THE CONFORMAL NEO-EULERIAN ORIENTATION MAP

被引:8
作者
FRANK, FC
机构
[1] HH Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, Royal Fort, Tyndall Avenue
来源
PHILOSOPHICAL MAGAZINE A-PHYSICS OF CONDENSED MATTER STRUCTURE DEFECTS AND MECHANICAL PROPERTIES | 1992年 / 65卷 / 05期
关键词
D O I
10.1080/01418619208201501
中图分类号
T [工业技术];
学科分类号
08 [工学];
摘要
The rotation vector C = I 2 tan1/4-omega (where I is the unit vector designating an axis of rotation and omega the angle of rotation about that axis) yields a conformal orientation map, at least in the sense that transformations by change of reference orientation are conformal transformations. C is equal to the Rodrigues vector R = I tan1/2-omega multiplied by the re-scaling factor g (R)=2/[1+(1+R2)1/2]. In this map the orbit for rotation about a fixed axis is a circular arc, spanning a diameter of a sphere of radius 2, representing a rotation of 2-pi: or, in an extended map a full circle representing a rotation of 4-pi. The locus of points representing orientations angularly equidistant from two given orientations is, in general, in the extended map, a pair of orthogonally intersecting spheres. A crystallographic example and a metallurgical application are given.
引用
收藏
页码:1141 / 1149
页数:9
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