广义椭圆四元数及其一些应用

IF 0.8 4区数学 Q2 MATHEMATICS

Turkish Journal of Mathematics Pub Date : 2023-01-01 DOI:10.55730/1300-0098.3364

H. B. Çolakoğlu, M. Özdemir

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引用次数: 1

摘要

本文利用广义标量积空间对四元数进行了推广，并利用四元数考察了任意给定椭球体上的椭圆旋转。四元数是一种较好的表示球面旋转的方法。为此，首先定义了以给定椭球为球体并确定偏对称矩阵的广义椭圆标量积空间，以及与该标量积空间相关的广义向量积;然后利用这些概念定义了广义椭圆四元数。最后，利用单位广义椭圆四元数研究了空间中任意椭球体上的椭圆旋转。通过数值算例对公式和结果进行了验证。

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Generalized elliptical quaternions with some applications

: In this article, quaternions, which is a preferred and elegant method for expressing spherical rotations, are generalized with the help of generalized scalar product spaces, and elliptical rotations on any given ellipsoid are examined by them. To this end, firstly, we define the generalized elliptical scalar product space which accepts the given ellipsoid as a sphere and determines skew symmetric matrices, and the generalized vector product related to this scalar product space. Then we define the generalized elliptical quaternions by using these notions. Finally, elliptical rotations on any ellipsoid in the space are examined by using the unit generalized elliptical quaternions. The formulas and results obtained are supported with numerical examples.

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来源期刊

Turkish Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

161

审稿时长

6-12 weeks

期刊介绍： The Turkish Journal of Mathematics is published electronically 6 times a year by the Scientific and Technological Research Council of Turkey (TÜBİTAK) and accepts English-language original research manuscripts in the field of mathematics. Contribution is open to researchers of all nationalities.