Spacelike Lines with Special Trajectories and Invariant Axodes

The association between the instantaneous invariants of a one-parameter Lorentzian spatial movement and the spacelike lines with certain trajectories is considered in this study. To be more precise, we present a theoretical formulation of a Lorentzian inflection line congruence, which is the spatial...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 15; no. 5; p. 1087
Main Authors Almoneef, Areej A., Abdel-Baky, Rashad A.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 15.05.2023
Subjects
Disteli-axis
Euclidean space
Euler–Savary equation
Geometry
Invariants
Kinematics
Mechanical engineering
Robotics
timelike axodes
Trajectories
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Summary:The association between the instantaneous invariants of a one-parameter Lorentzian spatial movement and the spacelike lines with certain trajectories is considered in this study. To be more precise, we present a theoretical formulation of a Lorentzian inflection line congruence, which is the spatial symmetrical of the inflection circle of planar kinematics. Finally, we establish novel Lorentzian explanations for the Disteli and Euler–Savary formulae. Our results add to a better understanding of the interaction between axodes and Lorentzian spatial movements, with potential implications in fields such as robotics and mechanical engineering.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15051087