2 papers
math-ph2026
Clothoid helices obtained via the Lie-Darboux method
H. C. Rosu, J. de la Cruz, P. Lemus-Basilio
The clothoid helices that have both curvature and torsion directly proportional to the arclength are obtained via the Lie-Darboux method and analyzed in some detail. Shifted counte…
math.GM2023
Riccati equations of opposite torsions from the Lie-Darboux method for spatial curves and possible applications
Paola Lemus-Basilio, Haret C. Rosu
A novel formulation of the Lie-Darboux method of obtaining the Riccati equations for the spatial curves in Euclidean three-dimensional space is presented. It leads to two Riccati e…