On the jerk in motion along a space curve

Abstract

Summary The jerk vector of a moving particle is the third time derivative of the position vector and thus the time derivative of the acceleration vector. A useful resolution of the acceleration vector of a particle traveling along a space curve is well known in the literature due to Siacci's study in 1879. A similar resolution of the jerk vector was given as a new contribution to field by Özen and Tosun in 2019. In the present article, we take into account a particle moving on a space curve which is equipped with the Bishop frame and study the aforesaid resolution of the jerk vector for this particle. Furthermore, we have given an illustrative example to explain how the our result works.

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

“…Thus, we have r i = ‖r i ‖ = √ |⟨r i , r i ⟩| ≠ 0 for i = 2, 3. On the other hand, from Equation (11), it is clear that r i = ‖r i ‖ = √ |⟨r i , r i ⟩| ≠ 0 for i = 1. Secondly, we find that ⟨ r * i , r * i ⟩ = 0 for the curves 𝛾 i , i = 1, 3 when b i = q i .…”

“…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].…”

“…In 2019, Özen et al [10] determined the jerk vector in the osculating and rectifying planes along the tangential direction and radial directions using the Frenet–Serret frame. In 2020, Güner [11] studied the resolution of the jerk vector for the curves in by using the Bishop frame. Also, in 2020, Özen et al [7] introduced the resolution of the jerk vector for the curves in by using the modified orthogonal frame.…”

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

“…Özen et al [13] studied resolutions of the acceleration and jerk vectors for modified curves in Euclidean 3-space E 3 . Güner [14] studied resolutions of the jerk vector for Bishop curves in Euclidean 3-space E 3 . Tosun and Hızarcıoglu [15] studied resolutions of the jerk vector for Darboux curves on regular surfaces in Euclidean 3-space E 3 .…”