刚体运动是物理中一个很理想的概念,即指一个物体在运动中,它的形状和大小不发生改变.在几何学里,刚体运动在某种意义上可以看作一种坐标变换.笔者刻画了正交标架与刚体运动的关系定理;作为应用,证明了在刚体运动下,作为确定一般空间曲线的形状和大小的完全不变量系统(弧长、曲率和挠率)保持不变;满足空间曲线的完全不变量系统的两条曲线可以重合.特别地,笔者总结出求两条给定曲线重合的刚体运动表达式的具体步骤,并给出一个实例加以阐述.n physics, a rigid body is an idealization of a solid body in which the shape and size remain constant regardless of external forces exerted on it. In geometry, a rigid motion is usually regarded as a coordinate transformation in certain sense. In this paper, the authors characterize the relation between orthogo- nal fames and rigid motion, and as its applications, they showed that under a rigid motion, the fully invari- ant algebraic systems （such as arc-length, curvature, torsion） determining the shape and size of a space curve can be preserved; and two given curves satisfying same fully invariant algebraic system can be coincided each other. Especially, the authors make an induction from a concrete example to illustrate how to solve a rigid motion such that two given space curves coincide together.广西自然科学资金项目(2011GXNSFA018127);广西民族大学重点科学研究项目(2012MDZD033
