Index of Functions: A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X 
Index Page
cspice_dcyldr

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

Abstract


   CSPICE_DCYLDR computes the Jacobian matrix of the transformation from
   rectangular to cylindrical coordinates.

I/O


   Given:

      x,
      y,
      z        the rectangular coordinates of the point(s) at which the
               Jacobian of the map from rectangular to cylindrical coordinates
               is desired.

               [1,n] = size(x); double = class(x)
               [1,n] = size(y); double = class(y)
               [1,n] = size(z); double = class(z)

   the call:

      [jacobi] = cspice_dcyldr( x, y, z )

   returns:

      jacobi   the matrix(es) of partial derivatives of the conversion between
               rectangular and cylindrical coordinates.

               If [1,1] = size(x) then [3,3]   = size(jacobi)
               If [1,n] = size(x) then [3,3,n] = size(jacobi)
                                        double = class(jacobi)

               It has the form:

                  .-                            -.
                  |  dr/dx     dr/dy    dr/dz    |
                  |                              |
                  |  dlon/dx   dlon/dy  dlon/dz  |
                  |                              |
                  |  dz/dx     dz/dy    dz/dz    |
                  `-                            -'

               evaluated at the input values of `x', `y', and `z'.

               `jacobi' returns with the same vectorization measure (N) as
               `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 cylindrical 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: dcyldr_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.


      function dcyldr_ex1()

         %
         % Load SPK, PCK and LSK kernels, use a meta kernel for
         % convenience.
         %
         cspice_furnsh( 'dcyldr_ex1.tm' );

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

         [state, lt] = cspice_spkezr( 'Earth', et,    'IAU_MARS',         ...
                                      'LT+S',  'Mars'          );

         %
         % Convert position to cylindrical coordinates.
         %
         [r, clon, z] = cspice_reccyl( state(1:3) );

         %
         % Convert velocity to cylindrical coordinates.
         %
         [jacobi] = cspice_dcyldr( state(1), state(2), state(3) );

         cylvel   = jacobi * state(4:6);

         %
         % As a check, convert the cylindrical state back to
         % rectangular coordinates.
         %
         [rectan] = cspice_cylrec( r, clon, z );

         [jacobi] = cspice_drdcyl( r, clon, z );

         drectn   = jacobi * cylvel;

         fprintf( ' \n' )
         fprintf( 'Rectangular coordinates:\n' )
         fprintf( ' \n' )
         fprintf( ' X (km)                 =  %17.8e\n', state(1) )
         fprintf( ' Y (km)                 =  %17.8e\n', state(2) )
         fprintf( ' Z (km)                 =  %17.8e\n', state(3) )
         fprintf( ' \n' )
         fprintf( 'Rectangular velocity:\n' )
         fprintf( ' \n' )
         fprintf( ' dX/dt (km/s)           =  %17.8e\n', state(4) )
         fprintf( ' dY/dt (km/s)           =  %17.8e\n', state(5) )
         fprintf( ' dZ/dt (km/s)           =  %17.8e\n', state(6) )
         fprintf( ' \n' )
         fprintf( 'Cylindrical coordinates:\n' )
         fprintf( ' \n' )
         fprintf( ' Radius    (km)         =  %17.8e\n', r )
         fprintf( ' Longitude (deg)        =  %17.8e\n', clon/cspice_rpd )
         fprintf( ' Z         (km)         =  %17.8e\n', z )
         fprintf( ' \n' )
         fprintf( 'Cylindrical velocity:\n' )
         fprintf( ' \n' )
         fprintf( ' d Radius/dt    (km/s)  =  %17.8e\n', cylvel(1) )
         fprintf( ' d Longitude/dt (deg/s) =  %17.8e\n',                  ...
                                                     cylvel(2)/cspice_rpd )
         fprintf( ' d Z/dt         (km/s)  =  %17.8e\n', cylvel(3) )
         fprintf( ' \n' )
         fprintf( 'Rectangular coordinates from inverse mapping:\n' )
         fprintf( ' \n' )
         fprintf( ' X (km)                 =  %17.8e\n', rectan(1) )
         fprintf( ' Y (km)                 =  %17.8e\n', rectan(2) )
         fprintf( ' Z (km)                 =  %17.8e\n', rectan(3) )
         fprintf( ' \n' )
         fprintf( 'Rectangular velocity from inverse mapping:\n' )
         fprintf( ' \n' )
         fprintf( ' dX/dt (km/s)           =  %17.8e\n', drectn(1) )
         fprintf( ' dY/dt (km/s)           =  %17.8e\n', drectn(2) )
         fprintf( ' dZ/dt (km/s)           =  %17.8e\n', drectn(3) )
         fprintf( ' \n' )

         %
         % It's always good form to unload kernels after use,
         % particularly in Matlab due to data persistence.
         %
         cspice_kclear


      When this program was executed on a Mac/Intel/Octave6.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

      Cylindrical coordinates:

       Radius    (km)         =     3.33170387e+08
       Longitude (deg)        =     1.03202903e+02
       Z         (km)         =     4.74704840e+07

      Cylindrical velocity:

       d Radius/dt    (km/s)  =    -8.34966283e+00
       d Longitude/dt (deg/s) =    -4.05392876e-03
       d Z/dt         (km/s)  =    -2.08811490e+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 cylindrical coordinates to gain insights about phenomena
   in this coordinate frame.

   To transform rectangular velocities to derivatives of
   coordinates in a cylindrical 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 cylindrical coordinates is given by the matrix
   equation:

                    t          |                     t
      (dr, dlon, dz)   = 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 any of the input arguments, `x', `y' or `z', is undefined,
       an error is signaled by the Matlab error handling system.

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

   4)  If the input vectorizable arguments `x', `y' and `z' do not
       have the same measure of vectorization (N), an error is
       signaled by the Mice interface.

Files


   None.

Restrictions


   None.

Required_Reading


   MICE.REQ

Literature_References


   None.

Author_and_Institution


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

Version


   -Mice Version 1.1.0, 01-NOV-2021 (EDW) (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.

       Eliminated use of "lasterror" in rethrow.

       Removed reference to the function's corresponding CSPICE header from
       -Required_Reading section.

   -Mice Version 1.0.0, 11-NOV-2013 (EDW) (SCK)

Index_Entries


   Jacobian of cylindrical w.r.t. rectangular coordinates


Fri Dec 31 18:44:23 2021