Practicing Index Notation proofs

Asked Sep 01 '17 at 14:35

Active Sep 01 '17 at 14:50

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I am practicing proving things with index notation in order to get a good grasp of the way it works. One of the problems that I came up against is $\nabla(\frac{1}{2}v^2) = \vec{v}\times(\nabla\times\vec{v})+(\vec{v} \cdot \nabla)\vec{v} $

You can write the right hand side as $\epsilon_{ijk}v_i\epsilon_{xyj}\partial_xv_y + v_i\partial_iv_k$ this comes down to $v_iv_i\partial_k - v_i\partial_iv_k + v_i\partial_iv_k$ the last two terms cancel so you are left with $\nabla v^2$ but where is the half?

edited Sep 01 '17 at 14:50

asked Sep 01 '17 at 14:35

Coolcrab

1

I would advise starting on the right hand side... – Peter Sep 01 '17 at 14:37
Yes, it's normally better to start on the more complicated side for algebraic proofs. – Chappers Sep 01 '17 at 14:48
I updated the question, I get most of it but not the half. – Coolcrab Sep 01 '17 at 14:50

Practicing Index Notation proofs

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