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Trapped Radiation ENvironment model Development


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


    Subroutine UT550 - select a coordinate transformation


      INTEGER*4 kfrom, kto, ifail
      REAL*8    trans(3,3)

      CALL UT550 (kfrom,kto,trans,ifail)


    input coordinate system [in]
    output coordinate system [in]
    transformation matrix [out]
    Error flag (see diagnostics) [out]


    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, ktocoordinate system
    1Geographic coordinate (GEO)
    2 Geocentric equatorial inertial coordinate (GEI)
    3Geomagnetic coordinate (MAG)
    4Solar magnetic coordinate (SM)
    5Geocentric solar magnetospheric coordinate (GSM)
    6Geocentric 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 Earth-Sun 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.


  • Olson, W.P., Coordinate Transformations Used in Magnetospheric Physics, McDonnell-Douglas Astronautics Company Paper WD1145 (1970).
  • Russell, C.T.,Geophysical Coordinate Transformations, Cosmic Electrodynamics 2 (1971) 184-196.


    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.


Common Blocks

    UC140, magnetic field description
    UC160, general constants


Called by




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).