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   It is often convenient to describe the motion of an object
   in latitudinal coordinates. It is also convenient to manipulate
   vectors associated with the object in rectangular coordinates.

   The transformation of a latitudinal state into an equivalent
   rectangular state makes use of the Jacobian of the
   transformation between the two systems.

   Given a state in latitudinal coordinates,

        ( r, lon, lat, dr, dlon, dlat )

   the velocity in rectangular coordinates is given by the mat