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Question in linear algebra, derivation of a certain relation
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[QUOTE="antonni, post: 5300755, member: 524168"] Hello good people, please refer to this: [ATTACH=full]92425[/ATTACH] (notice the mistake in [I]9.31[/I]: cos(psi) switches places with cos(phi)sin(psi) to the best of my understanding) Now, I am trying to derive [I]9.30[/I] and for this, according to the book, we solve [I]9.32[/I]. The problem is I can not understand [I]9.32[/I], the meaning of it. I see it like this: 1) Group the strain tensor elements in each direction: [B]ST1[/B]=(s11+s21+s31)*[B]e1 ; ST2[/B]=(s22+s12+s32)*[B]e2[/B] ; [B]ST3[/B]=(s33+s13+s23)*[B]e3 [/B]then the "s " stands for epsilon (strain) and the numbers are the strain element of the tensor. [B]e1,2,3[/B] are unit vectors in [B]S1,2,3[/B] directions respectively. 2) Now, simply project the [B]ST1,2,3[/B] on the unit vector in the phi-psi direction, the [B]h[/B] of [I]9.31[/I]. That way you get the magnitude of the strain in the phi-psi direction, which is what we want and what should be [I]9.30[/I] according to the book. (of course s21=s12, s13=s31 & s23=s32) I do it the like this: component of [B]ST1[/B] on [B]h [/B]= ([B]h[/B] dot [B]ST1[/B]) / |[B]h[/B]| ; similarly for [B]ST2[/B] and [B]ST3[/B]. component of [B]ST1[/B] on [B]h [/B]= ([B]h[/B] dot [B]ST1[/B]) / |[B]h[/B]| = h1*(s11+s21+s31) ; similarly for [B]ST2[/B] and [B]ST3[/B]. As you can see I do not get the [I]9.30[/I]. Where is my mistake? Thank you very much Anton [/QUOTE]
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