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 dazldr_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
       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.
#### Required_Reading
       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.

          Task description
          ================

          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

             KERNELS_TO_LOAD = ( 'de430.bsp',
                                 '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;

             /.
             Load SPICE kernels.
             ./
             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
#### Link to routine dazldr_c source file dazldr_c.c

    Fri Dec 31 18:41:04 2021