# Thread: Einstein indicial notation problem

1. ## Re: Einstein indicial notation problem

Originally Posted by milad
thanks .I will try to do the same in 3D .
You're welcome. It works in 3d, but too much to post.

2. ## Re: Einstein indicial notation problem

A2ik means each member powered to 2 . Aij*Ajk=A2ik is true only if A is a diagonal tensor .which I think you didn't notice . thank you so much for your time and effort .

3. ## Re: Einstein indicial notation problem

Originally Posted by milad
A2ik means each member powered to 2 . Aij*Ajk=A2ik is true only if A is a diagonal tensor .which I think you didn't notice . thank you so much for your time and effort .
It does not. A2ik means the ik component of A2.

A = laijl and Aij, the ij component of A, is aij.

4. ## Re: Einstein indicial notation problem

I showed the answer to my professor but he says I must do all the work in index notation .

5. ## Re: Einstein indicial notation problem

Originally Posted by milad
I showed the answer to my professor but he says I must do all the work in index notation .
With principal directions in 3d

(s112+s222+s332)2 = s114+s224+s334 + 2(s112s222+ s112s332+ s222s332)

(s11+s22+s33)2 = s112+s222+s332 + 2(s11s22+ s11s33+ s22s33) = 0 because sii=0. So
s112+s222+s332 = -2(s11s22+ s11s33+ s22s33)

(s112+s222+s332)2 = 4[s112s222+s112s332+s222s332 + 2(s11+s22+s33)(s11s22s33)] and sii=0. So
s112s222+s112s332+s222s332 = ¼(s112+s222+s332)2 and substitute this into first eq to get:

s114+s224+s334 = ½(s112+s222+s332)2 , or in indicial notation:

sii4 = sii2sjj2

The above in indicial notation is:

(sii2)2 = sii4 + 2A
(sii)2 = sii2 + 2B = 0
sii2 = -2B
(sii2)2 = 4B2 = 4A, if you can show B2 = A
Then
sii4 = sii2sjj2

I can’t express things like s11s22+ s11s33+ s22s33 in indicial notation.
Surely your Prof at some point has to show you how to do this problem in indicial notation.
Please let us know.

EDIT: Had to juggle with Latex help again to get my Word sub-super script version to post.

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