Page 23 - Introduction to Continuum Mechanics

8 Indicial Notation

i.e.,

We note that

If e 1 ,e 2 ,e 3 form a right-handed triad, then

which can be written for short as

Now, if a = a ie i, and b = b ie i, then

i.e.,

The following useful identity can be proven (see Prob. 2A7)

2A5 Manipulations with the Indicial Notation
(a) Substitution
If

and

then, in order to substitute the b i's in (ii) into (i) we first change the free index in (ii) from i to
m and the dummy index m to some other letter, say n so that

Now, (i) and (iii) give

Note (iv) represents three equations each having the sum of nine terms on its right-hand side.