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Abstract
I/O
Examples
Particulars
Required Reading
Version
Index_Entries

Abstract


   CSPICE_DRDGEO computes the Jacobian of the transformation from
   geodetic to rectangular coordinates.

I/O


   Given:

      lon   geodetic longitude of point (radians).

            [1,n] = size(lon); double = class(lon)

      lat   geodetic latitude of point (radians).

            [1,n] = size(lat); double = class(lat)

      alt   Altitude of point above the reference spheroid. Units of `alt'
            must match those of `re'.

            [1,n] = size(alt); double = class(alt)

      re    equatorial radius of a reference spheroid. This spheroid is a
            volume of revolution:  its horizontal cross sections are circular.
             The shape of the spheroid is defined by an equatorial radius `re'
            and a polar radius `rp'.  Units of 're' must match those of 'alt'.

            [1,1] = size(re); double = class(re)

      f     the flattening coefficient

            [1,1] = size(f); double = class(f)

               f = (re-rp) / re

             where rp is the polar radius of the spheroid. (More importantly
             rp = re*(1-f).) The units of `rp' match those of `re'.

   the call:

      jacobi = cspice_drdgeo( lon, lat, alt, re, f)

   returns:

      jacobi   the matrix of partial derivatives of the conversion between
               geodetic and rectangular coordinates. It has the form

               If [1,1] = size(lon) then [3,3]   = size(jacobi)
               If [1,n] = size(lon) then [3,3,n] = size(jacobi)
                                          double = class(jacobi)

                  -                             -
                 |  dx/dlon   dx/dlat  dx/dalt   |
                 |                               |
                 |  dy/dlon   dy/dlat  dy/dalt   |
                 |                               |
                 |  dz/dlon   dz/dlat  dz/dalt   |
                  -                             -

               evaluated at the input values of lon, lat and alt.

               The formulae for computing x, y, and z from
               geodetic coordinates are given below.

                  x = [alt +        re/g(lat,f)]*cos(lon)*cos(lat)


                  y = [alt +        re/g(lat,f)]*sin(lon)*cos(lat)

                                    2
                  z = [alt + re*(1-f) /g(lat,f)]*         sin(lat)

               where

                   re is the polar radius of the reference spheroid.

                   f  is the flattening factor (the polar radius is
                       obtained by multiplying the equatorial radius by 1-f).

                   g( lat, f ) is given by

                                2             2     2
                      sqrt ( cos (lat) + (1-f) * sin (lat) )

Examples


   None.

Particulars


   It is often convenient to describe the motion of an object in
   the geodetic coordinate system.  However, when performing
   vector computations its hard to beat rectangular coordinates.

   To transform states given with respect to geodetic coordinates
   to states with respect to rectangular coordinates, one makes use
   of the Jacobian of the transformation between the two systems.

   Given a state in geodetic coordinates

        ( lon, lat, alt, dlon, dlat, dalt )

   the velocity in rectangular coordinates is given by the matrix
   equation:

                  t          |                                 t
      (dx, dy, dz)   = jacobi|             * (dlon, dlat, dalt)
                             |(lon,lat,alt)


   This routine computes the matrix

            |
      jacobi|
            |(lon,lat,alt)

Required Reading


   For important details concerning this module's function, please refer to
   the CSPICE routine drdgeo_c.

   MICE.REQ

Version


   -Mice Version 1.0.0, 12-MAR-2012, EDW (JPL), SCK (JPL)

Index_Entries


   Jacobian of rectangular w.r.t. geodetic coordinates


Wed Apr  5 18:00:30 2017