Page 333 - Introduction to Continuum Mechanics

Change of Frame 317

therefore,

That is

This is not the transformation law for an objective vector. Therefore the velocity vector is
non-objective as expected.
(b) From the result of part (a), we have

and

Subtraction of the above two equations then gives

But dx* = Qdx, therefore

Thus,

Example 5.32.3
Show that in a change of frame, the deformation gradient F transforms according to the
equation

Solution. We have, for the starred frame

and for the unstarred frame