Abstract 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.

中文翻译：

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力学中的几何不确定性和空间中的随机曲线

摘要 本文提出了一种在空间曲线情况下对几何不确定性进行建模的方法。在强调了几何不确定性在力学各领域的重要性之后，利用 Serret-Frenet 公式在自然或内在参考系中分析了随机的“不规则或不完美曲线”集合。结果表明，Riccati 随机微分算子在复域中描述了这个随机集。曲率和扭转由具有离散谱的弱齐次随机函数建模。数值结果显示了所提出方法的应用。