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Abstract
I/O
Examples
Particulars
Required Reading
Version
Index_Entries

Abstract


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

I/O


   Given:

      r       the distance of a point from the origin.

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

      colat   the angle between the point and the positive z-axis, in radians.

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

      lon     the angle of the point measured from the xz plane in radians.
              The angle increases in the counterclockwise sense about
              the +z axis.

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

   the call:

      jacobi = cspice_drdsph( r, colat, lon)

   returns:

      jacobi   the matrix of partial derivatives of the conversion between
               spherical and rectangular coordinates, evaluated at the input
               coordinates. This matrix has the form

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

                   -                                 -
                  |  dx/dr     dx/dcolat     dx/dlon  |
                  |                                   |
                  |  dy/dr     dy/dcolat     dy/dlon  |
                  |                                   |
                  |  dz/dr     dz/dcolat     dz/dlon  |
                   -                                 -

               evaluated at the input values of r, lon and lat.
               Here x, y, and z are given by the familiar formulae

                  x = r*cos(lon)*sin(colat)
                  y = r*sin(lon)*sin(colat)
                  z = r*cos(colat)

Examples


   None.

Particulars


   It is often convenient to describe the motion of an object in
   the spherical coordinate system.  However, when performing
   vector computations its hard to beat rectangular coordinates.

   To transform states given with respect to spherical coordinates
   to states with respect to rectangular coordinates, one uses
   the Jacobian of the transformation between the two systems.

   Given a state in spherical coordinates

      ( r, colat, lon, dr, dcolat, dlon )

   the velocity in rectangular coordinates is given by the matrix
   equation:
                  t          |                                   t
      (dx, dy, dz)   = jacobi|              * (dr, dcolat, dlon )
                             |(r,colat,lon)

   This routine computes the matrix

            |
      jacobi|
            |(r,colat,lon)


Required Reading


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

   MICE.REQ

Version


   -Mice Version 1.0.0, 09-NOV-2012, EDW (JPL), SCK (JPL)

Index_Entries


   Jacobian of rectangular w.r.t. spherical coordinates


Wed Apr  5 18:00:30 2017