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Required Reading


   CSPICE_DRDPGR computes the Jacobian matrix of the transformation
   from planetographic to rectangular coordinates.



      body   name of the body with which the planetographic coordinate system
             is associated.

             [1,m] = size(body); char = class(body)

             `body' is used by this routine to look up from the
             kernel pool the prime meridian rate coefficient giving
             the body's spin sense.

      lon    planetographic longitude of the input point. This is the angle
             between the prime meridian and the meridian containing the input
             point. For bodies having prograde (aka direct) rotation, the
             direction of increasing longitude is positive west:  from the +X
             axis of the rectangular coordinate system toward the -Y axis. For
             bodies having retrograde rotation, the direction of increasing
             longitude is positive east: from the +X axis toward the +Y axis.

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

             The earth, moon, and sun are exceptions:
             planetographic longitude is measured positive east for
             these bodies.

             The default interpretation of longitude by this
             and the other planetographic coordinate conversion
             routines can be overridden; see the discussion in
             Particulars below for details.

             Longitude is measured in radians. On input, the range
             of longitude is unrestricted.

      lat    planetographic latitude of the input point.  For a point P on the
             reference spheroid, this is the angle  between the XY plane and
             the outward normal vector at P. For a point P not on the
             reference spheroid, the planetographic latitude is that of the
             closest point to P on the spheroid.

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

             Latitude is measured in radians.  On input, the range of
             latitude is unrestricted.

      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

             [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_drdpgr( body, lon, lat, alt, re, f)


      jacobi   the matrix of partial derivatives of the conversion from
               planetographic to rectangular coordinates evaluated at the
               input coordinates. This matrix 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'.




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

   To transform states given with respect to planetographic
   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 planetographic coordinates

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

   the velocity in rectangular coordinates is given by the matrix

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

   This routine computes the matrix


   In the planetographic coordinate system, longitude is defined
   using the spin sense of the body.  Longitude is positive to the
   west if the spin is prograde and positive to the east if the spin
   is retrograde.  The spin sense is given by the sign of the first
   degree term of the time-dependent polynomial for the body's prime
   meridian Euler angle "W":  the spin is retrograde if this term is
   negative and prograde otherwise.  For the sun, planets, most
   natural satellites, and selected asteroids, the polynomial
   expression for W may be found in a SPICE PCK kernel.

   The earth, moon, and sun are exceptions: planetographic longitude
   is measured positive east for these bodies.

   If you wish to override the default sense of positive longitude
   for a particular body, you can do so by defining the kernel


   where <body ID> represents the NAIF ID code of the body. This
   variable may be assigned either of the values


   For example, you can have this routine treat the longitude
   of the earth as increasing to the west using the kernel
   variable assignment


   Normally such assignments are made by placing them in a text
   kernel and loading that kernel via cspice_furnsh.

   The definition of this kernel variable controls the behavior of
   the CSPICE planetographic routines


   It does not affect the other SPICE coordinate conversion

Required Reading

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



   -Mice Version 1.0.0, 09-NOV-2012, EDW (JPL), SCK (JPL)


   Jacobian of rectangular w.r.t. planetographic coordinates

Wed Apr  5 18:00:30 2017