Cartesian coordinates of an intrinsically defined curve

Q2 Engineering

INCAS Bulletin Pub Date : 2023-12-02 DOI:10.13111/2066-8201.2023.15.4.18

S. Radnef

引用次数: 0

Abstract

Summarizing some old research on the dynamics of a pointall body along its own trajectory, this paper established the differential relationships between the principal curvatures of a 3D curve, that is the normal curvature and the torsional curvature, and its Cartesian coordinates. The differential system thus derived is actually a dynamical system of a representative point of the curve moving along it. This dynamic system is analyzed to see the possibilities of finding analytical solutions in finite terms, using Frobenius' integrability theorem for the general case and usual integration methods for the particular case consisting of the constant ratio between the two curvatures.

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本构曲线的笛卡尔坐标

本文总结了以往关于点体沿自身轨迹运动动力学的一些研究，建立了三维曲线的主曲率(法曲率和扭转曲率)与其笛卡尔坐标的微分关系。这样推导出的微分系统实际上是曲线的一个代表点沿着它运动的动力系统。对这一动态系统进行了分析，利用一般情况下的Frobenius可积性定理和由两个曲率之间的常数比组成的特殊情况的常用积分方法，探讨了在有限项下找到解析解的可能性。

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

INCAS Bulletin Engineering-Aerospace Engineering

自引率

0.00%

发文量

审稿时长

8 weeks

期刊介绍： INCAS BULLETIN is a scientific quartely journal published by INCAS – National Institute for Aerospace Research “Elie Carafoli” (under the aegis of The Romanian Academy) Its current focus is the aerospace field, covering fluid mechanics, aerodynamics, flight theory, aeroelasticity, structures, applied control, mechatronics, experimental aerodynamics, computational methods. All submitted papers are peer-reviewed. The journal will publish reports and short research original papers of substance. Unique features distinguishing this journal: R & D reports in aerospace sciences in Romania The INCAS BULLETIN of the National Institute for Aerospace Research "Elie Carafoli" includes the following sections: 1) FULL PAPERS. -Strength of materials, elasticity, plasticity, aeroelasticity, static and dynamic analysis of structures, vibrations and impact. -Systems, mechatronics and control in aerospace. -Materials and tribology. -Kinematics and dynamics of mechanisms, friction, lubrication. -Measurement technique. -Aeroacoustics, ventilation, wind motors. -Management in Aerospace Activities. 2) TECHNICAL-SCIENTIFIC NOTES and REPORTS. Includes: case studies, technical-scientific notes and reports on published areas. 3) INCAS NEWS. Promote and emphasise INCAS technical base and achievements. 4) BOOK REVIEWS.