[gmx-users] Remove rotation around the center of mass
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wenjin.brooks.li at gmail.com
Wed Jun 4 01:02:05 CEST 2014
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.
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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