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

   None. 

   Variable  I/O  Description 
   --------  ---  -------------------------------------------------- 
   x          I   X-coordinate of point. 
   y          I   Y-coordinate of point. 
   z          I   Z-coordinate of point. 
   jacobi     O   Matrix of partial derivatives. 

   x, 
   y, 
   z          are the rectangular coordinates of the point at 
              which the Jacobian of the map from rectangular 
              to latitudinal coordinates is desired. 

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

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

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

   None. 

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

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

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

   This routine computes the matrix  

            | 
      jacobi| 
            |(x, y, z) 

   Suppose one is given the bodyfixed rectangular state of an object 
   ( x(t), y(t), z(t), dx(t), dy(t), dz(t) ) as a function of time t. 

   To find the derivatives of the coordinates of the object in 
   bodyfixed latitudinal coordinates, one simply multiplies the 
   Jacobian of the transformation from rectangular to latitudinal 
   coordinates (evaluated at x(t), y(t), z(t) ) by the rectangular 
   velocity vector of the object at time t. 

   In code this looks like: 

      #include "SpiceUsr.h"
            .
            .
            .

      /.
      Load the rectangular velocity vector vector recv. 
      ./ 
      recv[0] = dx ( t );
      recv[1] = dy ( t );
      recv[2] = dz ( t );

      /.
      Determine the Jacobian of the transformation from rectangular to 
      latitudinal coordinates at the rectangular coordinates at time t. 
      ./
      dlatdr_c ( x(t), y(t), z(t), jacobi );

      /.
      Multiply the Jacobian on the right by the rectangular 
      velocity to obtain the latitudinal coordinate derivatives  
      latv. 
      ./ 
      mxv_c ( jacobi, recv, latv );

   None. 

   1) If the input point is on the z-axis (x and y = 0), the 
      Jacobian is undefined.  The error SPICE(POINTONZAXIS) 
      will be signaled. 

   None. 

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

   None. 

   -CSPICE Version 1.0.0, 13-JUL-2001 (WLT) (NJB)

   Jacobian of rectangular w.r.t. latitudinal coordinates