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

 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.
```

```   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

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
naif0009.tls                  Leapseconds

\begindata

'pck00008.tpc',
'naif0009.tls'  )

\begintext

End of meta-kernel

Example code begins here.

/.
./
#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.
./

/.
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.

```   Compute a unit cross product and its derivative
`Fri Dec 31 18:41:05 2021`