Spacelike Lines with Special Trajectories and Invariant Axodes

Abstract

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.