三维Minkowski空间中第二类松弛弹性线的内蕴方程
Intrinsic equations for a relaxed elastic line of second kind in Minkowski 3-space
摘要：
设$α$是三维Minkowski空间中连通定向曲面$S$上的弧，由弧长$s$、挠率$τ$和弧长$l$参数化。$α$的总平方扭转$H$由$% H=\int_{0}^{l}τ^{2}ds$定义。如果在$S$上的所有长度为$l$的弧族中，$H$的值最小化的变分问题的极值与$α$具有相同的初始点和初始方向，则该弧称为第二类松弛弹性线。本文在三维Minkowski空间中得到了第二类松弛弹性线在定向曲面上的微分方程和边界条件。
英文摘要：
Let $α$ be an arc on a connected oriented surface $S$ in Minkowski 3-space, parameterized by arc length $s$, with torsion $τ$ and length $l$. The total square torsion $H$ of $α$ is defined by $% H=\int_{0}^{l}τ^{2}ds$. The arc is called a relaxed elastic line of second kind if it is an extremal for the variational problem of minimizing the value of $H$ within the family of all arcs of length $l$ on $S$ having the same initial point and initial direction as $α$. In this study, we obtain differential equation and boundary conditions for a relaxed elastic line of second kind on an oriented surface in Minkowski 3-space.
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