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rav2xf_c

 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.
```

```   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

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

'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;

/.
./
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)

code example based on existing example.

```   State transformation to rotation and angular velocity
`Fri Dec 31 18:41:11 2021`