If we have a function:
\begin{equation} f(x,x',y,y',t) \end{equation} and we are trying to minimise this subject to a constraint of
\begin{equation} g(x,x',y,y',t) \end{equation}
Would we simply have a set of two euler lagrange equations for each dependent variable, here we have x and y...
I've got ∇×(∇×R)=∇(∇.R)-∇2R [call it eq.1]
However I have the identity ∇×(A×B)=A(∇.B)-B(∇⋅A)+ (B⋅∇)A-(A⋅∇)B [call it eq.2]
Substituting in A=∇ and R=B into eq.2 we get ∇×(∇×R)=∇(∇.R)-R(∇⋅∇)+ (R⋅∇)∇-(∇⋅∇)R
which i work out to be ∇×(∇×R)=∇(∇.R)-R(∇⋅∇)+ (R⋅∇)∇-∇2R
Basically I don't understand...