Lecture 10

We can use continuum equation to change the right side of the
equation to
∫ ∫
∂(νvi )
− x j x k d 3 x = νv i (x k δ ji + x j δ ki )d 3 x, (15)
∂x i
where the second term is obtained using the divergence theorem.
This is now recognizable in the left hand side of (12), so we now
have the tensor virial theorem
1
2dt 2I jk = 2T jk + Π jk + W jk . (16)
d 2
Note that we can get the scalar virial theorem by taking trace of
the tensor virial theorem.