Kinematics of Persistent Rigid Motions Traced by Adapted Frames Along Null Cartan Curves

ABSTRACT One‐parameter rigid motions along null Cartan curves in the three‐dimensional Lorentz–Minkowski space are considered. More specifically, we aim to investigate four different variants of frame motions associated with a null Cartan curve: the Cartan motion , the alternative frame motion , the Bishop motion , and the generalized Bishop motion . We show under what conditions the present frame motion is persistent, in other words, we prove when the pitch of the instantaneous twist of the motion is constant. Unlike the Euclidean case and the Lorentzian cases for nonnull curves, we are able to characterize explicitly the null Cartan curves generating persistent frame motions. We also investigate the fixed and moving axode surfaces of the four different frame motions. Examples are provided to illustrate our results.