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 dgeodr_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
       dgeodr_c ( Derivative of geodetic w.r.t. rectangular )

       void dgeodr_c ( SpiceDouble   x,
                       SpiceDouble   y,
                       SpiceDouble   z,
                       SpiceDouble   re,
                       SpiceDouble   f,
                       SpiceDouble   jacobi[3][3] )
#### Abstract
       Compute the Jacobian matrix of the transformation from
       rectangular to geodetic 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.
       re         I   Equatorial radius of the reference spheroid.
       f          I   Flattening coefficient.
       jacobi     O   Matrix of partial derivatives.
#### Detailed_Input
       x,
       y,
       z           are the rectangular coordinates of the point at
                   which the Jacobian of the map from rectangular
                   to geodetic coordinates is desired.

       re          Equatorial radius of the reference spheroid.

       f           Flattening coefficient = (re-rp) / re,  where rp is
                   the polar radius of the spheroid. (More importantly
                   rp = re*(1-f).)
#### Detailed_Output
       jacobi      is the matrix of partial derivatives of the conversion
                   between rectangular and geodetic coordinates. It
                   has the form

                       .-                            -.
                       |  dlon/dx   dlon/dy  dlon/dz  |
                       |  dlat/dx   dlat/dy  dlat/dz  |
                       |  dalt/dx   dalt/dy  dalt/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 and Y = 0), the Jacobian
           is undefined, the error SPICE(POINTONZAXIS) is signaled by a
           routine in the call tree of this routine.

       2)  If the flattening coefficient is greater than or equal to one,
           the error SPICE(VALUEOUTOFRANGE) is signaled by a routine in the
           call tree of this routine.

       3)  If the equatorial radius is not positive, the error
           SPICE(BADRADIUS) 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 geodetic coordinates to gain insights about phenomena
       in this coordinate frame.

       To transform rectangular velocities to derivatives of coordinates
       in a geodetic system, one uses the Jacobian of the transformation
       between the two systems.

       Given a state in rectangular coordinates

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

       the velocity in geodetic coordinates is given by the matrix
       equation:
                            t          |                     t
          (dlon, dlat, dalt)   = jacobi|       * (dx, dy, dz)
                                       |(x,y,z)

       This routine computes the matrix

                |
          jacobi|
                |(x, y, z)
#### 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 geodetic state of the earth as seen from
          Mars in the IAU_MARS reference frame at January 1, 2005 TDB.
          Map this state back to rectangular coordinates as a check.

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

             KPL/MK

             File name: dgeodr_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
                pck00010.tpc                  Planet orientation and
                                              radii
                naif0009.tls                  Leapseconds

             \begindata

                KERNELS_TO_LOAD = ( 'de421.bsp',
                                    'pck00010.tpc',
                                    'naif0009.tls'  )

             \begintext

             End of meta-kernel

          Example code begins here.

          /.
             Program dgeodr_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local variables
             ./
             SpiceDouble          alt;
             SpiceDouble          drectn [3];
             SpiceDouble          et;
             SpiceDouble          f;
             SpiceDouble          jacobi [3][3];
             SpiceDouble          lat;
             SpiceDouble          lon;
             SpiceDouble          lt;
             SpiceDouble          geovel [3];
             SpiceDouble          radii  [3];
             SpiceDouble          re;
             SpiceDouble          rectan [3];
             SpiceDouble          rp;
             SpiceDouble          state  [6];

             SpiceInt             n;

             /.
             Load SPK, PCK, and LSK kernels, use a meta kernel for
             convenience.
             ./
             furnsh_c ( "dgeodr_ex1.tm" );

             /.
             Look up the radii for Mars.  Although we
             omit it here, we could first call badkpv_c
             to make sure the variable BODY499_RADII
             has three elements and numeric data type.
             If the variable is not present in the kernel
             pool, bodvrd_c will signal an error.
             ./
             bodvrd_c ( "MARS", "RADII", 3, &n, radii );

             /.
             Compute flattening coefficient.
             ./
             re  =  radii[0];
             rp  =  radii[2];
             f   =  ( re - rp ) / re;

             /.
             Look up the apparent state of earth as seen from Mars at
             January 1, 2005 TDB, relative to the IAU_MARS reference
             frame.
             ./
             str2et_c ( "January 1, 2005 TDB", &et );

             spkezr_c ( "Earth", et, "IAU_MARS", "LT+S", "Mars", state, &lt );

             /.
             Convert position to geodetic coordinates.
             ./
             recgeo_c ( state, re, f, &lon, &lat, &alt );

             /.
             Convert velocity to geodetic coordinates.
             ./

             dgeodr_c ( state[0], state[1], state[2], re, f, jacobi );

             mxv_c ( jacobi, state+3, geovel );

