极小旋转标架定义的流形几何

THE GEOMETRIC PROPERTY OF ROTATION MINIMIZING FRAME BASED ON A MANIFOLD MODEL

从极小旋转标架(Rotation Minimizing Frame,RMF)定义出发,建立与RMF相关流形的模型,然后以微分流形为工具对RMF定义中的自由度进行尽可能的化简,从而把定义中的微分代数方程转化为一个常微分方程.这有助于对RMF数学本质的进一步理解.另一方面,以RMF作为基础得到了一般的运动标架所需要满足的常微分方程,并且对RMF对应曲线的测地线性质进行了分析.

In this paper,the number of variables in the original definition of Rotation Minimizing Frame（RMF） is reduced by constructing a manifold model.By the tool of Differential Manifold,the Differential-Algebra equations is converted into a first-order ordinary differential equation（ODE）.It is good for understanding the essence of RMF.On the other side,the ODE of a generic frame and the geodesic property of RMF ＇s curve in the manifold have been presented on the basis of the result of RMF ＇s ODE.