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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.

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

I/O


   Given:

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

      re   scalar double precision describing 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'.

      f    scalar double precision describing the flattening coefficient

               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:

      cspice_dgeodr, x, y, z, re, f, jacobi

   returns:

      jacobi   double precision 3x3 matrix describing the matrix of partial
               derivatives of the conversion between rectangular and geodetic
               coordinates, evaluated at the input coordinates. This matrix
               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'.

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


   ICY.REQ

Version


   -Icy Version 1.0.0, 28-DEC-2010, EDW (JPL)

Index_Entries


   Jacobian of geodetic  w.r.t. rectangular coordinates





Wed Apr  5 17:57:59 2017