By using a Pontryagin’s principle, we study the optimal shape of a rotating nano rod and determine the optimal cross-section that is stable against buckling due to centrifugal forces. We generalize the results of the earlier studies focused on the constant cross-sectional area of nano rods. The problem of the optimal shape of a Bernoulli–Euler rotating rod is analyzed first. The optimal nano rod with fixed volume was found to have larger critical rotation speed than the optimally shaped Bernoulli–Euler rod with the same volume. Similarly, for fixed rotational speed, the optimally shaped nano rod was found to have smaller volume than the optimally shaped Bernoulli–Euler rod.

通过使用庞特里亚金原理，我们研究了旋转纳米棒的最佳形状，并确定了稳定的最佳横截面，该横截面可稳定地抵抗离心力引起的屈曲。我们概括了早期研究的结果，重点是纳米棒的恒定横截面积。首先分析了伯努利-欧拉旋转杆的最佳形状问题。发现具有固定体积的最佳纳米棒比具有相同体积的最佳形状的Bernoulli-Euler棒具有更大的临界转速。同样，对于固定的转速，发现最佳形状的纳米棒的体积小于最佳形状的Bernoulli-Euler棒的体积。