Geometrical uncertainty in mechanics and random curves in space

The paper proposes an approach to model the geometrical uncertainty in case of curves in space. After highlighting the importance of the geometrical uncertainty in various fields of mechanics, the random set of “irregular or imperfect curves” is analysed in the natural or intrinsic reference system by the formulas of Serret–Frenet. It is shown that the Riccati’s random differential operator, in complex domain, describes this random set. The curvature and torsion are modelled by weakly homogeneous random functions with discrete spectrum. Numerical results show the application of the proposed approach.