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cspice_dgeodr

Table of contents
Abstract
I/O
Parameters
Examples
Particulars
Exceptions
Files
Restrictions
Required_Reading
Literature_References
Author_and_Institution
Version
Index_Entries


Abstract


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

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.

               help, x
                  DOUBLE = Scalar
               help, y
                  DOUBLE = Scalar
               help, z
                  DOUBLE = Scalar

      re       scalar double precision describing equatorial radius of a
               reference spheroid.

               help, re
                  DOUBLE = Scalar

               This spheroid is a volume of revolution: its horizontal cross
               sections is 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.

               help, f
                  DOUBLE = Scalar

               (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.

               help, jacobi
                  DOUBLE = Array[3,3]

               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'.

Parameters


   None.

Examples


   Any 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.

   1) Find the geodetic state of the earth as seen from
      Mars in the IAU_MARS 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
      kernels.


         KPL/MK

         File name: dgeodr_ex1.tm

         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
            ---------                     --------
            de421.bsp                     Planetary ephemeris
            pck00010.tpc                  Planet orientation and
                                          radii
            naif0009.tls                  Leapseconds


         \begindata

            KERNELS_TO_LOAD = ( 'de421.bsp',
                                'pck00010.tpc',
                                'naif0009.tls'  )

         \begintext

         End of meta-kernel


      Example code begins here.


      PRO dgeodr_ex1

         ;;
         ;; Load SPK, PCK, and LSK kernels, use a meta kernel for
         ;; convenience.
         ;;
         cspice_furnsh, 'dgeodr_ex1.tm'

         ;;
         ;; Look up the radii for Mars.  Although we
         ;; omit it here, we could first call cspice_badkpv
         ;; to make sure the variable BODY499_RADII
         ;; has three elements and numeric data type.
         ;; If the variable is not present in the kernel
         ;; pool, cspice_bodvrd will signal an error.
         ;;
         cspice_bodvrd, 'MARS', 'RADII', 3, radii

         ;;
         ;; Compute flattening coefficient.
         ;;
         re  =  radii[0]
         rp  =  radii[2]
         f   =  ( re - rp ) / re

         ;;
         ;; Look up the apparent state of earth as seen from Mars at
         ;; January 1, 2005 TDB, relative to the IAU_MARS reference
         ;; frame.
         ;;
         cspice_str2et, 'January 1, 2005 TDB', et

         cspice_spkezr, 'Earth', et, 'IAU_MARS', 'LT+S', 'Mars', state, ltime

         ;;
         ;; Convert position to geodetic coordinates.
         ;;
         cspice_recgeo, state[0:2], re, f, lon, lat, alt

         ;;
         ;; Convert velocity to geodetic coordinates.
         ;;
         cspice_dgeodr, state[0], state[1], state[2], re, f, jacobi

         cspice_mxv, jacobi, state[3:5], geovel

         ;;
         ;; As a check, convert the geodetic state back to
         ;; rectangular coordinates.
         ;;
         cspice_georec, lon, lat, alt, re, f, rectan

