A new method for resolving the jerk and jounce vectors in Euclidean 3‐space

Tawfiq, Abdelrhman Magdi; Cesarano, Clemente; Elsharkawy, Ayman

doi:10.1002/mma.9016

Cited by 3 publications

(1 citation statement)

References 15 publications

(20 reference statements)

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“…Also, in 2022, Elshenhab et al [14] studied acceleration and jerk vectors according to the quasi-frame in Euclidean 3-space. More recently, Tawfiq et al [15] introduced a new method resolving the jerk and jounce vectors in Euclidean 3-space. Some other studies studied the jerk [7,10,11,[16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

On the jerk and snap in motion along non‐lightlike curves in Minkowski 3‐space

Elsharkawy,

Cesarano,

Alhazmi

2024

Math Methods in App Sciences

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In this paper, we study the jerk vector that is the rate of change of the acceleration vector over time. In three‐dimensional space, the decomposition of the jerk vector is a new concept in the field. This decomposition expresses the jerk vector as the sum of three unique components in specific directions: the tangential direction, the radial direction in the osculating plane, and the radial direction in the rectifying plane. The snap vector is the rate of change of the jerk vector over time. In this paper, the authors examine non‐relativistic particles moving along non‐lightlike Frenet curves at low speeds compared to the speed of light in Minkowski 3‐space. They resolve the jerk and snap vectors using Frenet–Serret frames. Additionally, the cases for motion along non‐lightlike Frenet planar curves in the Minkowski 3‐space are given as corollaries. To help understand these results, the paper provides some illustrative examples

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Section: Introductionmentioning

confidence: 99%

On the jerk and snap in motion along non‐lightlike curves in Minkowski 3‐space

Elsharkawy,

Cesarano,

Alhazmi

2024

Math Methods in App Sciences

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Exploring Hasimoto surfaces within equiform geometry in Minkowski space

Elsharkawy

2024

Phys. Scr.

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In this study, we investigate the equiform geometry of Hasimoto surfaces within the context of three-dimensional Minkowski space. We analyze the geometric characteristics inherent to these surfaces, focusing on their Gaussian and mean equiform curvatures. This analysis encompasses three distinct scenarios involving non-lightlike curves. Additionally, we propose a method for characterizing the parameter curves associated with the equiform Hasimoto surfaces in Minkowski space. To illustrate our findings, we present several examples of these surfaces within this geometric framework.

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Quasi-position vector curves in Galilean 4-space

Elsharkawy,

Elsharkawy

2024

Front. Phys.

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The Frenet frame is not suitable for describing the behavior of the curve in the Galilean space since it is not defined everywhere. In this study, an alternative frame, the so-called quasi-frame, is investigated in Galilean 4-space. Furthermore, the quasi-formulas in Galilean 4-space are deduced and quasi-curvatures are obtained in terms of the quasi-frame and its derivatives. Quasi-rectifying, quasi-normal, and quasi-osculating curves are studied in Galilean 4-space. We prove that there is no quasi-normal and accordingly normal curve in Galilean 4-space.

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A new method for resolving the jerk and jounce vectors in Euclidean 3‐space

Cited by 3 publications

References 15 publications

On the jerk and snap in motion along non‐lightlike curves in Minkowski 3‐space

On the jerk and snap in motion along non‐lightlike curves in Minkowski 3‐space

Exploring Hasimoto surfaces within equiform geometry in Minkowski space

Quasi-position vector curves in Galilean 4-space

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