          lt;
             SpiceDouble          state  [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 ( "ducrss_ex1.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 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.
             ./
             dvhat_c ( state, x_new );
             ducrss_c ( state, zinert, z_new );
             ducrss_c ( z_new, state, 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

       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.

#### Literature_References

       None.

#### Author_and_Institution

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

#### Version

       -CSPICE Version 1.1.0, 02-JUL-2021 (JDR)

           Rebuilt the wrapper to directly call the f2c'd version of the API,
           which scales the inputs to reduce chance of numeric overflow.

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

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

#### Index_Entries

       Compute a unit cross product and its derivative

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

    Fri Dec 31 18:41:05 2021