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dvhat_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

dvhat_c ( Derivative and unit vector "V-hat" of a state)

void dvhat_c ( ConstSpiceDouble s1  ,
SpiceDouble      sout )

Abstract

Find the unit vector corresponding to a state vector and the
derivative of the unit vector.

None.

DERIVATIVE
MATH
VECTOR

Brief_I/O

VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
s1         I   State to be normalized.
sout       O   Unit vector s1 / |s1|, and its time derivative.

Detailed_Input

s1          is any double precision state. If the position
component of the state is the zero vector, this
routine will detect it and will not attempt to divide
by zero.

Detailed_Output

sout        is a state containing the unit vector pointing in
the direction of position component of `s1' and the
derivative of the unit vector with respect to time.

`sout' may overwrite `s1'.

None.

Exceptions

Error free.

1)  If `s1' represents the zero vector, then the position
component of `sout' will also be the zero vector. The
velocity component will be the velocity component
of `s1'.

None.

Particulars

Let `s1' be a state vector with position and velocity components P
and V respectively. From these components one can compute the
unit vector parallel to P, call it `u' and the derivative of `u'
with respect to time, `du'. This pair (u,du) is the state returned
by this routine in `sout'.

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 `state' gives the apparent state of a body with
respect to an observer. This routine can be used to compute the
instantaneous angular rate of the object across the sky as seen
from the observers vantage.

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

KPL/MK

File name: dvhat_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
naif0009.tls                  Leapseconds

\begindata

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

\begintext

End of meta-kernel

Example code begins here.

/.
Program dvhat_ex1
./
#include <stdio.h>
#include <math.h>
#include "SpiceUsr.h"

int main()
{

SpiceDouble       et;
SpiceDouble       lt;
SpiceDouble       omega;
SpiceDouble       state  ;
SpiceDouble       ustate ;

SpiceChar       * epoch  = "Jan 1 2009";
SpiceChar       * target = "MOON";
SpiceChar       * frame  = "J2000";
SpiceChar       * abcorr = "LT+S";
SpiceChar       * obsrvr = "EARTH BARYCENTER";

/.
Load SPK, PCK, and LSK kernels, use a meta kernel for
convenience.
./
furnsh_c ( "dvhat_ex1.tm" );

/.
Define an arbitrary epoch, convert the epoch to ephemeris time.
./
str2et_c ( epoch, &et );

/.
Calculate the state of the moon with respect to the earth-moon
barycenter in J2000, corrected for light time and stellar
aberration at `et'.
./

spkezr_c ( target, et, frame, abcorr, obsrvr, state, &lt );

/.
Calculate the unit vector of `state' and the derivative of the
unit vector.
./
dvhat_c ( state, ustate );

/.
Calculate the instantaneous angular velocity from the magnitude
of the derivative of the unit vector.

v = r x omega

||omega|| = ||v||  for  r . v = 0
-----
||r||

||omega|| = ||v||  for  ||r|| = 1
./
omega = vnorm_c ( ustate+3 );

printf( "Instantaneous angular velocity (rad/sec): %18.12e\n",
omega );

return ( 0 );
}

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

None.

None.

Author_and_Institution

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

Version

-CSPICE Version 1.0.2, 02-JUL-2021 (JDR)