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Applied Mechanics Lab

Mechanics of Continua and Structures

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Co-rotational basis

We showed in a previous section that a tensor can be written as T=TijEiEj,

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

Mathematica file demonstrating co-rotational basis

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