A theoretical analysis of pitch stability during gliding in flying snakes

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.