I Question about Cartesian Tensors

Worn_Out_Tools
Messages
6
Reaction score
1
I am not a mathematician but an Engineer-in-Training studying mechanics. That being said why does equation I-10 equal 1 when k equals i and 0 when k does not equal i?

IMG_0111.jpeg
 
Last edited by a moderator:
Physics news on Phys.org
Worn_Out_Tools said:
I am not a mathematician but an Engineer-in-Training studying mechanics. That being said why does equation I-10 equal 1 when k equals i and 0 when k does not equal i?
Consider the case of ##x'_0=1, x'_1=0, x'_2=0##. In this case, only the terms with ##k=0## contribute to the sum in the eqn. I-9, which becomes ##x'_i=a_{ij}a_{0j}##. For ##i=0## it becomes ##1=a_{0j}a_{0j}##, for ##i=1## it becomes ##0=a_{1j}a_{0j}##, etc. For all combinations of ##k## and ##i##, you get the eqn. I-10.
 
Last edited:
“a” is defined as shorthand for the cosine function earlier in the book. So 1 = cos(0,j) * cos (0,j)?
 
Worn_Out_Tools said:
“a” is defined as shorthand for the cosine function earlier in the book. So 1 = cos(0,j) * cos (0,j)?
No. ##i, j, k## are indices.
 
Back
Top