Interpretation of elements of the logarithm of a rotation matrix as rotation components around coordinate axes of a reference frame
Interpretation of elements of the logarithm of a rotation matrix as rotation components around coordinate axes of a reference frame
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DOI：
10.1007/s10910-016-0644-5
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发表时间：
2016-09-01
影响因子：
1.7
通讯作者：
Hayashi, Kunio
中科院分区：
文献类型：
--
作者：
Onaka, Susumu;Hayashi, Kunio
当我们考虑材料中的微观结构时，晶体取向是一个重要因素。相对于参考系，某些晶体取向可以由围绕单位矢量的旋转角表示。讨论了围绕参考系坐标轴的旋转分量的划分。对于对应于轴/角度对的旋转矩阵，其对数是具有三个独立元素的斜对称张量，和。结果表明，这些元素可以被解释为围绕坐标轴的旋转角的总和。称之为对数角的元素和可以作为旋转分量来评估材料中的晶体取向。
Crystal orientation is an important factor when we consider microstructures in materials. With respect to a reference frame, certain crystal orientation can be expressed by a rotation angle around a unit vector . Partitioning of into rotation components around coordinate axes of the reference frame is discussed. For a rotation matrix corresponding to the axis/angle pair, its logarithm is a skew symmetric tensor with three independent elements, and . It is shown that these elements can be interpreted to be sums of the divided rotation angles around the coordinate axes. The elements and of called the log angles can be used as the rotation components to evaluate crystal orientation in materials.