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The moments as seen by PEACE are measured in a frame (hereafter the P-frame) in which the x-axis (
) is aligned with the HEEA sensor
head and
is the spin-axis. A schematic representation of the principle PEACE geometry is shown in Figure 5.2. This system is different from the engineered `body coordinates' (B-frame). In the B-frame the
is
the spin axis and
is 26.2 degrees antispinward of the Sun sensor. We wish to output our data in the physically informative GSE
frame, so we must use attitude (AUX) data with the knowledge of the geometry of the various measurement frames to transform from the
spacecraft to GSE frame.
Figure 5.2:
Schematic showing the principle geometry of the PEACE experiment.
|
In general, a tensor
can be transformed to a
new frame
by:
 |
(5.1) |
where
is a transformation matrix. The transformation from the raw P-frame to the GSE-frame consists of four steps. Firstly there
is a 60 degree rotation about
to take
into
, described by:
Next there is a 90 degree flip to take
into
- this is a 90 degree rotation about
:
Now we are in the B-frame, we must transform into the GSE frame. The inputs of latitude
and longitude
, and knowledge of the Sun's azimuthal position at PEACE's 0 degree (22.4 degrees) allow construction of two transformation matrices which deal with the spin axis orientation:
and the offset between
and the PEACE 0 degree azimuthal:
The normalisation factor
is
 |
(5.2) |
This choice of factor accounts for the constraint that the
axis is 22.4 degrees spinward of
and must have a positive
component.
Applied in the above sequence, the above matrices transform a tensor or vector from the raw P-frame into the desired GSE frame. All outputs from the solver are in GSE coordinates.
Next: Useful information
Up: Calibration
Previous: Gain correction factors
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Steve Schwartz
2005-03-26