Lancret螺旋
Lancret helices
摘要：
在基尔霍夫杆模型的框架内，研究了具有非定常弯曲和扭转刚度的非均匀对称杆的螺旋构型。从静力学的基尔霍夫方程组出发，得到了一组关于杆中心线曲率和挠率的微分方程，并利用Lancret定理求出了螺旋线解。我们得到一个独立的螺旋解的非均匀杆的曲率和扭矩取决于沿杆的弯曲系数的变化形式。这些结果得到的非均匀杆没有固有曲率，并为一个特定的情况下的固有曲率。
英文摘要：
Helical configurations of inhomogeneous symmetric rods with non-constant bending and twisting stiffness are studied within the framework of the Kirchhoff rod model. From the static Kirchhoff equations, we obtain a set of differential equations for the curvature and torsion of the centerline of the rod and the Lancret's theorem is used to find helical solutions. We obtain a free standing helical solution for an inhomogeneous rod whose curvature and torsion depend on the form of variation of the bending coefficient along the rod. These results are obtained for inhomogeneous rods without intrinsic curvature, and for a particular case of intrinsic curvature.
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