[Wien] Question on EFG and eigenvectors and sugestion for the output

[Martin Pieper]

You are, of course, correct on both points! 

Am Freitag, 7. Dezember 2007 15:53 schrieb Florent Boucher:
> Dear Martin,
> first my name is Florent, not Florence ;-)

My apologies on this first point :-)
 
> I am not in agreement with you concerning the choice of the axis.
> I will try to explain my point of view.
>
>  From the calculation, we have the sign of all the Vii eigenvalues. So
> we have the sign of Vzz, Vyy and Vxx
> Once you have the eigenvalues, you calculate the eignvectors and those
> eigenvectors can be either in one direction or in the opposite (as you
> mentioned with the s matrix).
> So, it is all the time possible to define a right-handed choice of axis
> once you have ordered the eigenvalues according to | Vzz| >= |Vyy| >= |Vxx|
> We will call this the set_1 for the eigenvectors and it will give a the
> set_1 of Eulerian Angles with respect to the cartesian axis.
>
> Now you can apply the following rotation matrices that still keep the
> right-handed definition.
>
> R2 = [ 1,0,0; 0,-1,0; 0,0,-1]
> R3 = [-1,0,0; 0, 1,0; 0,0,-1]
> R4 = [-1,0,0; 0,-1,0; 0,0, 1]
>

True. These are obviously rotations and, thereby, my argument that you switch 
from right- to left-handed sets when you change the direction of all except 
one basis vector is simply nonsense. 

Thanks a lot for catching this

Martin Pieper


> This will give four different possibilities of Eulerian angles but all
> will have the correct (and well define) sign for the Vii.
>
> You can do the same for the CSA.
>
> Finally, you will have 16 different combinations of Eulerian Angles to
> orient the EFG with respect to the CSA and all will be perfectly
> equivalent.
>
> Now, if your EFG tensor have additional symmetry, etaq=0, you can
> exchange x and y and the number of eulerian angles combinations is double.
>
> I hope I am right ...
>
> Regards
> Florent

-- 
Dr. Martin W. Pieper
Institut f. Physik, 
Karl-Franzens Universität Graz
Universitätsplatz 5, 
A - 8010 Graz, AUSTRIA
Tel.: +43-316-380-8564, Fax: +43-316-380-9816,
email: martin.pieper at ifp.tuwien.ac.at