[gmx-users] principal moments of ellipsoid

lammps lammps lammp2forum at gmail.com
Tue May 10 14:09:04 CEST 2011

```Not R_x, R_y, and R_z.

What I want to obtain  are the three three principal moments of the
ellipsoidal macromolecule.

They are different quantities.

2011/5/10 Erik Marklund <erikm at xray.bmc.uu.se>

> Mark Abraham skrev 2011-05-10 12.31:
>
> On 10/05/2011 8:23 PM, lammps lammps wrote:
>>
>>> Hi,
>>> I want to study the shape change of a macromolecule which seems like a
>>> ellipsoid.  So, I need obtain the three principal moments of the molecules.
>>> Is the command of g_gyrate helpful for me? The sum of the three principal
>>> moments should be equal to the <Rg^2>.  However, I used the command g_gyrate
>>> -f traj.gro -s nvt.tpr -n anly.ndx -o shape.xvg -p obtain the Rg and other
>>> three qualities.
>>> It seems that the sum of the last three qualities is not equal to the
>>> Rg^2. Is there something wrong?
>>>
>>
>> Why should that sum equal Rg^2?
>>
>> Mark
>>
> Shouldn't it be half of that sum?
>
>  Rg^2 = 1/N Sum([r_k - <r>]^2),
>
> where r are vectors and masses are set to unity for conveniance. If
> decomposed in orthonormal axes x, y, and z, it yealds
>
>  Rg^2 = 1/N Sum([x_k-<x>]^2 + [y_k-<y>]^2 + [z_k-<z>]^2).
>
> The radius of gyration around e.g. the x-axis is
>
>  Rg_x^2 = !/N Sum([y_k-<y>]^2 + [z_k-<z_k>]^2).
>
> Hence Rg^2 = (Rg_x^2+Rg_y^2+Rg_z^2) / 2.
>
> That matches the numbers I get from my tests.
>
> --
> -----------------------------------------------
> Erik Marklund, PhD student
> Dept. of Cell and Molecular Biology, Uppsala University.
> Husargatan 3, Box 596,    75124 Uppsala, Sweden
> phone:    +46 18 471 4537        fax: +46 18 511 755
> erikm at xray.bmc.uu.se    http://folding.bmc.uu.se/
>
>
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