Fourth-order kinematic analysis: Advanced decomposition methods for particle motion in modified orthogonal frame
Year: 2025
Type: article
Abstract: The analysis of higher-order derivatives of position, particularly the snap (fourth derivative), provides critical insights into complex motion dynamics in fields such as robotics, aerospace, and biomechanics. This research investigates novel decomposition techniques for the fourth-order derivative of position (snap vector) of a particle traveling along spatial curves within three-dimensional Euclidean geometry. We establish comprehensive analytical expressions that decompose the snap vector into components corresponding to modified orthonormal basis vectors. Furthermore, we present an innovative alternative formulation that partitions the snap vector into tangential and radial components within the osculating and rectifying planes. The developed theoretical framework is validated through computational examples, illustrating the practical implementation and effectiveness of the proposed decomposition methodologies.
Source: PLoS ONE
Authors: Fatimah Alghamdi, Ayman Elsharkawy
Institutions: University of Jeddah, Tanta University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,382
Funder: Ministry of Education, India
OpenAlex ID: W7117645873