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

被引：0

作者：

Dmitry Shirokov

机构：

[1] National Research University Higher School of Economics,

[2] Institute for Information Transmission Problems of Russian Academy of Sciences,undefined

来源：

Advances in Applied Clifford Algebras | 2019年 / 29卷

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：

暂无

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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

共 6 条

[1]

Marchuk N(2011)Parametrisations of elements of spinor and orthogonal groups using exterior exponents Adv. Appl. Clifford Algebras 21 583-590

[2]

Marchuk N(2008)Unitary spaces on Clifford algebras Adv. Appl. Clifford Algebras 18 237-254

[3]

Shirokov D(2017)Method of averaging in Clifford algebras Adv. Appl. Clifford Algebras 27 149-163

[4]

Shirokov D(2015)Contractions on ranks and quaternion types in Clifford algebras Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki 19 117-135

[5]

Shirokov D(2015)Calculations of elements of spin groups using generalized Pauli’s theorem Adv. Appl. Clifford Algebras 25 227-244

[6]

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