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dazldr_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

```   dazldr_c ( Derivative of AZ/EL w.r.t. rectangular )

void dazldr_c ( SpiceDouble         x,
SpiceDouble         y,
SpiceDouble         z,
SpiceBoolean        azccw,
SpiceBoolean        elplsz,
SpiceDouble         jacobi [3][3] )

```

#### Abstract

```   Compute the Jacobian matrix of the transformation from
rectangular to azimuth/elevation coordinates.
```

```   None.
```

#### Keywords

```   COORDINATES
DERIVATIVES
MATRIX

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
x          I   x-coordinate of point.
y          I   y-coordinate of point.
z          I   z-coordinate of point.
azccw      I   Flag indicating how azimuth is measured.
elplsz     I   Flag indicating how elevation is measured.
jacobi     O   Matrix of partial derivatives.
```

#### Detailed_Input

```   x,
y,
z           are the rectangular coordinates of the point at
which the Jacobian matrix of the map from rectangular
to azimuth/elevation coordinates is desired.

azccw       is a flag indicating how the azimuth is measured.

If `azccw' is SPICETRUE, the azimuth increases in the
counterclockwise direction; otherwise it increases
in the clockwise direction.

elplsz      is a flag indicating how the elevation is measured.

If `elplsz' is SPICETRUE, the elevation increases from the
XY plane toward +Z; otherwise toward -Z.
```

#### Detailed_Output

```   jacobi      is the matrix of partial derivatives of the
transformation from rectangular to azimuth/elevation
coordinates. It has the form

.-                            -.
|  dr/dx     dr/dy     dr/dz   |
|  daz/dx    daz/dy    daz/dz  |
|  del/dx    del/dy    del/dz  |
`-                            -'

evaluated at the input values of `x', `y', and `z'.
```

#### Parameters

```   None.
```

#### Exceptions

```   1)  If the input point is on the Z-axis ( x = 0 and y = 0 ), the
Jacobian matrix is undefined and therefore, the error
SPICE(POINTONZAXIS) is signaled by a routine in the call tree
of this routine.
```

#### Files

```   None.
```

#### Particulars

```   When performing vector calculations with velocities it is
usually most convenient to work in rectangular coordinates.
However, once the vector manipulations have been performed
it is often desirable to convert the rectangular representations
into azimuth/elevation coordinates to gain insights about
phenomena in this coordinate system.

To transform rectangular velocities to derivatives of coordinates
in an azimuth/elevation coordinate system, one uses the Jacobian
matrix of the transformation between the two systems.

Given a state in rectangular coordinates

( x, y, z, dx, dy, dz )

the corresponding azimuth/elevation coordinate derivatives are
given by the matrix equation:

t          |                      t
(dr, daz, del)   = jacobi|        * (dx, dy, dz)
|(x,y,z)

This routine computes the matrix

|
jacobi|
|(x, y, z)

In the azimuth/elevation coordinate system, several conventions
exist on how azimuth and elevation are measured. Using the `azccw'
and `elplsz' flags, users indicate which conventions shall be used.
See the descriptions of these input arguments for details.
```

#### 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) Find the azimuth/elevation state of Venus as seen from the
DSS-14 station at a given epoch. Map this state back to
rectangular coordinates as a check.

================

In this example, we will obtain the apparent state of Venus as
seen from the DSS-14 station in the DSS-14 topocentric
reference frame. We will use a station frames kernel and
transform the resulting rectangular coordinates to azimuth,
elevation and range and its derivatives using recazl_c and
dazldr_c.

We will map this state back to rectangular coordinates using
azlrec_c and drdazl_c.

In order to introduce the usage of the logical flags `azccw'
and `elplsz', we will request the azimuth to be measured
clockwise and the elevation positive towards +Z
axis of the DSS-14_TOPO reference frame.

Kernels
=======

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

KPL/MK

File name: dazldr_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
---------                        --------
de430.bsp                        Planetary ephemeris
naif0011.tls                     Leapseconds
earth_720101_070426.bpc          Earth historical
binary PCK
earthstns_itrf93_050714.bsp      DSN station SPK
earth_topo_050714.tf             DSN station FK

\begindata

'naif0011.tls',
'earth_720101_070426.bpc',
'earthstns_itrf93_050714.bsp',
'earth_topo_050714.tf'         )

\begintext

End of meta-kernel.

Example code begins here.

