Proving a vector identity using tensors

[Random Variable]

I'm having a hard time proving that curl(curlF)=grad(divF)-div(gradF) using that crazy suffix notation.

Anything in brackets is a subscript.

EDIT: I think I figure it out. Don't look below if you get dizzy easily.



curl(curlF) = e[ijk]?/?x[j]curlF[k] = ?[ijk]?/?x[j](e[klm]?/?x[l]F[m])
= e[ijk]e[klm]?/?x[j]?/dx[l]F[m] = (d[il]d[jm] - d[im]d[il])?/?x[j]?/?x[l]F[m]
= ?/?x[j]?/?x[i.]F[j] - ?/?x[j]?/?x[j]F[l] = grad(divF) - div(gradF)?

 

[AStar617]

On behalf of all of ATOT:



/thread

 

[MrDudeMan]

very hard to read in that form...write it in word using the equation editor and then screen shot it and post a picture. it hurts my head to try to read that.

 

[Cooler]

Originally posted by: Random Variable
I'm having a hard time proving that curl(curlF)=grad(divF)-div(gradF) using that crazy suffix notation.

Anything in brackets is a subscript.

curl(curl F) = e[ijk]?(curlF)[k]/?x[j] = e[ijk](?(e[ijk]?F[k]/?x[j])/?x[j])
= e[ijk]e[ijk]?²F[k]/?x²[j]

Something's wrong because e[ijk]e[ijk]=6. Should the second epilson have a different subscript.

EDIT: I would so much rather prove it the long way. :|

You a EE major?

 

[JonnyStarks]

*head explodes*

 

[Random Variable]

Originally posted by: JonnyStarks
*head explodes*

sorry

 

[arcenite]

For what it's worth, you confused the ****** out of me

 

[KillerCharlie]

Tensor notation makes me run away.