         cspice_drdgeo, lon, lat, alt, re, f, jacobi

         cspice_mxv, jacobi, geovel, drectn

         print, ' '
         print, 'Rectangular coordinates:'
         print, ' '
         print, format='(A,E18.8)', ' X (km)                 = ', state[0]
         print, format='(A,E18.8)', ' Y (km)                 = ', state[1]
         print, format='(A,E18.8)', ' Z (km)                 = ', state[2]
         print, ' '
         print, 'Rectangular velocity:'
         print, ' '
         print, format='(A,E18.8)', ' dX/dt (km/s)           = ', state[3]
         print, format='(A,E18.8)', ' dY/dt (km/s)           = ', state[4]
         print, format='(A,E18.8)', ' dZ/dt (km/s)           = ', state[5]
         print, ' '
         print, 'Ellipsoid shape parameters: '
         print, ' '
         print, format='(A,E18.8)', ' Equatorial radius (km) = ', re
         print, format='(A,E18.8)', ' Polar radius      (km) = ', rp
         print, format='(A,E18.8)', ' Flattening coefficient = ', f
         print, ' '
         print, 'Geodetic coordinates:'
         print, ' '
         print, format='(A,E18.8)', ' Longitude (deg)        = ',            $
                                                           lon / cspice_rpd()
         print, format='(A,E18.8)', ' Latitude  (deg)        = ',            $
                                                           lat / cspice_rpd()
         print, format='(A,E18.8)', ' Altitude  (km)         = ', alt
         print, ' '
         print, 'Geodetic velocity:'
         print, ' '
         print, format='(A,E18.8)', ' d Longitude/dt (deg/s) = ',            $
                                                       geovel[0]/cspice_rpd()
         print, format='(A,E18.8)', ' d Latitude/dt  (deg/s) = ',            $
                                                       geovel[1]/cspice_rpd()
         print, format='(A,E18.8)', ' d Altitude/dt  (km/s)  = ', geovel[2]
         print, ' '
         print, 'Rectangular coordinates from inverse mapping:'
         print, ' '
         print, format='(A,E18.8)', ' X (km)                 = ', rectan[0]
         print, format='(A,E18.8)', ' Y (km)                 = ', rectan[1]
         print, format='(A,E18.8)', ' Z (km)                 = ', rectan[2]
         print, ' '
         print, 'Rectangular velocity from inverse mapping:'
         print, ' '
         print, format='(A,E18.8)', ' dX/dt (km/s)           = ', drectn[0]
         print, format='(A,E18.8)', ' dY/dt (km/s)           = ', drectn[1]
         print, format='(A,E18.8)', ' dZ/dt (km/s)           = ', drectn[2]
         print, ' '

      END


      When this program was executed on a Mac/Intel/IDL8.x/64-bit
      platform, the output was:


      Rectangular coordinates:

       X (km)                 =    -7.60961826E+07
       Y (km)                 =     3.24363805E+08
       Z (km)                 =     4.74704840E+07

      Rectangular velocity:

       dX/dt (km/s)           =     2.29520749E+04
       dY/dt (km/s)           =     5.37601112E+03
       dZ/dt (km/s)           =    -2.08811490E+01

      Ellipsoid shape parameters:

       Equatorial radius (km) =     3.39619000E+03
       Polar radius      (km) =     3.37620000E+03
       Flattening coefficient =     5.88600756E-03

      Geodetic coordinates:

       Longitude (deg)        =     1.03202903E+02
       Latitude  (deg)        =     8.10898757E+00
       Altitude  (km)         =     3.36531823E+08

      Geodetic velocity:

       d Longitude/dt (deg/s) =    -4.05392876E-03
       d Latitude/dt  (deg/s) =    -3.31899337E-06
       d Altitude/dt  (km/s)  =    -1.12116015E+01

      Rectangular coordinates from inverse mapping:

       X (km)                 =    -7.60961826E+07
       Y (km)                 =     3.24363805E+08
       Z (km)                 =     4.74704840E+07

      Rectangular velocity from inverse mapping:

       dX/dt (km/s)           =     2.29520749E+04
       dY/dt (km/s)           =     5.37601112E+03
       dZ/dt (km/s)           =    -2.08811490E+01


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)

Exceptions


   1)  If the input point is on the z-axis (x = 0 and y = 0), the
       Jacobian is undefined, the error SPICE(POINTONZAXIS) is
       signaled by a routine in the call tree of this routine.

   2)  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.

   3)  If the equatorial radius is not positive, the error
       SPICE(BADRADIUS) is signaled by a routine in the call tree of
       this routine.

   4)  If any of the input arguments, `x', `y', `z', `re' or `f', is
       undefined, an error is signaled by the IDL error handling
       system.

   5)  If any of the input arguments, `x', `y', `z', `re' or `f', is
       not of the expected type, or it does not have the expected
       dimensions and size, an error is signaled by the Icy
       interface.

   6)  If the output argument `jacobi' is not a named variable, an
       error is signaled by the Icy interface.

Files


   None.

Restrictions


   None.

Required_Reading


   ICY.REQ

Literature_References


   None.

Author_and_Institution


   J. Diaz del Rio     (ODC Space)
   E.D. Wright         (JPL)

Version


   -Icy Version 1.0.1, 01-NOV-2021 (JDR)

       Edited the header to comply with NAIF standard. Added complete code
       example.

       Added -Parameters, -Exceptions, -Files, -Restrictions,
       -Literature_References and -Author_and_Institution sections.

       Removed reference to the routine's corresponding CSPICE header from
       -Abstract section.

       Added arguments' type and size information in the -I/O section.

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

Index_Entries


   Jacobian of geodetic  w.r.t. rectangular coordinates



Fri Dec 31 18:43:03 2021