Calculation of Elements of Spin Groups Using Method of Averaging in Clifford's Geometric Algebra

被引：9

作者：

Shirokov, Dmitry ^{[1
,2
]}

机构：

[1] Natl Res Univ, Higher Sch Econ, Myasnitskaya Str 20, Moscow 101000, Russia

[2] Russian Acad Sci, Inst Informat Transmiss Problems, Bolshoy Karetny Per 19, Moscow 127051, Russia

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2019年 / 29卷 / 03期

基金：

俄罗斯科学基金会;

关键词：

Spin group; Clifford algebra; Geometric algebra; Rotor; Method of averaging; Orthogonal group; Two-sheeted cover; 15A66; 11E88; 15B10; 20B05;

D O I：

10.1007/s00006-019-0967-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a method of computing elements of spin groups in the case of arbitrary dimension. This method generalizes Hestenes method for the case of dimension 4. We use the method of averaging in Clifford's geometric algebra previously proposed by the author. We present explicit formulas for elements of spin group that correspond to the elements of orthogonal groups as two-sheeted covering. These formulas allow us to compute rotors, which connect two different frames related by a rotation in geometric algebra of arbitrary dimension.

引用

页数：12

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