Table of contents
CSPICE_DSPHDR computes the Jacobian matrix of the transformation from
rectangular to spherical coordinates.
Given:
x,
y,
z the rectangular coordinates of the point(s) at which the
Jacobian of the map from rectangular to spherical
coordinates is desired.
[1,n] = size(x); double = class(x)
[1,n] = size(y); double = class(y)
[1,n] = size(z); double = class(z)
the call:
[jacobi] = cspice_dsphdr( x, y, z )
returns:
jacobi the matrix(es) of partial derivatives of the conversion
between rectangular and spherical coordinates.
If [1,1] = size(x) then [3,3] = size(jacobi)
If [1,n] = size(x) then [3,3,n] = size(jacobi)
double = class(jacobi)
It has the form
.- -.
| dr/dx dr/dy dr/dz |
| dcolat/dx dcolat/dy dcolat/dz |
| dlon/dx dlon/dy dlon/dz |
`- -'
evaluated at the input values of `x', `y', and `z'.
`jacobi' returns with the same vectorization measure (N)
as `x', `y' and `z'.
None.
Any numerical results shown for this example may differ between
platforms as the results depend on the SPICE kernels used as input
and the machine specific arithmetic implementation.
1) Find the spherical state of the Earth as seen from
Mars in the IAU_MARS reference frame at January 1, 2005 TDB.
Map this state back to rectangular coordinates as a check.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: dsphdr_ex1.tm
This meta-kernel is intended to support operation of SPICE
example programs. The kernels shown here should not be
assumed to contain adequate or correct versions of data
required by SPICE-based user applications.
In order for an application to use this meta-kernel, the
kernels referenced here must be present in the user's
current working directory.
The names and contents of the kernels referenced
by this meta-kernel are as follows:
File name Contents
--------- --------
de421.bsp Planetary ephemeris
pck00010.tpc Planet orientation and
radii
naif0009.tls Leapseconds
\begindata
KERNELS_TO_LOAD = ( 'de421.bsp',
'pck00010.tpc',
'naif0009.tls' )
\begintext
End of meta-kernel
Example code begins here.
function dsphdr_ex1()
%
% Load SPK, PCK and LSK kernels, use a meta kernel for
% convenience.
%
cspice_furnsh( 'dsphdr_ex1.tm' );
%
% Look up the apparent state of earth as seen from Mars
% at January 1, 2005 TDB, relative to the IAU_MARS reference
% frame.
%
[et] = cspice_str2et( 'January 1, 2005 TDB' );
[state, lt] = cspice_spkezr( 'Earth', et, 'IAU_MARS', ...
'LT+S', 'Mars' );
%
% Convert position to spherical coordinates.
%
[r, colat, slon] = cspice_recsph( state(1:3) );
%
% Convert velocity to spherical coordinates.
%
[jacobi] = cspice_dsphdr( state(1), state(2), state(3) );
sphvel = jacobi * state(4:6);
%
% As a check, convert the spherical state back to
% rectangular coordinates.
%
[rectan] = cspice_sphrec( r, colat, slon );
[jacobi] = cspice_drdsph( r, colat, slon );
drectn = jacobi * sphvel;
fprintf( ' \n' )
fprintf( 'Rectangular coordinates:\n' )
fprintf( ' \n' )
fprintf( ' X (km) = %17.8e\n', state(1) )
fprintf( ' Y (km) = %17.8e\n', state(2) )
fprintf( ' Z (km) = %17.8e\n', state(3) )
fprintf( ' \n' )
fprintf( 'Rectangular velocity:\n' )
fprintf( ' \n' )
fprintf( ' dX/dt (km/s) = %17.8e\n', state(4) )
fprintf( ' dY/dt (km/s) = %17.8e\n', state(5) )
fprintf( ' dZ/dt (km/s) = %17.8e\n', state(6) )
fprintf( ' \n' )
fprintf( 'Spherical coordinates:\n' )
fprintf( ' \n' )
fprintf( ' Radius (km) = %17.8e\n', r )
fprintf( ' Colatitude (deg) = %17.8e\n', colat/cspice_rpd )
fprintf( ' Longitude (deg) = %17.8e\n', slon/cspice_rpd )
fprintf( ' \n' )
fprintf( 'Spherical velocity:\n' )
fprintf( ' \n' )
fprintf( ' d Radius/dt (km/s) = %17.8e\n', sphvel(1) )
fprintf( ' d Colatitude/dt (deg/s) = %17.8e\n', ...
