This paper investigates whether Lorentz geometry can be systematically implemented to study the geometric kinematics of persistent rigid motions in three-dimensional Minkowski space. The notion of persistence of a one-parameter rigid motion is identified by the property that the instantaneous twist of the motion has a constant pitch. The main difference between three-dimensional Euclidean and Minkowski spaces is that the pitch of twists will take three different values in Minkowski space depending on the causal character of the curve on which the motions are based. Furthermore, based on the fundamentals of screw theory, the paper establishes necessary and sufficient criteria for modeling the persistence of some significant frame motions, including Frenet–Serret, adapted frame, and Bishop motions. Then, the axode surfaces of these special motions and their geometric concepts are defined. Finally, for a thorough treatment of special frame motions in three-dimensional Minkowski space, this paper reveals some illustrative examples of persistent rigid motions and axode surfaces.

本文研究了洛伦兹几何是否可以系统地应用于研究三维闵可夫斯基空间中持久刚性运动的几何运动学。单参数刚性运动的持续性概念由运动的瞬时扭曲具有恒定螺距的特性确定。三维欧几里得空间和闵可夫斯基空间之间的主要区别在于，根据运动所基于的曲线的因果特征，扭曲的螺距在闵可夫斯基空间中将采用三个不同的值。此外，基于螺旋理论的基本原理，本文建立了必要且充分的标准来模拟一些重要框架运动的持续性，包括 Frenet-Serret、自适应框架和 Bishop 运动。然后，定义了这些特殊运动的轴表面及其几何概念。最后，为了彻底处理三维闵可夫斯基空间中的特殊坐标系运动，本文揭示了一些持久刚性运动和轴表面的说明性例子。