A length of chain rotating about a vertical axis, fixed only at the pivot, adopts a shape that is defined by the number of nodes. The maximum number of nodes is determined by rotation frequency. To date no exact or approximate analytical solutions have been found except for the linearized case (small angles). In this paper angular solutions are determined for the nonlinear helicoseir rotating at high frequency with large angular excursions. Good approximations are found for the shape of the fundamental mode. Simple physical arguments explain previously observed helicoseir characteristics in a new way.

中文翻译：

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螺旋桨的非线性模式

仅在枢轴上固定的绕垂直轴旋转的链条的长度采用由节点数定义的形状。节点的最大数量由旋转频率确定。迄今为止，除线性情况（小角度）外，尚未找到精确或近似的解析解。在本文中，确定了在大角度偏移下以高频旋转的非线性螺旋桨的角度解。对于基本模式的形状，找到了很好的近似值。简单的物理争论以一种新的方式解释了先前观察到的螺旋藻特性。