AN EXCURSION INTO LARGE ROTATIONS
AN EXCURSION INTO LARGE ROTATIONS
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DOI：
10.1016/0045-7825(82)90069-x
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发表时间：
1982-01-01
影响因子：
7.2
通讯作者：
ARGYRIS, J
中科院分区：
文献类型：
--
作者：
ARGYRIS, J
本文对文献[1]中提出的空间有限转动的矩阵形式进行了进一步的探讨。它示出了如何一致的，但微妙的矩阵演算不可避免地会导致一些优雅的表达式的变换或旋转matrixTap有关的旋转围绕任意轴。还分析了关于固定或从动轴的多个旋转的情况。特别注意的是一个单一的复合旋转矢量相当于两个连续的任意旋转的显式推导。这一主题在一些情况下进行了详细讨论。还考虑了在[2，3]中首次提出的半切旋转，其中交换性保持不变。此外，还给出了大转动的初等几何分析。最后，我们推导出在附录中，使用明智的重新制定的四分之一，复合pseudovector代表的综合效果ofnrotations.In作者的意见，目前的方法似乎更可取的纯矢量计划，甚至更是一个indicial制定-和计算更方便。
The present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in [1]. It is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrixTappertaining to a rotation about an arbitrary axis. Also analysed is the case of multiple rotations about fixed or follower axes. Particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations. This theme is discussed in some detail for a number of cases. Semitangential rotations—for which commutativity holds—first proposed in [2, 3]are also considered. Furthermore, an elementary geometrical analysis of large rotations is also given. Finally, we deduce in an appendix, using a judicious reformulation of quarternions, the compound pseudovector representing the combined effect ofnrotations.In the author's opinion the present approach appears preferable to a pure vectorial scheme—and even more so to an indicial formulation— and is computationally more convenient.