极小旋转标架定义的流形几何

吴梦;马国庆;杨周旺;邓建松

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (11) : 1562-1573.

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系统科学与数学 ›› 2010, Vol. 30 ›› Issue (11) : 1562-1573. DOI: 10.12341/jssms09427
论文

极小旋转标架定义的流形几何

    吴梦, 马国庆, 杨周旺, 邓建松
作者信息 +

The Geometric Property of Rotation Minimizing Frame Based on a Manifold Model

    WU Meng, MA Guoqing, YANG Zhouwang, DENG Jiansong
Author information +
文章历史 +

摘要

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.

Abstract

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.

关键词

极小旋转标架定义 / 扫掠曲面 / 代数微分方程组.

Key words

Rotation minimizing frame / sweep surface / differential-algebraic equations.

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吴梦 , 马国庆 , 杨周旺 , 邓建松. 极小旋转标架定义的流形几何. 系统科学与数学, 2010, 30(11): 1562-1573. https://doi.org/10.12341/jssms09427
WU Meng , MA Guoqing , YANG Zhouwang , DENG Jiansong. The Geometric Property of Rotation Minimizing Frame Based on a Manifold Model. Journal of Systems Science and Mathematical Sciences, 2010, 30(11): 1562-1573 https://doi.org/10.12341/jssms09427
中图分类号: 00A06   
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