@article{Alluhaibi2023, 
author = {Nadia Alluhaibi and Rashad A. Abdel-Baky},
title = {Kinematic-geometry of lines with special trajectories in spatial kinematics},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {5},
pages = {10887-10904},
keywords = {E. Study's map, axodes, line congruence, Disteli's formulae, height dual functions},
url = {https://www.sciopen.com/article/10.3934/math.2023552},
doi = {10.3934/math.2023552},
abstract = {This paper derives the expressions for kinematic-geometry of lines with special trajectories in spatial kinematics by means of the E. Study map. A particular assurance goes to the 2nd order movement characteristics for extracting a new proof of the Disteli formulae of the axodes. Meanwhile, a new height dual function is defined and utilized to investigate the geometrical properties of the Disteli-axis. Consequently, as an implementation, the spatial equivalent of the cubic of stationary curvature is established and researched. Finally, Disteli formulae of a line-trajectory are extracted and inspected in detail.}
}