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 xf2rav_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

       xf2rav_c ( Transform to rotation and angular velocity)

       void xf2rav_c ( ConstSpiceDouble   xform [6][6],
                       SpiceDouble        rot   [3][3],
                       SpiceDouble        av    [3]     )

#### Abstract

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

#### Required_Reading

       ROTATION

#### Keywords

       FRAMES

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       xform      I   is a state transformation matrix.
       rot        O   is the rotation associated with `xform'.
       av         O   is the angular velocity associated with `xform'.

#### Detailed_Input

       xform       is a state transformation matrix from one frame
                   FRAME1 to some other frame FRAME2.

#### Detailed_Output

       rot         is a rotation 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 )

                   The components of `av' are given relative to FRAME1.

#### Parameters

       None.

#### Exceptions

       Error free.

       1)  No checks are performed on `xform' to ensure that it is indeed
           a state transformation matrix.

#### Files

       None.

#### Particulars

       This routine is essentially a macro routine for converting
       state transformation matrices into the equivalent representation
       in terms of a rotation and angular velocity.

       This routine is an inverse of the routine rav2xf_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) Suppose that you wanted to determine the angular velocity
          of the Earth body-fixed reference frame with respect to
          J2000 at a particular epoch ET. The following code example
          illustrates a procedure for computing the angular velocity.

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

             KPL/MK

             File name: xf2rav_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
                ---------                     --------
                earth_720101_070426.bpc       Earth historical
                                              binary PCK
                naif0012.tls                  Leapseconds

             \begindata

                KERNELS_TO_LOAD = ( 'earth_720101_070426.bpc',
                                    'naif0012.tls'            )

             \begintext

             End of meta-kernel

          Example code begins here.

          /.
             Program xf2rav_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local parameters.
             ./
             #define META         "xf2rav_ex1.tm"
             #define UTCSTR       "2005-OCT-10 16:00:00"

             /.
             Local variables.
             ./
             SpiceDouble          av     [3];
             SpiceDouble          et;
             SpiceDouble          ftmtrx [6][6];
             SpiceDouble          rot    [3][3];

             SpiceInt             i;

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

             /.
             Convert the input time to seconds past J2000 TDB.
             ./
             str2et_c ( UTCSTR, &et );

             /.
             Get the transformation matrix from J2000 frame to
             ITRF93.
             ./
             sxform_c ( "J2000", "ITRF93", et, ftmtrx );

             /.
             Now get the angular velocity by calling xf2rav_c
             ./
             xf2rav_c ( ftmtrx, rot, av );

             /.
             Display the results.
             ./
             printf( "Rotation matrix:\n" );
             for ( i = 0; i < 3; i++ )
             {

                printf( "%16.11f %15.11f %15.11f\n",
                        rot[i][0], rot[i][1], rot[i][2] );

             }

             printf( "\n" );
             printf( "Angular velocity:\n" );
             printf( "%16.11f %15.11f %15.11f\n", av[0], av[1], av[2] );

             return ( 0 );
          }

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

          Rotation matrix:
            -0.18603277688  -0.98254352801   0.00014659080
             0.98254338275  -0.18603282936  -0.00053610915
             0.00055402128   0.00004429795   0.99999984555

          Angular velocity:
             0.00000004025   0.00000000324   0.00007292114

#### 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, 19-MAY-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 xf2rav_c source file xf2rav_c.c

    Fri Dec 31 18:41:15 2021