{"title":"Cartesian coordinates of an intrinsically defined curve","authors":"S. Radnef","doi":"10.13111/2066-8201.2023.15.4.18","DOIUrl":null,"url":null,"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.","PeriodicalId":37556,"journal":{"name":"INCAS Bulletin","volume":"112 48","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"INCAS Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13111/2066-8201.2023.15.4.18","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Engineering","Score":null,"Total":0}
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.
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.
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