[gmx-users] Principal axes of inertia and g_principal

[nicola staffolani]

Dear Antonio,

thank you very much for your kind & clear reply!

Best regards,

Nicola


2014-09-12 4:34 GMT+02:00 Antonio Baptista <baptista at itqb.unl.pt>:

> 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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-- 
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