It is generally accepted in biology and engineering that insects are unstable when they hover. Existing approaches based on direct averaging do not fully capture the dynamic features and stability features of insect flight. Here we show a passive stabilization mechanism that insects use through their natural wing vibrations: vibration stabilization. This stabilization technique cannot be captured using the averaging approach commonly used in the literature. In contrast, it is explained using a special type of calculus: the chronological calculus. Our result is supported by experiments on a real Hawkmoth suspended in pitch disturbance. This finding could be particularly useful to biologists, as the vibration stabilization mechanism can be exploited by many other creatures as well. In addition, our results can lead to more optimal designs for bio-inspired flying robots by relaxing the requirements for feedback control of the flight.
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