On Jun 4, 2014, at 5:00 AM, gromacs.org_gmx-users-requ...@maillist.sys.kth.se wrote: > From: Mark Abraham <mark.j.abra...@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-us...@gromacs.org> > Cc: Discussion list for GROMACS users > <gromacs.org_gmx-users@maillist.sys.kth.se> > Reply-To: gmx-us...@gromacs.org > > > On Wed, Jun 4, 2014 at 1:01 AM, gmail <wenjin.brooks...@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. 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) 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 >> >> >> -- >> Gromacs Users mailing list >> >> * Please search the archive at >> http://www.gromacs.org/Support/Mailing_Lists/GMX-Users_List before >> posting! >> >> * Can't post? Read http://www.gromacs.org/Support/Mailing_Lists >> >> * For (un)subscribe requests visit >> https://maillist.sys.kth.se/mailman/listinfo/gromacs.org_gmx-users or >> send a mail to gmx-users-requ...@gromacs.org. >> > -- Gromacs Users mailing list * Please search the archive at http://www.gromacs.org/Support/Mailing_Lists/GMX-Users_List before posting! * Can't post? Read http://www.gromacs.org/Support/Mailing_Lists * For (un)subscribe requests visit https://maillist.sys.kth.se/mailman/listinfo/gromacs.org_gmx-users or send a mail to gmx-users-requ...@gromacs.org.