Relationships for the Relative Motion of a Tensor Described in Any Two Rotational Reference Frame
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摘要: 提出了用矢阵表示的张量对时间的相对导数的概念.研究表明,通过借助于矢阵概念,在涉及多个坐标系时,张量的相对导数得到了更加清晰和严格地描述.由此,并借助于反对称张量,给出了张量的一阶绝对导数和相对导数之间的关系式,并又进一步给出了张量的二阶绝对导数和相对导数之间的关系.结果表明,当运动需要分别在两个转动坐标系中进行描述时,由于张量的特殊性,其"速度"(广义的)合成和"加速度"(广义的)合成既类似于矢量的速度合成和加速度合成又有着本质的差别,为此还提出了关于张量的"速度"和"加速度"合成定理,特别是又进一步将它们推广到任意两个转动坐标系的情形.Abstract: 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.
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Key words:
- kinematics /
- relative derivative /
- tensor /
- flight dynamics
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