[gmx-users] Principal axes of inertia and g_principal

[Antonio Baptista]

Hi Nicola,

On Thu, 11 Sep 2014, nicola staffolani wrote:

> ​Dear GMX community,
>
> regarding the program g_principal and acknowledged the bug reported here
> <http://permalink.gmane.org/gmane.science.biology.gromacs.user/66719>​
> ​, I would like to understand what the meaning of the output of this
> program is.
> So, left aside moi.dat, the output files are axis1.dat, axis2.dat &
> axis3.dat.
> Supposing that I have already corrected the output files (or reinstalled
> GROMACS having fixed the bug in the source file as explained always here
> <http://t110399.science-biology-gromacs-user.biotalk.us/g-principal-bug-or-very-bad-choice-of-filenames-t110399.html>),
> in each of the files, for each time instant there are three coordinates: x,
> y and z: what do they mean? My interpretation is that if I connect the
> point, whose coordinates are those printed out in the output files, with
> the origin of the Cartesian axes, then I get a line coinciding with the
> corresponding (principal) axis: is this interpretation correct?

Yes, that is correct. In other words, they are the coordinates of the 
point P=O+v, where O is the origin and v is the vector of unit norm that 
points along that principal axis. Of course, for graphical representation 
purposes, you would displace each of those 3 principal axis vectors to 
make them point away from the center of mass of your system, since the 
whole idea is to get a reference frame which is "natural" to that system 
(e.g., see Goldstein or any other book on rigid body mechanics).

>
> To get the principal axes, I have to diagonalize the moment of inertia
> symmetric 3×3 matrix; one way to do it is by solving the 3rd order equation
> for the eigenvalues: is this the way by which GROMACS finds then the
> eigenvectors of the moment of inertia matrix, from which it calculates the
> aforementioned coordinates?

As I pointed in the links you mentioned, I didn't look very deep into the 
GROMACS code, but the vectors that g_principal writes (after the 
correction) are exactly the ones obtained from the diagonalization you 
describe. But check it yourself for a simple case. My rule of thumb: never 
trust an analysis tool until you check it yourself... :)

Best,
Antonio

>
> Thank you in advance,
>
> Nicola       ​
>
> -- 
> Nicola Staffolani PhD
> Biophysics & Nanoscience Centre <http://www.unitus.it/biophysics>
> Università della Tuscia
> Largo dell'Università s.n.c., I-01100 Viterbo
> email: n.staffolani at unitus.it
> tel.: +39 0761 35 70 27; fax: +39 0761 35 71 36
> -- 
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--
Antonio M. Baptista
Instituto de Tecnologia Quimica e Biologica, Universidade Nova de Lisboa
Av. da Republica - EAN, 2780-157 Oeiras, Portugal
phone: +351-214469619         email: baptista at itqb.unl.pt
fax:   +351-214411277         WWW:   http://www.itqb.unl.pt/~baptista
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