[gmx-users] Remove rotation around the center of mass

[Mark Abraham]

On Wed, Jun 4, 2014 at 4:36 PM, gmail <wenjin.brooks.li at gmail.com> wrote:

>
> On Jun 4, 2014, at 5:00 AM,
> gromacs.org_gmx-users-request at maillist.sys.kth.se wrote:
> > From: Mark Abraham <mark.j.abraham at gmail.com>
> > Subject: Re: [gmx-users] Remove rotation around the center of mass
> > Date: June 4, 2014 at 3:31:39 AM CDT
> > To: Discussion list for GROMACS users <gmx-users at gromacs.org>
> > Cc: Discussion list for GROMACS users <
> gromacs.org_gmx-users at maillist.sys.kth.se>
> > Reply-To: gmx-users at gromacs.org
> >
> >
> > On Wed, Jun 4, 2014 at 1:01 AM, gmail <wenjin.brooks.li at gmail.com>
> wrote:
> >
> >> Dear gmx-users,
> >>
> >> I have some questions on the way that gromacs remove the rotation around
> >> the center of mass when set "comm-mode = Angular”
> >>
> >> I have checked the related code for removing the rotation and have a
> >> question on how gromacs estimate the inertia tensor I.
> >>
> >> In gromacs, the inertia tensor is estimated as follows,
> >>
> >> I=sum m_i*[x_i*x_i]-M*[x_c*x_c]
> >>
> >> here, m_i is the mass of atom i;
> >>          x_i is the Cartesian coordinate of atom i;
> >>          x_c is the center of mass;
> >>          M is the total mass of the system.
> >>          [x*x] represents the outer product between x and x.
> >>
> >> One can easily get that
> >>
> >> I=sum m_i*[y_i*y_i]  with y_i = x_i - x_c     ———(1)
> >>
> >> However, from standard mechanics textbook, the inertia is given as
> >>
> >> I=sum m_i*{(y_i.y_i)E - [y_i*y_i]}       ———— (2)
> >>
> >> here,  y_i.y_i is the inner product between y_i and y_i;
> >>          E is a 3*3 identity matrix.
> >>
> >> I want to know the reason that gromacs use Eq. (1) instead of Eq. (2) to
> >> calculate the inertia tensor.
> >>
> >
> > Without having looked at the code, I imagine GROMACS would calculate the
> > moment of inertia about the specified center, rather than bothering with
> > computing the tensor. Eq (2) is expressed in coordinates relative to an
> > arbitrary origin, to what does it reduce if you choose the COM as the
> > origin?
> >
> > Mark
> >
>
> Eq. (2) is the one relative to the COM, as I used y_i not x_i.
>

That's not definitive. Under what convention was the equation *derived*?


> So, there is a difference in using Eq. (1) instead of Eq. (2), and
> I still do not get the reason to use Eq. (1), any further explanation?
>
> In addition, gromacs code does calculate the tensor with Eq. (1)
>

What do you get if you compute with the other one?

Mark


>
> Wenjin
>
> > Since gromacs estimate the angular velocity (w) with
> >>
> >> w=I^-1*L
> >> Here, I^-1 is the inverse of the inertia tensor I;
> >>          L is the angular momentum.
> >>
> >> The angular velocity will be different using Eq. (1) comparing to Eq.
> (2)
> >>
> >> Does anyone know why gromacs use Eq. (1) not Eq. (2)?
> >>
> >> Thanks,
> >> Wenjin
> >>
> >>
> >> --
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>
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