Relationships for the Relative Motion of a Tensor Described in Any Two Rotational Reference Frame

The definitions of the relative derivatives of a tensor with respect to time in any reference frame by using the notation of vectrix were proposed. It was shown that with the help of vectrix one can treat the relative derivatives of a tensor more clearly and more rigorously when multiple reference frames were concerned. With the help of the notation of the skew-symmetric tensor,the expression for the 1st order absolute and relative derivatives of a tensor was presented, and the expression for the 2nd order absolute and relative derivatives of a tensor was offered further. When motion was necessarily described in two rotational reference frames, because the specific property of a tensor, although the composition of its "velocity" and the composition of its "acceleration" were similar to that of a vector to some extent in the form of expressions, there were still exists great distinction between them. As a result, the composition theories for the "velocity" and "acceleration" of a tensor were proposed, and they were further extended to the case of the relationships of motion between any two rotational reference frames.