Table of contents
CSPICE_DCYLDR computes the Jacobian matrix of the transformation from
rectangular to cylindrical coordinates.
Given:
x,
y,
z the rectangular coordinates of the point at which the Jacobian
of the map from rectangular to cylindrical coordinates is
desired.
help, x
DOUBLE = Scalar
help, y
DOUBLE = Scalar
help, z
DOUBLE = Scalar
the call:
cspice_dcyldr, x, y, z, jacobi
returns:
jacobi the matrix of partial derivatives of the conversion between
rectangular and cylindrical coordinates.
help, jacobi
DOUBLE = Array[3,3]
It has the form
.- -.
| 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'.
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 cylindrical 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: dcyldr_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.
PRO dcyldr_ex1
;;
;; Load SPK, PCK and LSK kernels, use a meta kernel for
;; convenience.
;;
cspice_furnsh, 'dcyldr_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.
;;
cspice_str2et, 'January 1, 2005 TDB', et
cspice_spkezr, 'Earth', et, 'IAU_MARS', 'LT+S', 'Mars', state, ltime
;;
;; Convert position to cylindrical coordinates.
;;
cspice_reccyl, state[0:2], r, clon, z
;;
;; Convert velocity to cylindrical coordinates.
;;
cspice_dcyldr, state[0], state[1], state[2], jacobi
cspice_mxv, jacobi, state[3:5], cylvel
;;
;; As a check, convert the cylindrical state back to
;; rectangular coordinates.
;;
cspice_cylrec, r, clon, z, rectan
cspice_drdcyl, r, clon, z, jacobi
cspice_mxv, jacobi, cylvel, drectn
print, ' '
print, 'Rectangular coordinates:'
print, ' '
print, format='(A,E18.8)', ' X (km) = ', state[0]
print, format='(A,E18.8)', ' Y (km) = ', state[1]
print, format='(A,E18.8)', ' Z (km) = ', state[2]
print, ' '
print, 'Rectangular velocity:'
print, ' '
print, format='(A,E18.8)', ' dX/dt (km/s) = ', state[3]
print, format='(A,E18.8)', ' dY/dt (km/s) = ', state[4]
print, format='(A,E18.8)', ' dZ/dt (km/s) = ', state[5]
print, ' '
print, 'Cylindrical coordinates:'
print, ' '
print, format='(A,E18.8)', ' Radius (km) = ', r
print, format='(A,E18.8)', ' Longitude (deg) = ', $
clon/cspice_rpd()
print, format='(A,E18.8)', ' Z (km) = ', z
print, ' '
print, 'Cylindrical velocity:'
print, ' '
print, format='(A,E18.8)', ' d Radius/dt (km/s) = ', cylvel[0]
print, format='(A,E18.8)', ' d Longitude/dt (deg/s) = ', $
cylvel[1]/cspice_rpd()
print, format='(A,E18.8)', ' d Z/dt (km/s) = ', cylvel[2]
print, ' '
print, 'Rectangular coordinates from inverse mapping:'
print, ' '
print, format='(A,E18.8)', ' X (km) = ', rectan[0]
print, format='(A,E18.8)', ' Y (km) = ', rectan[1]
print, format='(A,E18.8)', ' Z (km) = ', rectan[2]
print, ' '
print, 'Rectangular velocity from inverse mapping:'
print, ' '
print, format='(A,E18.8)', ' dX/dt (km/s) = ', drectn[0]
print, format='(A,E18.8)', ' dY/dt (km/s) = ', drectn[1]
print, format='(A,E18.8)', ' dZ/dt (km/s) = ', drectn[2]
print, ' '
END
When this program was executed on a Mac/Intel/IDL8.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
Cylindrical coordinates:
Radius (km) = 3.33170387E+08
Longitude (deg) = 1.03202903E+02
Z (km) = 4.74704840E+07
Cylindrical velocity:
d Radius/dt (km/s) = -8.34966283E+00
d Longitude/dt (deg/s) = -4.05392876E-03
d Z/dt (km/s) = -2.08811490E+01
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 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
equation:
t | t
(dr, dlon, dz) = 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 = 0 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 IDL 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 Icy interface.
4) If the output argument `jacobi' is not a named variable, an
error is signaled by the Icy interface.
None.
None.
ICY.REQ
None.
J. Diaz del Rio (ODC Space)
E.D. Wright (JPL)
-Icy Version 1.0.1, 01-NOV-2021 (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.
Removed reference to the routine's corresponding CSPICE header from
-Abstract section.
Added arguments' type and size information in the -I/O section.
-Icy Version 1.0.0, 11-NOV-2013 (EDW)
Jacobian of cylindrical w.r.t. rectangular coordinates
|