Explicit Parameterization of Euler’s Elastica
Explicit Parameterization of Euler’s Elastica
复制标题
欧拉 Elastica 的显式参数化
DOI：
--
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
V. Vassilev
中科院分区：
文献类型：
--
作者：
P. Djondjorov;M. Hadzhilazova;I. Mladenov;V. Vassilev
考虑一些非标准的参数拉格朗日，得到了一个虚构的动力学系统，它等价于寻找薄板的所有可能形状的欧拉问题。通过积分相应的微分方程组，我们得到了欧拉弹性曲线的新的显式参数化。较详细地研究了挠性弹性体的几何，特别是“八”字形的几何，概述了弹性体问题与数学摆的密切关系。
The consideration of some non-standard parametric Lagrangian leads to a fictitious dynamical system which turns out to be equivalent to the Euler problem for finding out all possible shapes of the lamina. Integrating the respective differential equations one arrives at novel explicit parameterizations of the Euler’s elastica curves. The geometry of the inflexional elastica and especially that of the figure “eight” shape is studied in some detail and the close relationship between the elastica problem and mathematical pendulum is outlined.