Page 332 - Introduction to Continuum Mechanics

316 The Elastic Solid

Example 5.32.1

Show (a) dx is an objective vector (b) ds is an objective scalar
Solution. From Eq. (5.32.1)

we have

therefore

so that dx is an objective vector
(b) From Eq. (5.32.6),

that is, ds is an objective scalar.

Example 5.32.2
Show that in a change of frame, (a) the velocity vector v transforms in accordance with the
following equation and is therefore not objective

(b)the velocity gradient transform in accordance with the following equation and is also not
objective

Solution, (a) From Eqs. (5.32.1)