Explicit Examples of Motions of Inextensible Curves in Spherical Space S3

Mohamed, Samah Gaber

doi:10.12785/amisl/020302

Cited by 4 publications

(1 citation statement)

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“…Also, they studied kinematics of moving generalized curves indimensional Euclidean space in terms of intrinsic geometries. Mohamed [19] studied the motions of inextensible curves in spherical space S 3 .…”

Section: Introductionmentioning

confidence: 99%

Generated Surfaces via Inextensible Flows of Curves inR3

Hussien

Mohamed

2016

Journal of Applied Mathematics

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We study the inextensible flows of curves in 3-dimensional Euclidean spaceR3. The main purpose of this paper is constructing and plotting the surfaces that are generated from the motion of inextensible curves inR3. Also, we study some geometric properties of those surfaces. We give some examples about the inextensible flows of curves inR3and we determine the curves from their intrinsic equations (curvature and torsion). Finally, we determine and plot the surfaces that are generated by the motion of those curves by using Mathematica 7.

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Section: Introductionmentioning

confidence: 99%

Generated Surfaces via Inextensible Flows of Curves inR3

Hussien

Mohamed

2016

Journal of Applied Mathematics

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Binormal motions of inextensible curves in de-sitter spaceS2,1

Mohamed

2017

Journal of the Egyptian Mathematical Society

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New Applications on the Flows of Space-like curves specified by Normal acceleration in Minkowski Space ℝ²,¹

Al Elaiw,

Gaber

2023

Applied Mathematics and Nonlinear Sciences

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This paper investigates the kinematic motions of space-like and time-like curves specified by acceleration fields in Minkowski space ℝ2,1. Through the motion, the relationship between the acceleration fields and velocity fields is determined. In this study, we focus on studying the flows of inextensible space-like curves with a space-like principal normal vector specified by a normal acceleration that equals the curvature of the curve. Through the motion of the inextensible space-like curve with normal acceleration, we prove that the position vector of the curve satisfies a one-dimensional wave equation. We present some novel applications and visualize the flows of curves and their curvatures.

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Explicit Examples of Motions of Inextensible Curves in Spherical Space S3

Cited by 4 publications

References 24 publications

Generated Surfaces via Inextensible Flows of Curves inR3

Generated Surfaces via Inextensible Flows of Curves inR3

Binormal motions of inextensible curves in de-sitter spaceS2,1

New Applications on the Flows of Space-like curves specified by Normal acceleration in Minkowski Space ℝ²,¹

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Explicit Examples of Motions of Inextensible Curves in Spherical Space S3

Cited by 4 publications

References 24 publications

Generated Surfaces via Inextensible Flows of Curves inR3

Generated Surfaces via Inextensible Flows of Curves inR3

Binormal motions of inextensible curves in de-sitter spaceS2,1

New Applications on the Flows of Space-like curves specified by Normal acceleration in Minkowski Space ℝ2,1

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Product

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New Applications on the Flows of Space-like curves specified by Normal acceleration in Minkowski Space ℝ²,¹