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A novel formulation of the Lie-Darboux method of obtaining the Riccatiequations for the spatial curves in Euclidean three-dimensional space ispresented. It leads to two Riccati equations that differ by the sign oftorsion. The case of cylindrical helices is used as an illustrative example.Possible applications in Physics are suggested.

Riccati equations of opposite torsions from the Lie-Darboux method for spatial curves and possible applications