CSPICE_DLATDR computes the Jacobian of the transformation from
rectangular to latitudinal coordinates.
z the rectangular coordinates of the point at which the Jacobian of
the map from rectangular to latitudinal coordinates is desired.
[1,n] = size(z); double = class(z)
jacobi = cspice_dlatdr( x, y, z)
jacobi the matrix of partial derivatives of the conversion between
rectangular and latitudinal 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 |
| dlat/dx dlat/dy dlat/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 latitudinal coordinates to gain insights about phenomena
in this coordinate frame.
To transform rectangular velocities to derivatives of coordinates
in a latitudinal 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 latitudinal coordinate derivatives are given by
the matrix equation:
t | t
(dr, dlon, dlat) = 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 dlatdr_c.
-Mice Version 1.0.0, 12-MAR-2012, EDW (JPL), SCK (JPL)
Jacobian of rectangular w.r.t. latitudinal coordinates