CSPICE_DCYLDR computes the Jacobian of the transformation from
rectangular to cylindrical coordinates.
x [1,n] = size(x); double = class(x)
y [1,n] = size(y); double = class(y)
z [1,n] = size(z); double = class(z)
the rectangular coordinates of the point at which the Jacobian of
the map from rectangular to cylindrical coordinates is desired.
jacobi = cspice_dcyldr( x, y, z)
jacobi the matrix of partial derivatives of the conversion between
rectangular and cylindrical coordinates. It has the form
If [1,1] = size(x) then [3,3] = size(jacobi)
If [1,n] = size(x) then [3,3,n] = size(jacobi)
double = class(jacobi)
| dr/dx dr/dy dr/dz |
| dlon/dx dlon/dy dlon/dz |
| dz/dx dz/dy dz/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 cylindrical coordinates to gain insights about phenomena
in this coordinate frame.
To transform rectangular velocities to derivatives of
coordinates in a cylindrical 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 cylindrical coordinates is given by the matrix
t | t
(dr, dlon, dz) = jacobi| * (dx, dy, dz)
This routine computes the matrix
For important details concerning this module's function, please refer to
the CSPICE routine dcyldr_c.
-Mice Version 1.0.0, 11-NOV-2013, EDW (JPL), SCK (JPL)
Jacobian of cylindrical w.r.t. rectangular coordinates