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So I have to find the dynamical matricx of a bcc lattice considering only nearest neighbours. Its like if the nearest neighbours were all attached to the atom in question by springs.

So first we need the equations of motion for the lattice. There are 8 nearest neighbours, so the equations of motion, which there should be 3 for each dimension, should have 8 terms due to the forces from the 8 neighbours. So we should also have a 3x3 matrix with each element in the matrix being a sum of 8 terms.

I'm just having a little difficulty in picturing what's going on.

So I oriented the x and y-axis so the directly point along 2 of the 4 directions of the neighbours. And the distance between the atoms is root(3)a/2. So I found that, with a little algebra and geometry, that there are 4 coefficients in these equations. I found that they are root(3)/2, root(3/2), 3/2 and 3, but I'm not sure if this is what I should be doing.

These are the coefficients of the forces, or magnitudes of the forces, in the specified direction of each atom, if we orient them as mentioned above. I won't write out the full equations since that would be very messy and difficult to do since there are 3 equations with 8 terms from each neighbour, plus the ma term.. Am I doing it right?