On Hyper-Dual Pell Lorentzian Vectors
Ali Atasoy *
Keskin Vocational School, Kırıkkale University, Kırıkkale, Türkiye.
Faik Babadag
Department of Mathematics, Kırıkkale University, Kırıkkale, Türkiye.
*Author to whom correspondence should be addressed.
Abstract
In this paper, hyper-dual Pell Lorentzian vectors are introduced in the three-dimensional Lorentzian space and formalize the hyper-dual Lorentzian scalar product. The principal findings include the analytical derivation of the hyper-dual Lorentzian angle and the establishment of new algebraic identities that govern the interaction between Pell recursive sequences and dual structures. The several geometric configurations are classified such as parallelism, intersection, and orthogonality for dual and hyper-dual components of the inner product. These results provide a robust mathematical framework for analyzing complex spatial displacements, offering significant potential for applications in kinematic modeling, robotic trajectory analysis, and rigid body dynamics within Lorentzian space. By integrating Pell sequences with hyper-dual Lorentzian geometry, this study provides an innovative approach to analyzing line geometry and spatial mechanisms.
Keywords: Hyper-dual Pell number, hyper-dual Pell-Lucas number, hyper-dual Pell Lorentzian vector, hyper-dual Lorentzian angle