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   drdpgr_c ( Derivative of rectangular w.r.t. planetographic ) 

   void drdpgr_c ( ConstSpiceChar  * body,
                   SpiceDouble       lon,
                   SpiceDouble       lat,
                   SpiceDouble       alt,
                   SpiceDouble       re,
                   SpiceDouble       f,
                   SpiceDouble       jacobi[3][3] )


   Compute the Jacobian matrix of the transformation from
   planetographic to rectangular coordinates.






   --------  ---  --------------------------------------------------
   body       I   Name of body with which coordinates are associated.
   lon        I   Planetographic longitude of a point (radians).
   lat        I   Planetographic latitude of a point (radians).
   alt        I   Altitude of a point above reference spheroid.
   re         I   Equatorial radius of the reference spheroid.
   f          I   Flattening coefficient.
   jacobi     O   Matrix of partial derivatives.


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

               `body' is used by this routine to look up from the
               kernel pool the prime meridian rate coefficient giving
               the body's spin sense. See the -Files and -Particulars
               header sections below for details.

   lon         is the 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.

               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         is the 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.

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

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

   re          is the 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

   f           is the flattening coefficient =

                  (re-rp) / re

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


   jacobi      is the matrix of partial derivatives of the conversion
               from planetographic to rectangular coordinates. It
               has the form

                  .-                              -.
                  |  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'.




   1)  If the body name `body' cannot be mapped to a NAIF ID code, and
       if `body' is not a string representation of an integer, the
       error SPICE(IDCODENOTFOUND) is signaled by a routine in the
       call tree of this routine.

   2)  If the kernel variable

          BODY<ID code>_PGR_POSITIVE_LON

       is present in the kernel pool but has a value other
       than one of


       the error SPICE(INVALIDOPTION) is signaled by a routine in the
       call tree of this routine. Case and blanks are ignored when
       these values are interpreted.

   3)  If polynomial coefficients for the prime meridian of `body' are
       not available in the kernel pool, and if the kernel variable
       BODY<ID code>_PGR_POSITIVE_LON is not present in the kernel
       pool, the error SPICE(MISSINGDATA) is signaled by a routine in
       the call tree of this routine.

   4)  If the equatorial radius is non-positive, the error
       SPICE(VALUEOUTOFRANGE) is signaled by a routine in the call
       tree of this routine.

   5)  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.

   6)  If the `body' input string pointer is null, the error
       SPICE(NULLPOINTER) is signaled.

   7)  If the `body' input string has zero length, the error
       SPICE(EMPTYSTRING) is signaled.


   This routine expects a kernel variable giving body's prime
   meridian angle as a function of time to be available in the
   kernel pool. Normally this item is provided by loading a PCK
   file. The required kernel variable is named

      BODY<body ID>_PM

   where <body ID> represents a string containing the NAIF integer
   ID code for `body'. For example, if `body' is "JUPITER", then
   the name of the kernel variable containing the prime meridian
   angle coefficients is


   See the PCK Required Reading for details concerning the prime
   meridian kernel variable.

   The optional kernel variable


   also is normally defined via loading a text kernel. When this
   variable is present in the kernel pool, the prime meridian
   coefficients for `body' are not required by this routine. See the
   -Particulars section below for details.


   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 furnsh_c.

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


   It does not affect the other CSPICE coordinate conversion


   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 planetographic state of the earth as seen from
      Mars in the J2000 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


         File name:

         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
            ---------                     --------
            de405.bsp                     Planetary ephemeris
            pck00008.tpc                  Planet orientation and
            naif0007.tls                  Leapseconds


            KERNELS_TO_LOAD = ( 'de405.bsp',
                                'naif0007.tls'  )


         End of meta-kernel

      Example code begins here.

         Program drdpgr_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             pgrvel [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
         furnsh_c ( "" );

         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 geometric state of earth as seen from Mars at
         January 1, 2005 TDB, relative to the J2000 reference
         str2et_c ( "January 1, 2005 TDB", &et);

         spkezr_c ( "Earth", et,    "J2000", "LT+S",
                    "Mars",  state, &lt             );

         Convert position to planetographic coordinates.
         recpgr_c ( "mars", state, re, f, &lon, &lat, &alt );

         Convert velocity to planetographic coordinates.

         dpgrdr_c ( "MARS",  state[0],  state[1],  state[2],
                    re,      f,         jacobi               );

         mxv_c ( jacobi, state+3, pgrvel );

