How do I go about evaluating:

if it helps I have and T is symetric

I'll give it a go:

T is symetric so the middle term disapears

where z = [0 0 1]'

I can go no further and suspect I have made an error before this point.

I would really like to get an answer of the form:

but that seems unlikely as I can see no way to conjure up the partial derivative w.r.t. t.

This problem is related to my earlier post:

Calculus of Variations - Noether's Theorem for fields