Index of Functions: A B C D E F G H I J K L M N O P Q R S T U V W X
Index Page rav2xf_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

       rav2xf_c ( Rotation and angular velocity to transform )

       void rav2xf_c ( ConstSpiceDouble    rot   [3][3],
                       ConstSpiceDouble    av    [3],
                       SpiceDouble         xform [6][6]  )

#### Abstract

       Determine a state transformation matrix from a rotation matrix
       and the angular velocity of the rotation.

#### Required_Reading

       ROTATION

#### Keywords

       FRAMES

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       rot        I   Rotation matrix.
       av         I   Angular velocity vector.
       xform      O   State transformation associated with `rot' and `av'.

#### Detailed_Input

       rot         is a rotation matrix that gives the transformation from
                   some frame FRAME1 to another frame FRAME2.

       av          is the angular velocity of the transformation.
                   In other words, if `p' is the position of a fixed
                   point in FRAME2, then from the point of view of
                   FRAME1, `p' rotates (in a right handed sense) about
                   an axis parallel to `av'. Moreover the rate of rotation
                   in radians per unit time is given by the length of
                   `av'.

                   More formally, the velocity `v' of `p' in FRAME1 is
                   given by
                                      T
                      v  =  av x ( rot  * p )

#### Detailed_Output

       xform       is a state transformation matrix associated
                   with `rot' and `av'. If `s1' is the state of an object
                   with respect to FRAME1, then the state `s2' of the
                   object with respect to FRAME2 is given by

                      s2  =  xform * s1

                   where "*" denotes Matrix-Vector multiplication.

#### Parameters

       None.

#### Exceptions

       Error free.

       1)  No checks are performed on `rot' to ensure that it is indeed
           a rotation matrix.

#### Files

       None.

#### Particulars

       This routine is essentially a macro routine for converting
       a rotation and angular velocity of the rotation to the
       equivalent state transformation matrix.

       This routine is an inverse of xf2rav_c.

#### 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) The following example program uses ckgpav_c to get C-matrix
          and associated angular velocity vector for an image whose
          SCLK count (un-encoded character string version) is known.

          From that matrix and angular velocity vector, the associated
          state transformation matrix is obtained.

          Note that we need to load a SCLK kernel to convert from clock
          string to "ticks." Although not required for older spacecraft
          clocks, most modern spacecraft ones require a leapseconds
          kernel to be loaded in addition to a SCLK kernel.

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

             KPL/MK

             File name: rav2xf_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
                --------------------   -----------------------
                cas00071.tsc           CASSINI SCLK
                04161_04164ra.bc       CASSINI spacecraft
                                       reconstructed CK

             \begindata

               KERNELS_TO_LOAD = ( 'cas00071.tsc'
                                   '04161_04164ra.bc' )

             \begintext

             End of meta-kernel

          Example code begins here.

          /.
             Program rav2xf_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Constants for this program.

             -- The code for the CASSINI spacecraft clock is -82.

             -- The code for CASSINI spacecraft reference frame is
                -82000.

             --  Spacecraft clock tolerance is 1.0 seconds. This may
                not be an acceptable tolerance for some applications.
                It must be converted to "ticks" (units of encoded
                SCLK) for input to ckgpav_c.

             -- The reference frame we want is J2000.
             ./
             #define META         "rav2xf_ex1.tm"
             #define REFFRM       "J2000"
             #define SCLKCH       "1/1465476046.160"
             #define SCLTOL       "1.0"
             #define SCID         -82
             #define INSTID       -82000

             /.
             Local variables.
             ./
             SpiceDouble          av     [3];
             SpiceDouble          clkout;
             SpiceDouble          cmat   [3][3];
             SpiceDouble          fxmat  [6][6];
             SpiceDouble          sclkdp;
             SpiceDouble          toltik;

             SpiceInt             i;

             SpiceBoolean         found;

             /.
             Load kernels.
             ./
             furnsh_c ( META );

             /.
             Convert tolerance from CASSINI formatted character
             string SCLK to ticks which are units of encoded SCLK.
             ./
             sctiks_c ( SCID, SCLTOL, &toltik );

             /.
             ckgpav_c requires encoded spacecraft clock.
             ./
             scencd_c ( SCID, SCLKCH, &sclkdp );

             ckgpav_c ( INSTID, sclkdp, toltik,  REFFRM,
                        cmat,   av,     &clkout, &found );

             /.
             Recall that `cmat' and `av' are the rotation and angular
             velocity of the transformation from J2000 to the
             spacecraft frame.
             ./
             if ( found )
             {

                /.
                Display `cmat' and `av'.
                ./
                printf( "Rotation matrix:\n" );
                for ( i = 0; i < 3; i++ )
                {

                   printf( "%10.6f %9.6f %9.6f\n",
                           cmat[i][0], cmat[i][1], cmat[i][2] );

                }

                printf( "Angular velocity:\n" );
                printf( "%20.16f %19.16f %19.16f\n", av[0], av[1], av[2] );

                /.
                Get state transformation from J2000 to the spacecraft
                frame.
                ./
                rav2xf_c ( cmat, av, fxmat );

                /.
                Display the results.
                ./
                printf( "\n" );
                printf( "State transformation matrix:\n" );
                for ( i = 0; i < 6; i++ )
                {

                   printf( "%10.6f %9.6f %9.6f %9.6f %9.6f %9.6f\n",
                           fxmat[i][0], fxmat[i][1], fxmat[i][2],
                           fxmat[i][3], fxmat[i][4], fxmat[i][5] );

                }
             }
             else
             {
                printf( "No rotation matrix/angular velocity found for %s\n",
                                                                       SCLKCH );
             }

             return ( 0 );
          }

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

          Rotation matrix:
           -0.604984  0.796222 -0.005028
           -0.784160 -0.596891 -0.169748
           -0.138158 -0.098752  0.985475
          Angular velocity:
            0.0000032866819065 -0.0000099372638338  0.0000197597699770

          State transformation matrix:
           -0.604984  0.796222 -0.005028  0.000000  0.000000  0.000000
           -0.784160 -0.596891 -0.169748  0.000000  0.000000  0.000000
           -0.138158 -0.098752  0.985475  0.000000  0.000000  0.000000
           -0.000016 -0.000012 -0.000003 -0.604984  0.796222 -0.005028
            0.000013 -0.000015 -0.000010 -0.784160 -0.596891 -0.169748
           -0.000008 -0.000006 -0.000002 -0.138158 -0.098752  0.985475

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

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

#### Version

       -CSPICE Version 1.0.2, 16-JUL-2020 (JDR)

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

           Added ROTATION to the required readings.

       -CSPICE Version 1.0.1, 12-APR-2007 (EDW)

           Edit to abstract.

       -CSPICE Version 1.0.0, 18-JUN-1999 (WLT) (NJB)

#### Index_Entries

       State transformation to rotation and angular velocity

#### Link to routine rav2xf_c source file rav2xf_c.c

    Fri Dec 31 18:41:11 2021