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

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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