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please refer to this:

(notice the mistake in9.31: cos(psi) switches places with cos(phi)sin(psi) to the best of my understanding)

Now, I am trying to derive9.30and for this, according to the book, we solve9.32. The problem is I can not understand9.32, the meaning of it.

I see it like this:

1) Group the strain tensor elements in each direction:

ST1=(s11+s21+s31)*e1 ; ST2=(s22+s12+s32)*e2;ST3=(s33+s13+s23)*e3then the "s " stands for epsilon (strain) and the numbers are the strain element of the tensor.

e1,2,3are unit vectors inS1,2,3directions respectively.

2) Now, simply project theST1,2,3on the unit vector in the phi-psi direction, thehof9.31. That way you get the magnitude of the strain in the phi-psi direction, which is what we want and what should be9.30according to the book. (of course s21=s12, s13=s31 & s23=s32)

I do it the like this:

component ofST1onh= (hdotST1) / |h| ; similarly forST2andST3.

component ofST1onh= (hdotST1) / |h| = h1*(s11+s21+s31) ; similarly forST2andST3.

As you can see I do not get the9.30.

Where is my mistake?

Thank you very much

Anton

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# I Question in linear algebra, derivation of a certain relation

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