438 IX- DYNAMICS OF DEFORMABLE BODIES. 



Accordingly we may write the strain as the resultant of two, 



U = U ! + u -2 9 V = v i + ^2 J W = W-L + W 2 , 



where 



denoting a pure strain, and 



48) v 2 = (^ a 2 ) x (c 2 - 

 denoting a rotation CD whose components are 



49) OIT = -9(03 <i)> 



Thus every small strain may be resolved into a pure strain and a 

 rotation. 



In order to bring out the symmetry let us write the pure strain 



% = s x x + g z y + g y z, 

 50) v 1 = g z x + s y y + g x 0, 



MI = 9y% + 9xy + 5,-er, 

 where 



Thus the six quantities g and co are respectively the half sums 

 and half differences of shift -coefficients symmetrical about the main 

 diagonal. 1 ) 



1) In the usual notation the #'s are defined as the above sums without the 

 coefficient i as stated by Todhunter and Pearson, A History of Elasticity and 

 Strength of Materials, Vol. I, p. 882, "The advantage which would arise from 



