Page 63 - Introduction to Continuum Mechanics

48 Tensors Calculus

Solution.

Since the base vectors are fixed,

Therefore,

Example 2C1.2

T
Show that for an orthogonal tensor Q(t), (dQ/dt)Q is an antisymmetric tensor.
r
Solution, Since QQ = I, we have

That is

Since

Therefore,

But

therefore,