椭圆螺旋运动的点-线位移

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-10 DOI:10.1016/j.jmaa.2025.129787

Galip F. Uçak , İsmail Gök

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引用次数: 0

摘要

本文的目的是在椭圆空间的框架内发展点线位移的概念，记为Ra1，a2,a3。本文首先总结了椭圆对偶四元数和椭圆螺旋运动的基本原理。其次，在椭圆型内积空间中严格定义了点线位移的概念，并对其代数性质进行了深入分析。最后，通过建立点线几何与椭圆对偶欧拉-罗德里格斯公式之间的关系的举例说明了所提出方法的实际意义。

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On point-line displacement with elliptic screw motion

The objective of this paper is to develop the concept of point-line displacement within the framework of elliptic space, denoted as

R_{a_{1}, a_{2}, a_{3}}

. The study begins by summarizing the fundamental principles of elliptic dual quaternions and elliptic screw motion. Next, the notion of point-line displacement is rigorously defined in the context of elliptic inner product spaces, and its algebraic properties are thoroughly analyzed. Finally, the practical relevance of the proposed approach is demonstrated through an illustrative example that establishes the relationship between point-line geometry and the elliptic dual Euler-Rodrigues formula.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.