CSPICE_DSPHDR computes the Jacobian of the transformation from
rectangular to spherical coordinates.
For important details concerning this module's function, please refer to
the CSPICE routine dsphdr_c.
z scalar double precision describing the rectangular coordinates
of the point at which the Jacobian of the map from rectangular
to spherical coordinates is desired.
cspice_dsphdr, x, y, z, jacobi
jacobi double precision 3x3 matrix of partial derivatives of the
conversion between rectangular and spherical coordinates.
It has the form
| 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.
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)
This routine computes the matrix
|(x, y, z)
-Icy Version 1.0.0, 12-NOV-2013, EDW (JPL)
Jacobian of spherical w.r.t. rectangular coordinates