             /.
             As a check, convert the geodetic state back to
             rectangular coordinates.
             ./
             georec_c ( lon, lat, alt, re, f, rectan );

             drdgeo_c ( lon, lat, alt, re, f, jacobi );

             mxv_c ( jacobi, geovel, drectn );

             printf( " \n" );
             printf( "Rectangular coordinates:\n" );
             printf( " \n" );
             printf( " X (km)                 =  %17.8e\n", state[0] );
             printf( " Y (km)                 =  %17.8e\n", state[1] );
             printf( " Z (km)                 =  %17.8e\n", state[2] );
             printf( " \n" );
             printf( "Rectangular velocity:\n" );
             printf( " \n" );
             printf( " dX/dt (km/s)           =  %17.8e\n", state[3] );
             printf( " dY/dt (km/s)           =  %17.8e\n", state[4] );
             printf( " dZ/dt (km/s)           =  %17.8e\n", state[5] );
             printf( " \n" );
             printf( "Ellipsoid shape parameters: \n" );
             printf( " \n" );
             printf( " Equatorial radius (km) =  %17.8e\n", re );
             printf( " Polar radius      (km) =  %17.8e\n", rp );
             printf( " Flattening coefficient =  %17.8e\n", f );
             printf( " \n" );
             printf( "Geodetic coordinates:\n" );
             printf( " \n" );
             printf( " Longitude (deg)        =  %17.8e\n", lon / rpd_c() );
             printf( " Latitude  (deg)        =  %17.8e\n", lat / rpd_c() );
             printf( " Altitude  (km)         =  %17.8e\n", alt );
             printf( " \n" );
             printf( "Geodetic velocity:\n" );
             printf( " \n" );
             printf( " d Longitude/dt (deg/s) =  %17.8e\n", geovel[0]/rpd_c() );
             printf( " d Latitude/dt  (deg/s) =  %17.8e\n", geovel[1]/rpd_c() );
             printf( " d Altitude/dt  (km/s)  =  %17.8e\n", geovel[2] );
             printf( " \n" );
             printf( "Rectangular coordinates from inverse mapping:\n" );
             printf( " \n" );
             printf( " X (km)                 =  %17.8e\n", rectan[0] );
             printf( " Y (km)                 =  %17.8e\n", rectan[1] );
             printf( " Z (km)                 =  %17.8e\n", rectan[2] );
             printf( " \n" );
             printf( "Rectangular velocity from inverse mapping:\n" );
             printf( " \n" );
             printf( " dX/dt (km/s)           =  %17.8e\n", drectn[0] );
             printf( " dY/dt (km/s)           =  %17.8e\n", drectn[1] );
             printf( " dZ/dt (km/s)           =  %17.8e\n", drectn[2] );
             printf( " \n" );

             return ( 0 );
          }

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

          Rectangular coordinates:

           X (km)                 =    -7.60961826e+07
           Y (km)                 =     3.24363805e+08
           Z (km)                 =     4.74704840e+07

          Rectangular velocity:

           dX/dt (km/s)           =     2.29520749e+04
           dY/dt (km/s)           =     5.37601112e+03
           dZ/dt (km/s)           =    -2.08811490e+01

          Ellipsoid shape parameters:

           Equatorial radius (km) =     3.39619000e+03
           Polar radius      (km) =     3.37620000e+03
           Flattening coefficient =     5.88600756e-03

          Geodetic coordinates:

           Longitude (deg)        =     1.03202903e+02
           Latitude  (deg)        =     8.10898757e+00
           Altitude  (km)         =     3.36531823e+08

          Geodetic velocity:

           d Longitude/dt (deg/s) =    -4.05392876e-03
           d Latitude/dt  (deg/s) =    -3.31899337e-06
           d Altitude/dt  (km/s)  =    -1.12116015e+01

          Rectangular coordinates from inverse mapping:

           X (km)                 =    -7.60961826e+07
           Y (km)                 =     3.24363805e+08
           Z (km)                 =     4.74704840e+07

          Rectangular velocity from inverse mapping:

           dX/dt (km/s)           =     2.29520749e+04
           dY/dt (km/s)           =     5.37601112e+03
           dZ/dt (km/s)           =    -2.08811490e+01
#### Restrictions
       None.
#### Literature_References
       None.
#### Author_and_Institution
       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
       W.L. Taber          (JPL)
#### Version
       -CSPICE Version 1.0.1, 01-NOV-2021 (JDR)

           Edited the header to comply with NAIF standard.
           Added complete code example.

       -CSPICE Version 1.0.0, 18-JUL-2001 (WLT) (NJB)
#### Index_Entries
       Jacobian of geodetic  w.r.t. rectangular coordinates
#### Link to routine dgeodr_c source file dgeodr_c.c

    Fri Dec 31 18:41:04 2021