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A theoretical analysis of pitch stability during gliding in flying snakes

机译：飞蛇滑行时音高稳定性的理论分析

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摘要

Flying snakes use their entire body as a continuously morphing 'wing' to produce lift and shallow their glide trajectory. Their dominant behavior during gliding is aerial undulation, in which lateral waves are sent posteriorly down the body. This highly dynamic behavior, which is unique among animal gliders, should have substantial effects on the flight dynamics and stability of the snakes, resulting from the continuous redistribution of mass and aerodynamic forces. In this study, we develop two-dimensional theoretical models to assess the stability characteristics of snakes in the pitch direction. Previously measured force coefficients are used to simulate aerodynamic forces acting on the models, and undulation is simulated by varying mass. Model 1 is a simple three-airfoil representation of the snake's body that possesses a passively stable equilibrium solution, whose basin of stability contains initial conditions observed in experimental gliding trajectories. Model 2 is more sophisticated, with more degrees of freedom allowing for postural changes to better represent the snake's real kinematics; in addition, a restoring moment is added to simulate potential active control. The application of static and dynamic stability criteria show that Model 2 is passively unstable, but can be stabilized with a restoring moment. Overall, these models suggest that undulation does not contribute to stability in pitch, and that flying snakes require a closed-loop control system formed around a passively stable dynamical framework.
机译：飞蛇将其整个身体用作不断变形的“翅膀”，以产生升起和变浅的滑行轨迹。它们在滑翔过程中的主要行为是空中起伏，其中向后向身体下方发送侧波。这种高度动态的行为在动物滑翔机中是独一无二的，这应归因于质量和空气动力的不断重新分配而对蛇的飞行动力学和稳定性产生实质性影响。在这项研究中，我们开发了二维理论模型来评估蛇在俯仰方向上的稳定性特征。先前测得的力系数用于模拟作用在模型上的空气动力，并且通过改变质量来模拟起伏。模型1是蛇身的简单三翼形式表示，具有被动稳定的平衡解，其稳定域包含实验滑行轨迹中观察到的初始条件。模型2更复杂，具有更大的自由度，可以进行姿势变化以更好地表示蛇的真实运动学。此外，还添加了一个恢复力矩来模拟潜在的主动控制。静态和动态稳定性标准的应用表明模型2是被动不稳定的，但是可以通过恢复力矩使其稳定。总体而言，这些模型表明起伏不会有助于音高的稳定性，而飞蛇则需要围绕被动稳定的动力框架形成的闭环控制系统。

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