Mechanics of Continua and Structures
We showed in a previous section that a tensor can be written as T=TijEi⊗Ej,
where Tij=Ei⋅(TEj)
Let the rotation linear operator map the vectors Ei to the vectors ei(t), i.e.,
ei(t)=RtEi.It can be shown that in the case of rotation tensors, the vectors ei(t) form an orthonormal set, i.e., ei(t)⋅ej(t)=δij, and, in fact, that they form a basis for E. The set (ei(t))i=1,2,3 is called the co-rotational basis (corresponding to (Ei)i=1,2,3). It can be shown that,
Rt=ei(t)⊗Ei