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    ON THE DARBOUX ROTATION AXIS OF CURVES IN THREE-DIMENSIONAL LIE GROUPS
    (Univ Nis, 2023) Ozturk, Ufuk; Erdal, Gulay
    This paper presents a study on the motion of the Darboux rotation axis for curves in three-dimensional Lie groups a bi-invariant metric using the Frenet frame. Our findings reveal that the motion of the axis can be resolved into two simultaneous rotational motions. Additionally, we develop a sequence of Darboux vectors that are useful in constructing uncomplicated mechanisms. We also introduce a curve with constant precession and conduct an exhaustive analysis of its characteristics.