FRENET-FRAME CONTINUITY AND EXISTENCE OF THE SERRET-FRENET EQUATIONS AT ZERO-CURVATURE POINTS [PDF]
, 2021 The continuity of the Frenet frame and existence of the Serret-Frenet equations at zero-curvature points are established for a general three-dimensional curve with arbitrary parameterization.
Ahmed Shabana (10639154)
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An Extension to the Frenet-Serret and Bishop Invariant Extended Kalman Filters for Tracking Accelerating Targets [PDF]
, 2022 This paper presents an extension to the original Frenet-Serret and Bishop frame target models used in the invariant extended Kalman filter (IEKF) to account for tangential accelerations for highly-manoeuvrable targets.
Anderson, David +3 more
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Serret-frenet formulas for octonionic curves [PDF]
, 2020 YUCE, SALIM/0000-0002-8296-6495In this paper, we define spatial octonionic curves (SOC) in R( )(7)and octonionic curves (OC) in R-8 by using octonions. Firstly, we determine Serret-Frenet equations, and curvatures of the SOC in R-7.
Bektaş, Özcan, Yüce, Salim
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Nonunit quaternion parametrization of a Petrov–Galerkin Cosserat rod finite element
Proceedings in Applied Mathematics and Mechanics, Volume 23, Issue 4, December 2023., 2023 Abstract The application of the Petrov–Galerkin projection method in Cosserat rod finite element formulations offers significant advantages in simplifying the expressions within the discrete virtual work functionals. Moreover, it enables a straight‐forward and systematic exchange of the ansatz functions, specifically for centerline positions and cross ...
Jonas Harsch, Simon R. Eugster
wiley +1 more source
Quaternionic Serret-Frenet Frames for Fuzzy Split Quaternion Numbers
, 2018 We build the concept of fuzzy split quaternion numbers of a natural extension of fuzzy real numbers in this study. Then, we give some differential geometric properties of this fuzzy quaternion.
Şimşek, Simge +2 more
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Development of Frenet-Serret Frame and the Apollonian Window [PDF]
, 2020 The present study focuses on developing a Frenet-Serret frame and the Apollonian Window. In the first part of the study Apollonian disks are generated for first four generations by developing visual basic codes in excel. For the second part of the study,
Karimushan, Syeda Fareeza
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On Frenet-Serret Invariants of Non-Null Curves in Lorentzian Space L5
, 2009 The aim of this paper is to determine Frenet-Serret invariants of non-null curves in Lorentzian 5-space. First, we define a vector product of four vectors, by this way, we present a method to calculate Frenet-Serret invariants of the non-null curves ...
Turgut, Melih +5 more
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General formulation of impedance in Frenet-Serret coordinate system [PDF]
, 2023 In accelerator physics, the concept of impedance is popularly used to describe the interactions of charged particles inside a bunch or between bunches in a train. Standard formulations of impedance assume that the driving charge has a constant velocity $\
Zhou, Demin, Tsai, Cheng-Ying
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Characterisation of Frenet-Serret and Bishop motions with applications to needle steering [PDF]
, 2013 Frenet-Serret and Bishop rigid-body motions have many potential applications in robotics, graphics and computer-aided design. In order to study these motions, new characterisations in terms of their velocity twists are derived.
Selig, JM
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Geometrically exact isogeometric Bernoulli-Euler beam based on the Frenet-Serret frame
, 2022 A novel geometrically exact model of the spatially curved Bernoulli-Euler beam is developed. The formulation utilizes the Frenet-Serret frame as the reference for updating the orientation of a cross section.
Gfrerer, M. H. +2 more
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