Nonholonomic Theory of Principal-direction Orthonormal Basis for a Layer of Surfaces  

曲面层的主方向正交基的非完整理论

作　　者：LI Jiayang XIE Xilin 李嘉扬;谢锡麟(复旦大学航空航天系,上海200433)

机构地区：[1]Department of Aeronautics and Astronautics,Fudan University,Shanghai 200433,China

出　　处：《复旦学报（自然科学版）》2024年第4期415-437,442,共24页Journal of Fudan University：Natural Science

基　　金：Project supported by the National Natural Science Foundation of China(11972120,11472082,12032016)。

摘　　要：In order to carry out tensor analysis in a neighborhood of a reference surface,the principal-direction orthogonal basis accompanying with Lame s coefficients or general curvilinear coordinate systems are widely used.A novel kind of field theory termed as the nonholonomic theory of the Principal-Direction Orthonormal Basis(PDOB)is presented systematically in the present paper,in which the formal Christoffel symbols are related directly to the principal and geodesic curvatures with respect to the principal directions of the surface.Furthermore,a systematic and simple way to determine the curvatures of the surface are presented with some examples.It provides a way to recognize qualitatively the bending property of a surface.为了在参考曲面的邻域中进行张量分析,常常采用带有拉梅系数的主方向单位正交基。本文系统地提出了一种称为曲面主方向正交基的非完整理论(PDOB),新的场论方法使得形式Christoffel符号与曲面的主曲率和测地线曲率直接相关。此外,本文通过一些示例提出了一种确定曲面曲率的系统且简单的方法,其亦可作为一种定性识别表面弯曲特性的方法。

关 键 词：nonholonomic theory principal-direction orthonormal basis principal curvature geodesic curvature 

分 类 号：O302[理学—力学]