Department of Mathematics, Cornell University, Ithaca, New York 14853, USA.
Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
Phys Rev Lett. 2020 Aug 21;125(8):088001. doi: 10.1103/PhysRevLett.125.088001.
We determine which helical equilibria of an isotropic Kirchhoff elastic rod with clamped ends are stable and which are unstable. Although the set of all helical equilibria is parametrized by four variables, with an additional fifth parameter determined by the rod's material, we show that only three of these five parameters are needed to distinguish between stable and unstable equilibria. We also show that the closure of the set of stable equilibria is star convex. With these results, we are able to compute and visualize the boundary between stable and unstable helices for the first time.
我们确定了两端固定的各向同性 Kirchhoff 弹性杆的哪些螺旋平衡是稳定的，哪些是不稳定的。尽管所有螺旋平衡的集合都由四个变量参数化，并且由棒材的材料确定第五个附加参数，但我们表明，在区分稳定和不稳定的平衡时，只需要这五个参数中的三个。我们还表明，稳定平衡的集合的闭包是星形凸的。有了这些结果，我们就能够首次计算和可视化稳定和不稳定螺旋之间的边界。
