The problem is the book isn't referring to the strain rate tensor itself (whose nature is expressed by writing \mathbf{S}), but to its components (so it would be an objective tensor): otherwise, it would have been trivial to state its independency of the frame of reference in which it is...
Thanks for the reply, but I'm not so much convinced by your argumentation. In fact, at page 80 it is stated:
All in all, on one hand "S_{ij} is independent of the frame of reference in which it is observed"; on the other hand, instead, "S_{ij} change as the coordinate system is rotated".
I am...
I've got a problem regarding tensors.
Premise: we are considering a fluid particle with a velocity \mathbf{u} and a position vector \mathbf{x}; S_{ij} is the strain rate tensor, defined in this way:
\displaystyle{S_{ij}=\frac{1}{2}\left(\frac{\partial u_i}{\partial x_j} +\frac{\partial...