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dpgrdr_c
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Procedure
Abstract
Required_Reading
Keywords
Brief_I/O
Detailed_Input
Detailed_Output
Parameters
Exceptions
Files
Particulars
Examples
Restrictions
Literature_References
Author_and_Institution
Version
Index_Entries

Procedure

   void dpgrdr_c ( ConstSpiceChar  * body,
                   SpiceDouble       x,
                   SpiceDouble       y,
                   SpiceDouble       z,
                   SpiceDouble       re,
                   SpiceDouble       f,
                   SpiceDouble       jacobi[3][3]  ) 

Abstract

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

Required_Reading

 
   None. 
 

Keywords

 
   COORDINATES 
   DERIVATIVES 
   MATRIX 
 

Brief_I/O

 
   Variable  I/O  Description 
   --------  ---  -------------------------------------------------- 
   body       I   Body with which coordinate system is associated. 
   x          I   X-coordinate of point. 
   y          I   Y-coordinate of point. 
   z          I   Z-coordinate of point. 
   re         I   Equatorial radius of the reference spheroid. 
   f          I   Flattening coefficient. 
   jacobi     O   Matrix of partial derivatives. 
 

Detailed_Input

 
   body       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. 
 
   x, 
   y, 
   z          are the rectangular coordinates of the point at 
              which the Jacobian of the map from rectangular 
              to planetographic coordinates is desired. 
 
   re         Equatorial radius of the reference spheroid. 
 
   f          Flattening coefficient = (re-rp) / re,  where rp is 
              the polar radius of the spheroid.  (More importantly 
              rp = re*(1-f).) 
 

Detailed_Output

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

Parameters

 
   None. 
 

Exceptions

 
   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) will be signaled. 
 
   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 
 
          'EAST' 
          'WEST' 
 
      the error SPICE(INVALIDOPTION) will be signaled.  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) will be signaled. 
       
   4) If the equatorial radius is non-positive, the error 
      SPICE(VALUEOUTOFRANGE) is signaled. 
 
   5) If the flattening coefficient is greater than or equal to one, 
      the error SPICE(VALUEOUTOFRANGE) is signaled. 
 
   6) If the input point is on the Z-axis (X = 0 and Y = 0), the 
      Jacobian matrix is undefined.  The error will be diagnosed 
      by routines in the call tree of this routine. 

   7) The error SPICE(EMPTYSTRING) is signaled if the input
      string `body' does not contain at least one character, since the
      input string cannot be converted to a Fortran-style string in
      this case.
      
   8) The error SPICE(NULLPOINTER) is signaled if the input string
      pointer `body' is null.
 

Files

 
   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  
 
      BODY599_PM 
 
   See the PCK Required Reading for details concerning the prime 
   meridian kernel variable. 
 
   The optional kernel variable  
    
      BODY<body ID>_PGR_POSITIVE_LON 
 
   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. 
 

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 
   planetographic coordinates to gain insights about phenomena in 
   this coordinate frame. 
 
   To transform rectangular velocities to derivatives of coordinates 
   in a planetographic 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 planetographic 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) 
 
 
   The planetographic definition of latitude is identical to the 
   planetodetic (also called "geodetic" in SPICE documentation) 
   definition. In the planetographic coordinate system, latitude is 
   defined using a reference spheroid.  The spheroid is 
   characterized by an equatorial radius and a polar radius. For a 
   point P on the spheroid, latitude is defined as the angle between 
   the X-Y plane and the outward surface normal at P.  For a point P 
   off the spheroid, latitude is defined as the latitude of the 
   nearest point to P on the spheroid.  Note if P is an interior 
   point, for example, if P is at the center of the spheroid, there 
   may not be a unique nearest point to P. 
 
   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 
   variable 
 
      BODY<body ID>_PGR_POSITIVE_LON 
 
   where <body ID> represents the NAIF ID code of the body. This 
   variable may be assigned either of the values 
 
      'WEST' 
      'EAST' 
 
   For example, you can have this routine treat the longitude 
   of the earth as increasing to the west using the kernel 
   variable assignment 
 
      BODY399_PGR_POSITIVE_LON = 'WEST' 
       
   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 
 
      pgrrec_c
      recpgr_c
      dpgrdr_c 
      drdpgr_c 
 
   It does not affect the other CSPICE coordinate conversion 
   routines. 
 

