# [gmx-users] principal moments of ellipsoid

Justin A. Lemkul jalemkul at vt.edu
Tue May 10 14:11:27 CEST 2011

```
lammps lammps wrote:
> 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.
>
>

Then isn't g_principal the more appropriate tool, rather than g_gyrate?

-Justin

>
>
> 2011/5/10 Erik Marklund <erikm at xray.bmc.uu.se <mailto: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 <mailto:erikm at xray.bmc.uu.se>
>      http://folding.bmc.uu.se/
>
>
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> --
>

--
========================================

Justin A. Lemkul
Ph.D. Candidate
ICTAS Doctoral Scholar
MILES-IGERT Trainee
Department of Biochemistry
Virginia Tech
Blacksburg, VA
jalemkul[at]vt.edu | (540) 231-9080
http://www.bevanlab.biochem.vt.edu/Pages/Personal/justin

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