Kinematic-geometry of a line trajectory and the invariants of the axodes

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2023-01-01 DOI:10.1515/dema-2022-0252

Yanlin Li, Fatemah Mofarreh, Rashad A. Abdel-Baky

引用次数: 5

Abstract

Abstract In this article, we investigate the relationships between the instantaneous invariants of a one-parameter spatial movement and the local invariants of the axodes. Specifically, we provide new proofs for the Euler-Savary and Disteli formulas using the E. Study map in spatial kinematics, showcasing its elegance and efficiency. In addition, we introduce two line congruences and thoroughly analyze their spatial equivalence. Our findings contribute to a deeper understanding of the interplay between spatial movements and axodes, with potential applications in fields such as robotics and mechanical engineering.

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直线轨迹的运动几何和轴的不变量

摘要本文研究了单参数空间运动的瞬时不变量与阳极局部不变量之间的关系。具体来说，我们使用E. Study映射在空间运动学中为Euler-Savary和Disteli公式提供了新的证明，展示了它的优雅和效率。此外，我们引入了两条直线同余，并对它们的空间等价性进行了深入的分析。我们的发现有助于更深入地了解空间运动和阳极之间的相互作用，在机器人和机械工程等领域具有潜在的应用。

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

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.