摘要
通过讨论圆环面上的测地线 ,研究在纤维缠绕时测地线的稳定性问题 .按传统观点 ,测地线在曲面上是最稳定的 ,其意为一条弹性柔软的细线 ,在给定曲面上拉紧时 ,其形状应是测地线 ,且不会使曲线变形 .上述提法仅在局部邻域中成立 .从整体角度分析 ,当拉紧弹性柔软细线时 ,将有两类不稳定测地线 .第一类不稳定产生于过两点可以有多条测地线 ,另一类是缠绕的测地线位于曲面的凹侧 ,此时就会产生搭桥现象 .这两类不稳定性在纤维缠绕中有着现实的意义 。
The stability problem of geodesics is discussed on torus in this paper.From the traditional view,the geodesic is most stable on a curved surface.It means that the shape of a flexible thin thread tightend on a given surface is a geodesic,and it does not deform.The above statement is only correct in the local area.From the global view,when a flexible thin thread is tightend,there will be two kinds of unstability.The one happens when many geodesics come through two given points,the other comes from that the wound filament is laid on the concave side of the surface.It will yield “bridging” phenomenon.These two kinds of unstability can not carry on in filament winding.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2001年第4期481-485,共5页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金 (60 0 730 2 3)
