Riccati parametric deformations of the Cornu spiral
H C Rosu, S C Mancas, E. Flores-Garduno
TL;DR
This paper introduces a parametric deformation of the Cornu spiral based on Riccati equations, explores its geometric properties through Argand plots, and uncovers a supersymmetric structure via factorization methods.
Contribution
It presents a novel deformation of the Cornu spiral using Riccati equations and reveals its supersymmetric structure through a factorization approach.
Findings
Deformation parameter is an integration constant in Riccati solutions.
Argand plots illustrate the geometric changes of the deformed spiral.
Supersymmetric (Darboux) structure is identified in the deformation.
Abstract
A parametric deformation of the Cornu spiral is introduced. The parameter is an integration constant which appears in the general solution of the Riccati equation related to the Fresnel integrals. Argand plots of the deformed spirals are presented and a supersymmetric (Darboux) structure of the deformation is revealed through the factorization approach.
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