Page 43 - Introduction to Continuum Mechanics

28 Tensors

C e
3 = 3
Thus, by either method, the transformation matrix is
'£- I n
2 ~2 °
_- 1^3
rol
[Q]
~ 2 2 °
0 0 1

Fig.2B.4

2B12 Transformation Laws for Cartesian Components of Vectors

Consider any vector a, then the components of a with respect to {e/} are
a/ = a-e/

and its components with respect to {e/ }are
a'j = a • e'i
Now, e/ = Q mi* m, [Eq. (2Bll.la)], therefore,

i.e.,

In matrix notation, Eq. (2B12.1a) is