A new approach to representations of homothetic motions in Lorentz space

IF 1.4 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-04-28 DOI:10.1515/ijnsns-2021-0235

D. Ünal, M. Güngör, M. Tosun

引用次数: 0

Abstract

Abstract In this study, Rodrigues parameters have been first calculated for a homothetic rotation around spacelike and timelike axis using one parameter homothetic motions in Lorentz 3-space E 1 3 ${\mathbb{E}}_{1}^{3}$ . The behavior of the vectors during the homothetic rotation, which is the increase or decrease (about size of one of the objects in motion) notion, has been investigated as a three dimensional shape with the help of Cinema 4D program. The behavioral differences have been observed on figures. Then, Lorentz motions that corresponding to the homothetic rotation matrices in terms of spacelike and timelike axes have been examined and expressed in E 1 3 ${\mathbb{E}}_{1}^{3}$ . Some definitions, theorems, corollaries and three dimensional figures have been given in Lorentz 3-space.

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洛伦兹空间中同质运动表示的一种新方法

摘要在这项研究中，首次使用洛伦兹3-空间E13${\mathbb{E}}_{1}^{3}$中的单参数同位运动计算了绕类时空轴的同位旋转的Rodrigues参数。在Cinema 4D程序的帮助下，向量在同位旋转过程中的行为，即增加或减少（大约运动中的一个物体的大小）的概念，已经被研究为三维形状。行为上的差异已经在数字上观察到了。然后，研究了与类时空轴上的同位旋转矩阵相对应的洛伦兹运动，并用E13$｛\mathbb｛E｝｝_｛1｝^｛3｝$表示。在洛伦兹3空间中给出了一些定义、定理、推论和三维图形。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Nonlinear Sciences and Numerical Simulation 工程技术-工程：综合

CiteScore

2.80

自引率

6.70%

发文量

117

审稿时长

13.7 months

期刊介绍： The International Journal of Nonlinear Sciences and Numerical Simulation publishes original papers on all subjects relevant to nonlinear sciences and numerical simulation. The journal is directed at Researchers in Nonlinear Sciences, Engineers, and Computational Scientists, Economists, and others, who either study the nature of nonlinear problems or conduct numerical simulations of nonlinear problems.