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Index Page drdazl_c

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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

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

       void drdazl_c ( SpiceDouble         range,
                       SpiceDouble         az,
                       SpiceDouble         el,
                       SpiceBoolean        azccw,
                       SpiceBoolean        elplsz,
                       SpiceDouble         jacobi [3][3] )

#### Abstract

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

#### Required_Reading

       None.

#### Keywords

       COORDINATES
       DERIVATIVES
       MATRIX

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       range      I   Distance of a point from the origin.
       az         I   Azimuth of input point in radians.
       el         I   Elevation of input point in radians.
       azccw      I   Flag indicating how azimuth is measured.
       elplsz     I   Flag indicating how elevation is measured.
       jacobi     O   Matrix of partial derivatives.

#### Detailed_Input

       range       is the distance from the origin of the input point
                   specified by `range', `az', and `el'.

                   Negative values for `range' are not allowed.

                   Units are arbitrary and are considered to match those
                   of the rectangular coordinate system associated with the
                   output matrix `jacobi'.

       az          is the azimuth of the point. This is the angle between
                   the projection onto the XY plane of the vector from
                   the origin to the point and the +X axis of the
                   reference frame. `az' is zero at the +X axis.

                   The way azimuth is measured depends on the value of
                   the logical flag `azccw'. See the description of the
                   argument `azccw' for details.

                   The range (i.e., the set of allowed values) of `az' is
                   unrestricted. See the -Exceptions section for a
                   discussion on the `az' range.

                   Units are radians.

       el          is the elevation of the point. This is the angle
                   between the vector from the origin to the point and
                   the XY plane. `el' is zero at the XY plane.

                   The way elevation is measured depends on the value of
                   the logical flag `elplsz'. See the description of the
                   argument `elplsz' for details.

                   The range (i.e., the set of allowed values) of `el' is
                   [-pi/2, pi/2], but no error checking is done to ensure
                   that `el' is within this range. See the -Exceptions
                   section for a discussion on the `el' range.

                   Units are radians.

       azccw       is a flag indicating how the azimuth is measured.

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

       elplsz      if 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 azimuth/elevation to rectangular
                   coordinates. It has the form

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

                   evaluated at the input values of `range', `az' and `el'.

                   `x', `y', and `z' are given by the familiar formulae

                      x = range * cos( az )          * cos( el )
                      y = range * sin( azsnse * az ) * cos( el )
                      z = range * sin( eldir  * el )

                   where `azsnse' is +1 when `azccw' is SPICETRUE and -1
                   otherwise, and `eldir' is +1 when `elplsz' is SPICETRUE
                   and -1 otherwise.

#### Parameters

       None.

#### Exceptions

       1)  If the value of the input parameter `range' is negative, the
           error SPICE(VALUEOUTOFRANGE) is signaled by a routine in the
           call tree of this routine.

       2)  If the value of the input argument `el' is outside the
           range [-pi/2, pi/2], the results may not be as
           expected.

       3)  If the value of the input argument `az' is outside the
           range [0, 2*pi], the value will be mapped to a value
           inside the range that differs from the input value by an
           integer multiple of 2*pi.

#### Files

       None.

#### Particulars

       It is often convenient to describe the motion of an object
       in azimuth/elevation coordinates. It is also convenient to
       manipulate vectors associated with the object in rectangular
       coordinates.

       The transformation of an azimuth/elevation state into an
       equivalent rectangular state makes use of the Jacobian matrix
       of the transformation between the two systems.

       Given a state in latitudinal coordinates,

          ( r, az, el, dr, daz, del )

       the velocity in rectangular coordinates is given by the matrix
       equation
                      t          |                             t
          (dx, dy, dz)   = jacobi|             * (dr, daz, del)
                                 |(r,az,el)

       This routine computes the matrix

                |
          jacobi|
                |(r,az,el)

       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: drdazl_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 drdazl_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local parameters
             ./
             #define META         "drdazl_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, 30-DEC-2021 (JDR)

#### Index_Entries

       Jacobian matrix of rectangular w.r.t. AZ/EL coordinates
       range, azimuth and elevation to rectangular derivative
       Range, AZ and EL to rectangular velocity conversion

#### Link to routine drdazl_c source file drdazl_c.c

    Fri Dec 31 18:41:04 2021