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The need for higher-order averaging in the stability analysis of hovering, flapping-wing flight

机译：悬停，襟翼飞行稳定性分析中需要高阶平均

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摘要

Because of the relatively high flapping frequency associated with hovering insects and flapping wing micro-air vehicles (FWMAVs), dynamic stability analysis typically involves direct averaging of the time-periodic dynamics over a flapping cycle. However, direct application of the averaging theorem may lead to false conclusions about the dynamics and stability of hovering insects and FWMAVs. Higher-order averaging techniques may be needed to understand the dynamics of flapping wing flight and to analyze its stability. We use second-order averaging to analyze the hovering dynamics of five insects in response to high-amplitude, high-frequency, periodic wing motion. We discuss the applicability of direct averaging versus second-order averaging for these insects.
机译：由于与盘旋昆虫和扑翼微型空中飞行器（FWMAV）相关的相对较高的扑动频率，动力稳定性分析通常涉及扑动周期内时间周期动力学的直接平均。但是，直接应用平均定理可能会导致关于盘旋昆虫和FWMAV的动力学和稳定性的错误结论。可能需要更高阶的平均技术来理解襟翼飞行的动力学并分析其稳定性。我们使用二阶平均来分析五种昆虫对高振幅，高频率，周期性的机翼运动的响应。我们讨论了这些昆虫的直接平均与二阶平均的适用性。

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