Proving the Three-Component Formula for Fluid Mechanics Forces

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dopey9
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Can someone help me with this proof
 
Attachments
  • Screenshot of a Microsoft Word document showing typed text: "Hi, I want to use cartesian coordinates to prove that for any vector F", followed by the identity ∇ x (∇ x F) = ∇ (∇•F) - ∇²F.
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  • Screenshot of a Microsoft Word document showing typed vector identity: curl of curl of F equals grad of div F minus laplacian of F, written with nabla symbols.
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Discussion

Well, Cartese away first, and we'll help you if you stumble! :smile:
 
I would recommend starting by supposing F is made up by three components, F_1 , F_2 ,F_3 then just expand out the left hand side!

It is tidous but you will see it will fall out

 

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