Examples

 
   Numerical results shown for this example may differ between 
   platforms as the results depend on the SPICE kernels used as 
   input and the machine specific arithmetic implementation. 
 

     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. 


           #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 a PCK file containing a triaxial
           ellipsoidal shape model and orientation
           data for Mars.
           ./
           furnsh_c ( "pck00008.tpc" );

           /.
           Load an SPK file giving ephemerides of earth and Mars.
           ./
           furnsh_c ( "de405.bsp" );

           /.
           Load a leapseconds kernel to support time conversion.
           ./
           furnsh_c ( "naif0007.tls" );

           /.
           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
           frame.
           ./
           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"
                    "\n"
                    "  X (km)                 = %18.9e\n"
                    "  Y (km)                 = %18.9e\n"
                    "  Z (km)                 = %18.9e\n"
                    "\n"
                    "Rectangular velocity:\n"
                    "\n"
                    "  dX/dt (km/s)           = %18.9e\n"
                    "  dY/dt (km/s)           = %18.9e\n"
                    "  dZ/dt (km/s)           = %18.9e\n"
                    "\n"
                    "Ellipsoid shape parameters:\n"
                    "\n"
                    "  Equatorial radius (km) = %18.9e\n"
                    "  Polar radius      (km) = %18.9e\n"
                    "  Flattening coefficient = %18.9e\n"
                    "\n"
                    "Planetographic coordinates:\n"
                    "\n"
                    "  Longitude (deg)        = %18.9e\n"
                    "  Latitude  (deg)        = %18.9e\n"
                    "  Altitude  (km)         = %18.9e\n"
                    "\n"
                    "Planetographic velocity:\n"
                    "\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"
                    "\n"
                    "Rectangular coordinates from inverse mapping:\n"
                    "\n"
                    "  X (km)                 = %18.9e\n"
                    "  Y (km)                 = %18.9e\n"
                    "  Z (km)                 = %18.9e\n"
                    "\n"
                    "Rectangular velocity from inverse mapping:\n"
                    "\n"
                    "  dX/dt (km/s)           = %18.9e\n"
                    "  dY/dt (km/s)           = %18.9e\n"
                    "  dZ/dt (km/s)           = %18.9e\n"
                    "\n",
                    state [0],
                    state [1],
                    state [2],
                    state [3],
                    state [4],
                    state [5],
                    re,
                    rp,
                    f,
                    lon / rpd_c(),
                    lat / rpd_c(),
                    alt,
                    pgrvel[0]/rpd_c(),
                    pgrvel[1]/rpd_c(),
                    pgrvel[2],
                    rectan [0],
                    rectan [1],
                    rectan [2],
                    drectn [0],
                    drectn [1],
                    drectn [2]                );

           return ( 0 );
        }


     Output from this program should be similar to the following
     (rounding and formatting differ across platforms):


        Rectangular coordinates:

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

        Rectangular velocity:

          dX/dt (km/s)           =   -4.704288238e+01
          dY/dt (km/s)           =    9.070217780e+00
          dZ/dt (km/s)           =    4.756562739e+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) =   -8.357386316e-06
          d Latitude/dt  (deg/s) =    1.593493548e-06
          d Altitude/dt  (km/s)  =   -1.121443268e+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)           =   -4.704288238e+01
          dY/dt (km/s)           =    9.070217780e+00
          dZ/dt (km/s)           =    4.756562739e+00

Restrictions

 
   None. 
 

Literature_References

 
   None. 
 

Author_and_Institution

 
   N.J. Bachman   (JPL) 
   W.L. Taber     (JPL) 
 

Version

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

Index_Entries

 
   Jacobian of planetographic  w.r.t. rectangular coordinates 
 
Wed Apr  5 17:54:31 2017