/.
Program dazldr_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local parameters
./
#define META         "dazldr_ex1.tm"

/.
Local variables
./
SpiceChar          * abcorr;
SpiceChar          * obs;
SpiceChar          * obstim;
SpiceChar          * ref;
SpiceChar          * target;

SpiceDouble          az;
SpiceDouble          azlvel [3];
SpiceDouble          drectn [3];
SpiceDouble          el;
SpiceDouble          et;
SpiceDouble          jacobi [3][3];
SpiceDouble          lt;
SpiceDouble          state  [6];
SpiceDouble          r;
SpiceDouble          rectan [3];

SpiceBoolean         azccw;
SpiceBoolean         elplsz;

/.
./
furnsh_c ( META );

/.
Convert the observation time to seconds past J2000 TDB.
./
obstim = "2003 OCT 13 06:00:00.000000 UTC";

str2et_c ( obstim, &et );

/.
Set the target, observer, observer frame, and
aberration corrections.
./
target = "VENUS";
obs    = "DSS-14";
ref    = "DSS-14_TOPO";
abcorr = "CN+S";

/.
Compute the observer-target state.
./
spkezr_c ( target, et, ref, abcorr, obs, state, &lt );

/.
Convert position to azimuth/elevation coordinates,
with azimuth increasing clockwise and elevation
positive towards +Z axis of the DSS-14_TOPO
reference frame
./
azccw  = SPICEFALSE;
elplsz = SPICETRUE;

recazl_c ( state, azccw, elplsz, &r, &az, &el );

/.
Convert velocity to azimuth/elevation coordinates.
./
dazldr_c ( state[0], state[1], state[2], azccw, elplsz, jacobi );

mxv_c ( jacobi, state+3, azlvel );

/.
As a check, convert the azimuth/elevation state back to
rectangular coordinates.
./
azlrec_c ( r, az, el, azccw, elplsz, rectan );

drdazl_c ( r, az, el, azccw, elplsz, jacobi );

mxv_c ( jacobi, azlvel, drectn );

printf( "\n" );
printf( "AZ/EL coordinates:\n" );
printf( "\n" );
printf( "   Range      (km)        =  %19.8f\n", r );
printf( "   Azimuth    (deg)       =  %19.8f\n", az * dpr_c() );
printf( "   Elevation  (deg)       =  %19.8f\n", el * dpr_c() );
printf( "\n" );
printf( "AZ/EL velocity:\n" );
printf( "\n" );
printf( "   d Range/dt     (km/s)  =  %19.8f\n", azlvel[0] );
printf( "   d Azimuth/dt   (deg/s) =  %19.8f\n",
azlvel[1] * dpr_c() );
printf( "   d Elevation/dt (deg/s) =  %19.8f\n",
azlvel[2] * dpr_c() );
printf( "\n" );
printf( "Rectangular coordinates:\n" );
printf( "\n" );
printf( "   X (km)                 =  %19.8f\n", state[0] );
printf( "   Y (km)                 =  %19.8f\n", state[1] );
printf( "   Z (km)                 =  %19.8f\n", state[2] );
printf( "\n" );
printf( "Rectangular velocity:\n" );
printf( "\n" );
printf( "   dX/dt (km/s)           =  %19.8f\n", state[3] );
printf( "   dY/dt (km/s)           =  %19.8f\n", state[4] );
printf( "   dZ/dt (km/s)           =  %19.8f\n", state[5] );
printf( "\n" );
printf( "Rectangular coordinates from inverse mapping:\n" );
printf( "\n" );
printf( "   X (km)                 =  %19.8f\n", rectan[0] );
printf( "   Y (km)                 =  %19.8f\n", rectan[1] );
printf( "   Z (km)                 =  %19.8f\n", rectan[2] );
printf( "\n" );
printf( "Rectangular velocity from inverse mapping:\n" );
printf( "\n" );
printf( "   dX/dt (km/s)           =  %19.8f\n", drectn[0] );
printf( "   dY/dt (km/s)           =  %19.8f\n", drectn[1] );
printf( "   dZ/dt (km/s)           =  %19.8f\n", drectn[2] );
printf( "\n" );

return ( 0 );
}

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

AZ/EL coordinates:

Range      (km)        =   245721478.99272084
Azimuth    (deg)       =         294.48543372
Elevation  (deg)       =         -48.94609726

AZ/EL velocity:

d Range/dt     (km/s)  =          -4.68189834
d Azimuth/dt   (deg/s) =           0.00402256
d Elevation/dt (deg/s) =          -0.00309156

Rectangular coordinates:

X (km)                 =    66886767.37916667
Y (km)                 =   146868551.77222887
Z (km)                 =  -185296611.10841590

Rectangular velocity:

dX/dt (km/s)           =        6166.04150307
dY/dt (km/s)           =      -13797.77164550
dZ/dt (km/s)           =       -8704.32385654

Rectangular coordinates from inverse mapping:

X (km)                 =    66886767.37916658
Y (km)                 =   146868551.77222890
Z (km)                 =  -185296611.10841590

Rectangular velocity from inverse mapping:

dX/dt (km/s)           =        6166.04150307
dY/dt (km/s)           =      -13797.77164550
dZ/dt (km/s)           =       -8704.32385654
```

#### Restrictions

```   None.
```

#### Literature_References

```   None.
```

#### Author_and_Institution

```   J. Diaz del Rio     (ODC Space)
```

#### Version

```   -CSPICE Version 1.0.0, 07-AUG-2021 (JDR)
```

#### Index_Entries

```   Jacobian matrix of AZ/EL w.r.t. rectangular coordinates
Rectangular to range, azimuth and elevation derivative
Rectangular to range, AZ and EL velocity conversion
```
`Fri Dec 31 18:41:04 2021`