sphvel(2)/cspice_rpd )
fprintf( ' d Longitude/dt (deg/s) = %17.8e\n', ...
sphvel(3)/cspice_rpd )
fprintf( ' \n' )
fprintf( 'Rectangular coordinates from inverse mapping:\n' )
fprintf( ' \n' )
fprintf( ' X (km) = %17.8e\n', rectan(1) )
fprintf( ' Y (km) = %17.8e\n', rectan(2) )
fprintf( ' Z (km) = %17.8e\n', rectan(3) )
fprintf( ' \n' )
fprintf( 'Rectangular velocity from inverse mapping:\n' )
fprintf( ' \n' )
fprintf( ' dX/dt (km/s) = %17.8e\n', drectn(1) )
fprintf( ' dY/dt (km/s) = %17.8e\n', drectn(2) )
fprintf( ' dZ/dt (km/s) = %17.8e\n', drectn(3) )
fprintf( ' \n' )
%
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
Rectangular coordinates:
X (km) = -7.60961826e+07
Y (km) = 3.24363805e+08
Z (km) = 4.74704840e+07
Rectangular velocity:
dX/dt (km/s) = 2.29520749e+04
dY/dt (km/s) = 5.37601112e+03
dZ/dt (km/s) = -2.08811490e+01
Spherical coordinates:
Radius (km) = 3.36535219e+08
Colatitude (deg) = 8.18910134e+01
Longitude (deg) = 1.03202903e+02
Spherical velocity:
d Radius/dt (km/s) = -1.12116011e+01
d Colatitude/dt (deg/s) = 3.31899303e-06
d Longitude/dt (deg/s) = -4.05392876e-03
Rectangular coordinates from inverse mapping:
X (km) = -7.60961826e+07
Y (km) = 3.24363805e+08
Z (km) = 4.74704840e+07
Rectangular velocity from inverse mapping:
dX/dt (km/s) = 2.29520749e+04
dY/dt (km/s) = 5.37601112e+03
dZ/dt (km/s) = -2.08811490e+01
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 spherical coordinates to gain insights about phenomena
in this coordinate frame.
To transform rectangular velocities to derivatives of coordinates
in a spherical 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 spherical coordinate derivatives are given by
the matrix equation:
t | t
(dr, dcolat, dlon) = jacobi| * (dx, dy, dz)
|(x,y,z)
This routine computes the matrix
|
jacobi|
|(x, y, z)
1) If the input point is on the z-axis (`x' and y = 0), the
Jacobian is undefined, the error SPICE(POINTONZAXIS) is
signaled by a routine in the call tree of this routine.
2) If any of the input arguments, `x', `y' or `z', is undefined,
an error is signaled by the Matlab error handling system.
3) If any of the input arguments, `x', `y' or `z', is not of the
expected type, or it does not have the expected dimensions and
size, an error is signaled by the Mice interface.
4) If the input vectorizable arguments `x', `y' and `z' do not
have the same measure of vectorization (N), an error is
signaled by the Mice interface.
None.
None.
MICE.REQ
None.
J. Diaz del Rio (ODC Space)
S.C. Krening (JPL)
E.D. Wright (JPL)
-Mice Version 1.1.0, 01-NOV-2021 (EDW) (JDR)
Edited the header to comply with NAIF standard.
Added complete code example.
Added -Parameters, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections.
Eliminated use of "lasterror" in rethrow.
Removed reference to the function's corresponding CSPICE header from
-Required_Reading section.
-Mice Version 1.0.0, 12-NOV-2013 (EDW) (SCK)
Jacobian of spherical w.r.t. rectangular coordinates
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