Resolutions of the Jerk and Snap Vectors for a Quasi Curve in Euclidean 3-Space

Hamouda, Ebrahem; Cesarano, Clemente; Askar, Sameh; Elsharkawy, Ayman

doi:10.3390/math9233128

Cited by 6 publications

(4 citation statements)

References 15 publications

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“…Recently, in 2020, Tosun and Hizarcıoglu [12] investigated the resolution of the jerk vector for curves on regular surfaces using the Darboux frame

{normal𝔼}^{3}

. Further, in 2021, Hamouda et al [13] studied jerk and snap vectors according to the quasi‐frame in Euclidean 3‐space. Also, in 2022, Elshenhab et al [14] studied acceleration and jerk vectors according to the quasi‐frame in Euclidean 3‐space.…”

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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“…Recently, in 2020, Tosun and Hizarcıoglu [12] investigated the resolution of the jerk vector for curves on regular surfaces using the Darboux frame

{normal𝔼}^{3}

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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“…From 1978 to 2020, the definition of the jerk and its applications are given in previous studies. [5][6][7][8][9][10][11] The time derivative of a particle's jerk vector defines jounce vector of that particle. But is the jounce vector an important concept to understand?…”

Section: Introductionmentioning

confidence: 99%

“…The movement of sensitive instruments needs to be kept within specified limits of both acceleration and jerk to avoid damage. From 1978 to 2020, the definition of the jerk and its applications are given in previous studies 5–11 …”

Section: Introductionmentioning

confidence: 99%

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

Tawfiq

Cesarano

Elsharkawy

2023

Math Methods in App Sciences

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Investigating the jounce vector in planar and space motion is the primary objective of this paper. For planar motion, the jounce vector is split into tangential-normal and radial-transverse components. Simple pendulum oscillation, a central force proportionate to distance, and Keplerian orbital motion are used as models for plane motion to show the geometric properties of the jounce vector. The jounce vector of a particle that is moving across three dimensions of Euclidean space is also investigated, and it is resolved in the tangential, radial, and other radial directions in the rectifying and osculating planes, respectively.The models used were an electron in a uniform magnetic field and a particle traveling along a spiral path.

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“…At all locations, the Q-frame is well-defined, it is straightforward to calculate, and its construction is unaffected by whether the curve is parameterized by arc-length or not. Among many papers dealing with this subject, we refer the reader to the following [16][17][18].…”

Section: Introductionmentioning

confidence: 99%