CSPICE_DGEODR computes the Jacobian of the transformation from
rectangular to geodetic coordinates.
z the rectangular coordinates of the point at which the Jacobian of
the map from rectangular to geodetic coordinates is desired.
[1,n] = size(z); double = class(z)
re 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'.
[1,1] = size(re); double = class(re)
f the flattening coefficient
[1,1] = size(f); double = class(f)
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'.
jacobi = cspice_dgeodr( x, y, z, re, f)
jacobi the matrix of partial derivatives of the conversion between
rectangular and geodetic coordinates, evaluated at the input
coordinates. This matrix has the form
[3,3] = size(jacobi); double = class(jacobi)
| 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)
For important details concerning this module's function, please refer to
the CSPICE routine dgeodr_c.
-Mice Version 1.0.0, 12-MAR-2012, EDW (JPL), SCK (JPL)
Jacobian of geodetic w.r.t. rectangular coordinates