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Abstract
I/O
Examples
Particulars
Required Reading
Version
Index_Entries

Abstract


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

I/O


   Given:

      x,
      y,
      z    the rectangular coordinates of the point at which the Jacobian of
           the map from rectangular to geodetic coordinates is desired.

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

      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'.

           [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_dgeodr( x, y, z, re, f)

   returns:

      jacobi   the matrix of partial derivatives of the conversion between
               rectangular and geodetic coordinates, evaluated at the input
               coordinates. This matrix has the form

               [3,3] = size(jacobi); double = class(jacobi)

                   -                            -
                  |  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.

Examples


   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)

Required Reading


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

   MICE.REQ

Version


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

Index_Entries


   Jacobian of geodetic  w.r.t. rectangular coordinates


Wed Apr  5 18:00:30 2017