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Abstract
I/O
Examples
Particulars
Required Reading
Version
Index_Entries

Abstract


   CSPICE_DSPHDR computes the Jacobian of the transformation from
   rectangular to spherical coordinates.

I/O


   Given:

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

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

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

          the rectangular coordinates of the point at which the Jacobian of
          the map from rectangular to spherical coordinates is desired.

   the call:

      jacobi = cspice_dsphdr( x, y, z)

   returns:

      jacobi   the matrix of partial derivatives of the conversion
               between rectangular and spherical coordinates.  It
               has the form

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

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

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

Examples


   None.

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 spherical coordinates to gain insights about phenomena
   in this coordinate frame.

   To transform rectangular velocities to derivatives of coordinates
   in a spherical 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 corresponding spherical coordinate derivatives are given by
   the matrix equation:

                        t          |                    t
      (dr, dcolat, dlon)   = jacobi|      * (dx, dy, dz)
                                   |(x,y,z)

   This routine computes the matrix

            |
      jacobi|
            |(x, y, z)


Required Reading


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

   MICE.REQ

Version


   -Mice Version 1.0.0, 12-NOV-2013, EDW (JPL), SCK (JPL)

Index_Entries


   Jacobian of spherical w.r.t. rectangular coordinates


Wed Apr  5 18:00:31 2017