CSPICE_DRDSPH computes the Jacobian of the transformation from
spherical to rectangular coordinates.
For important details concerning this module's function, please refer to
the CSPICE routine drdsph_c.
r scalar double precision describing the distance of a point
from the origin.
colat scalar double precision describing the angle between the
point and the positive z-axis, in radians.
lon scalar double precision describing the angle of the point
measured from the xz plane in radians. The angle increases
in the counterclockwise sense about the +z axis.
cspice_drdsph, r, colat, lon, jacobi
jacobi double precision 3x3 matrix describing the matrix of partial
derivatives of the conversion between spherical and rectangular
coordinates, evaluated at the input coordinates. This matrix has
| dx/dr dx/dcolat dx/dlon |
| dy/dr dy/dcolat dy/dlon |
| dz/dr dz/dcolat dz/dlon |
evaluated at the input values of 'r', 'lon', and 'lat'.
Here 'x', 'y', and 'z' are given by the familiar formulae
x = r*cos(lon)*sin(colat)
y = r*sin(lon)*sin(colat)
z = r*cos(colat)
It is often convenient to describe the motion of an object in
the spherical coordinate system. However, when performing
vector computations its hard to beat rectangular coordinates.
To transform states given with respect to spherical coordinates
to states with respect to rectangular coordinates, one uses
the Jacobian of the transformation between the two systems.
Given a state in spherical coordinates
( r, colat, lon, dr, dcolat, dlon )
the velocity in rectangular coordinates is given by the matrix
t | t
(dx, dy, dz) = jacobi| * (dr, dcolat, dlon )
This routine computes the matrix
-Icy Version 1.0.0, 11-NOV-2013, EDW (JPL)
Jacobian of rectangular w.r.t. spherical coordinates