CSPICE_DGEODR computes the Jacobian of the transformation from
rectangular to geodetic coordinates.
For important details concerning this module's function, please refer to
the CSPICE routine dgeodr_c.
z scalar double precision describing the rectangular
coordinates of the point at which the Jacobian of the map
from rectangular to geodetic coordinates is desired.
re scalar double precision describing equatorial radius of a reference
spheroid. This spheroid is a volume of revolution: its horizontal
cross sections are circular. The shape of the spheroid is
defined by an equatorial radius `re' and a polar radius `rp'.
f scalar double precision describing the flattening coefficient
f = (re-rp) / re
where rp is the polar radius of the spheroid. (More importantly
rp = re*(1-f).) The units of `rp' match those of `re'.
cspice_dgeodr, x, y, z, re, f, jacobi
jacobi double precision 3x3 matrix describing the matrix of partial
derivatives of the conversion between rectangular and geodetic
coordinates, evaluated at the input coordinates. This matrix
has the form
| dlon/dx dlon/dy dlon/dz |
| dlat/dx dlat/dy dlat/dz |
| dalt/dx dalt/dy dalt/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 geodetic coordinates to gain insights about phenomena
in this coordinate frame.
To transform rectangular velocities to derivatives of coordinates
in a geodetic 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 velocity in geodetic coordinates is given by the matrix
t | t
(dlon, dlat, dalt) = jacobi| * (dx, dy, dz)
This routine computes the matrix
|(x, y, z)
-Icy Version 1.0.0, 28-DEC-2010, EDW (JPL)
Jacobian of geodetic w.r.t. rectangular coordinates