         As a check, convert the planetographic state back to
         rectangular coordinates.
         pgrrec_c ( "mars", lon, lat, alt, re, f, rectan );
         drdpgr_c ( "mars", lon, lat, alt, re, f, jacobi );

         mxv_c ( jacobi, pgrvel, drectn );

         printf ( "\n"
                  "Rectangular coordinates:\n"
                  "  X (km)                 = %18.9e\n"
                  "  Y (km)                 = %18.9e\n"
                  "  Z (km)                 = %18.9e\n"
                  "Rectangular velocity:\n"
                  "  dX/dt (km/s)           = %18.9e\n"
                  "  dY/dt (km/s)           = %18.9e\n"
                  "  dZ/dt (km/s)           = %18.9e\n"
                  state [0],
                  state [1],
                  state [2],
                  state [3],
                  state [4],
                  state [5]                );

         printf ( "Ellipsoid shape parameters:\n"
                  "  Equatorial radius (km) = %18.9e\n"
                  "  Polar radius      (km) = %18.9e\n"
                  "  Flattening coefficient = %18.9e\n"
                  f                );

         printf ( "Planetographic coordinates:\n"
                  "  Longitude (deg)        = %18.9e\n"
                  "  Latitude  (deg)        = %18.9e\n"
                  "  Altitude  (km)         = %18.9e\n"
                  "Planetographic velocity:\n"
                  "  d Longitude/dt (deg/s) = %18.9e\n"
                  "  d Latitude/dt  (deg/s) = %18.9e\n"
                  "  d Altitude/dt  (km/s)  = %18.9e\n"
                  lon / rpd_c(),
                  lat / rpd_c(),
                  pgrvel[2]                );

         printf ( "Rectangular coordinates from inverse mapping:\n"
                  "  X (km)                 = %18.9e\n"
                  "  Y (km)                 = %18.9e\n"
                  "  Z (km)                 = %18.9e\n"
                  "Rectangular velocity from inverse mapping:\n"
                  "  dX/dt (km/s)           = %18.9e\n"
                  "  dY/dt (km/s)           = %18.9e\n"
                  "  dZ/dt (km/s)           = %18.9e\n"
                  rectan [0],
                  rectan [1],
                  rectan [2],
                  drectn [0],
                  drectn [1],
                  drectn [2]                );

         return ( 0 );

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

      Rectangular coordinates:

        X (km)                 =    1.460397325e+08
        Y (km)                 =    2.785466068e+08
        Z (km)                 =    1.197503153e+08

      Rectangular velocity:

        dX/dt (km/s)           =   -4.704327203e+01
        dY/dt (km/s)           =    9.073261343e+00
        dZ/dt (km/s)           =    4.757916936e+00

      Ellipsoid shape parameters:

        Equatorial radius (km) =    3.396190000e+03
        Polar radius      (km) =    3.376200000e+03
        Flattening coefficient =    5.886007556e-03

      Planetographic coordinates:

        Longitude (deg)        =    2.976676591e+02
        Latitude  (deg)        =    2.084450403e+01
        Altitude  (km)         =    3.365318254e+08

      Planetographic velocity:

        d Longitude/dt (deg/s) =   -8.357706644e-06
        d Latitude/dt  (deg/s) =    1.593556674e-06
        d Altitude/dt  (km/s)  =   -1.121160078e+01

      Rectangular coordinates from inverse mapping:

        X (km)                 =    1.460397325e+08
        Y (km)                 =    2.785466068e+08
        Z (km)                 =    1.197503153e+08

      Rectangular velocity from inverse mapping:

        dX/dt (km/s)           =   -4.704327203e+01
        dY/dt (km/s)           =    9.073261343e+00
        dZ/dt (km/s)           =    4.757916936e+00






   N.J. Bachman        (JPL)
   J. Diaz del Rio     (ODC Space)
   W.L. Taber          (JPL)


   -CSPICE Version 1.0.1, 10-AUG-2021 (JDR)

       Edited the header to comply with NAIF standard. Modified code example
       to use meta-kernel to load kernels.

       Updated example code to split printf statement in three in order to
       comply with ANSI-C maximum string literal of length.

   -CSPICE Version 1.0.0, 26-DEC-2004 (NJB) (WLT)


   Jacobian of rectangular w.r.t. planetographic coordinates
Fri Dec 31 18:41:04 2021