It is generally accepted among biology and engineering communities that insects are unstable at hover. However, existing approaches that rely on direct averaging do not fully capture the dynamical features and stability characteristics of insect flight. Here, we reveal a passive stabilization mechanism that insects exploit through their natural wing oscillations: vibrational stabilization. This stabilization technique cannot be captured using the averaging approach commonly used in literature. In contrast, it is elucidated using a special type of calculus: the chronological calculus. Our result is supported through experiments on a real hawkmoth subjected to pitch disturbance from hovering. This finding could be particularly useful to biologists because the vibrational stabilization mechanism may also be exploited by many other creatures. Moreover, our results may inspire more optimal designs for bioinspired flying robots by relaxing the feedback control requirements of flight.

生物学和工程学界普遍认为昆虫在盘旋时不稳定。但是，依赖于直接平均的现有方法不能完全捕获昆虫飞行的动力学特征和稳定性特征。在这里，我们揭示了昆虫通过其自然的机翼振动利用的被动稳定机制：振动稳定。使用文献中常用的平均方法无法捕获这种稳定技术。相反，它是使用一种特殊的演算类型进行阐明的：时间演算。我们的结果通过对遭受悬停音调干扰的真鹰蛾进行实验的支持。这一发现对于生物学家可能特别有用，因为振动稳定机制也可能被许多其他生物利用。此外，