UT550
[ Name  Synopsis  Arguments  Description  Diagnostics  Common Blocks  Dependencies  See Also  Reported Bugs  Examples ]
Name

Subroutine UT550  select a coordinate transformation
Synopsis
INTEGER*4 kfrom, kto, ifail REAL*8 trans(3,3) CALL UT550 (kfrom,kto,trans,ifail)
Arguments

kfrom
 input coordinate system [in]

kto
 output coordinate system [in]

trans
 transformation matrix [out]

ifail
 Error flag (see diagnostics) [out]
Description

The subroutine UT550 initializes the coordinate transformation.
The computed transformation can be applied then with the
help of subroutine UT555 or
UT556.
The arguments
kfrom
and kto
are
used to specify the input and output coordinate systems,
respectively.
The resulting matrix trans
allows to transform cartesian
coordinate of type kfrom
to type kto
.
The correspondance between indices and coordinate systems is shown in the table below
kfrom , kto  coordinate system 
1  Geographic coordinate (GEO) 
2  Geocentric equatorial inertial coordinate (GEI) 
3  Geomagnetic coordinate (MAG) 
4  Solar magnetic coordinate (SM) 
5  Geocentric solar magnetospheric coordinate (GSM) 
6  Geocentric solar ecliptic coordinate (GSE) 
The characteristics of the five coordinate systems are summarized in the next table. The origin of all these coordinate systems are located at the centre of the Earth.
X axis  Y axis  Z axis  
GEO  included in the Earth's equatorial plane and passing through the Greenwich meridian  Z x X 
parallel to the Earth's rotation axis and pointing to the North 
GEI  pointing to the first point of Aries, i.e. at the intersection between the Earth's equatorial plane and the ecliptic plane  Z x X 
parallel to the Earth's rotation axis and pointing to the North 
MAG  Y x Z 
perpendicular to both the geomagnetic dipole axis and the Earth's rotation axis in the East direction  parallel to the geomagnetic dipole axis and pointing to the North 
SM  Y x Z 
perpendicular to the EarthSun line towards dusk  parallel to the geomagnetic dipole axis and pointing to the North 
GSM  pointing towards the Sun  perpendicular to the geomagnetic dipole axis such that the Z axis is pointing to the North  X x Y 
GSE  pointing towards the Sun  Z x X 
perpendicular to the ecliptic plane and pointing to the North 
Note that the coordinate transformation generally depends
on the Sun position and/or the geomagnetic dipole field.
For this information, the subroutine UT550 makes use of the
data stored in the argument mint
and msun
of the common block UC140.
The common block UC140 can be initialized by the
subroutines UM510 and
UM520.
The Sun position can be modified
without affecting the external magnetic field model by a call
to subroutine UM522.
References
 Olson, W.P., Coordinate Transformations Used in Magnetospheric Physics, McDonnellDouglas Astronautics Company Paper WD1145 (1970).
 Russell, C.T.,Geophysical Coordinate Transformations, Cosmic Electrodynamics 2 (1971) 184196.
History

The subroutine UT550 does not exist in version 1.05 and earlier.
The transformation from/to the GSE coordinate system is
not included in version 2.00 and earlier.
The subroutine UT550 includes an error in versions 2.01 to 2.03 that affects transformation from/to the GSE coordinate system. Due to this error the GSE coordinate axes are reverted in some conditions. The error is corrected in version 2.05. Additional sporadic errors have been fixed in version 2.09.
Diagnostics
Common Blocks
Dependencies
Called by

None
Calls

None
See also

UM510, select a geomagnetic field model
UM522, position of the Sun
UT551, initialize an Euler rotation matrix
UT552, initialize a quaternion rotation matrix
UT555, coordinate conversion
UT556, vector conversion
Reported Bugs

v1.07, Erroneous behaviour of the coordinate transformations
relative to GSM and MAG coordinate systems, fixed in next versions
(this erroneous behaviour does not affect the subroutine UM523).
Examples

None